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How Inexact Models Can Guide Decision Making in Systems Pharmacology
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<div class="title">
<h1 class="title">How Inexact Models Can Guide Decision Making in Systems Pharmacology</h1>
<h5>Chris Rackauckas</h5>
<h5>October 3rd, 2019</h5>
</div>
<p>Pre-clinical Quantitiative Systems Pharmacology &#40;QSP&#41; is about trying to understand how a drug target effects an outcome. If I effect this part of the biological pathways, how will it induce toxicity? Will it be effective?</p>
<p>Recently I have been pulling in a lot of technical collegues to help with the development of next generation QSP tooling. Without a background in biological modeling, I found it difficult to explain the &quot;how&quot; and &quot;why&quot; of pharmacological modeling. Why is it differential equations, and where do these &quot;massively expensive global optimization&quot; runs come from? What kinds of problems can you solve with such models when you know that they are only approximate?</p>
<p>To solve these questions, I took a step back and tried to explain a decision making scenario with a simple model, to showcase how playing with a model can allow one to distinguish between intervention strategies and uncover a way forward. This is my attempt. Instead of talking about something small and foreign like chemical reaction concentrations, let&#39;s talk about something mathematically equivalent that&#39;s easy to visualize: ecological intervention.</p>
<h2>Basic Modeling and Fitting</h2>
<p>Let&#39;s take everyone&#39;s favorite ecology model: the Lotka-Volterra model. The model is the following:</p>
<ul>
<li><p>Left alone, the rabbit population will grow exponentially</p>
</li>
<li><p>Rabbits are eaten wolves in proportion to the number of wolves &#40;number of mouthes to feed&#41;, and inproportion to the number of rabbits &#40;ease of food access: you eat more at a buffet&#33;&#41;</p>
</li>
<li><p>Wolf populations grow exponentially, as long as there is a proportional amount of food around &#40;rabbits&#41;</p>
</li>
<li><p>Wolves die overtime of old age, and any generation dies at a similar age &#40;no major wolf medical discoveries&#41;</p>
</li>
</ul>
<p>The model is then the ODE:</p>
<pre class='hljl'>
<span class='hljl-k'>using</span><span class='hljl-t'> </span><span class='hljl-n'>OrdinaryDiffEq</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-n'>Plots</span><span class='hljl-t'>
</span><span class='hljl-k'>function</span><span class='hljl-t'> </span><span class='hljl-nf'>f</span><span class='hljl-p'>(</span><span class='hljl-n'>du</span><span class='hljl-p'>,</span><span class='hljl-n'>u</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-n'>t</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dx</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dy</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>3</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>4</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-k'>end</span><span class='hljl-t'>
</span><span class='hljl-n'>u0</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>;</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>tspan</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-p'>(</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>10.0</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>1.5</span><span class='hljl-p'>,</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>3.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>,</span><span class='hljl-n'>label</span><span class='hljl-oB'>=</span><span class='hljl-p'>[</span><span class='hljl-s'>&quot;Rabbits&quot;</span><span class='hljl-t'> </span><span class='hljl-s'>&quot;Wolves&quot;</span><span class='hljl-p'>])</span>
</pre>
<img src="data:image/png;base64,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" />
<p>Except, me showing you that picture glossed over a major detail that every piece of the model is only mechanistic, but also contains a parameter. For example, rabbits grow exponentially, but what&#39;s the growth rate? To make that plot I chose a value for that growth rate &#40;<code>1.5</code>&#41;, but in reality we need to get that from data since the results can be wildly different:</p>
<pre class='hljl'>
<span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>0.1</span><span class='hljl-p'>,</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>3.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<p>Here the exponential growth rate of rabbits too low to sustain a wolf population, so the wolf population dies out, but then this makes the rabbits have no predators and grow exponentially, which is a common route of ecological collapse as then they will destroy the local ecosystem. More on that later.</p>
<h2>Data and Model Issues</h2>
<p>But okay, we need parameters from data, but no single data source is great. One gives us a noisy sample of the population yearly, another every month for the first two years and only on the wolves, etc.:</p>
<pre class='hljl'>
<span class='hljl-k'>function</span><span class='hljl-t'> </span><span class='hljl-nf'>f_true</span><span class='hljl-p'>(</span><span class='hljl-n'>du</span><span class='hljl-p'>,</span><span class='hljl-n'>u</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-n'>t</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dx</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>5</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>^</span><span class='hljl-ni'>2</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dy</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>3</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>4</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-k'>end</span><span class='hljl-t'>
</span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>3.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.1</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f_true</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-n'>data1</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>sol</span><span class='hljl-p'>(</span><span class='hljl-ni'>0</span><span class='hljl-oB'>:</span><span class='hljl-ni'>1</span><span class='hljl-oB'>:</span><span class='hljl-ni'>10</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>data2</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>sol</span><span class='hljl-p'>(</span><span class='hljl-ni'>0</span><span class='hljl-oB'>:</span><span class='hljl-nfB'>0.1</span><span class='hljl-oB'>:</span><span class='hljl-ni'>2</span><span class='hljl-p'>;</span><span class='hljl-n'>idxs</span><span class='hljl-oB'>=</span><span class='hljl-ni'>2</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter</span><span class='hljl-p'>(</span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-p'>)</span>
</pre>
<img src="data:image/png;base64,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" />
<p>Oh, and notice that ODE is not the Lotka-Volterra model, but instead also adds a term <code>p&#91;5&#93;*u&#91;1&#93;^2</code> for a rabbit disease which requires high rabbit density.</p>
<h2>Assessing Intervention</h2>
<p>The local population is very snobby and wants the rabbit population decreased. You&#39;re trying to find out how to best intervene with the populations so that you decrease the rabbit population to always stay below 4 million rabbits, but without causing population collapse. What should you be targetting? The rabbit birth rate? The ability for predators to find rabbits?</p>
<p>&#40;In systems pharmacology, this is, which reactions should I interact with in order to achieve my target goals while not introducing toxic side effects?&#41;</p>
<p>In a complex system, these will all act differently, so you need to simulate what happens under uncertainty with the model. For example, if I attack birth rate too hard, we already saw that we can lead to population collapse, but is birth rate a more robust target then wolf lifespan &#40;i.e., could I change wolf lifespan more and get the same effect, but with less chance of collapse&#41;?</p>
<h2>The Modeler&#39;s Problem</h2>
<p>But one caveat: in order to do these simulations you need to know the model and its parameters, since you want to investigate what happens when you change the model&#39;s parameters. But you just have &quot;your best model&quot; and &quot;data&quot;. So you need to find out how to get &quot;the best model you can&quot; and the parameters of said model, since once you have that you can assess the targetting effects.</p>
<h2>The Modeler&#39;s Approach</h2>
<p>Let&#39;s start with the model we have:</p>
<pre class='hljl'>
<span class='hljl-k'>function</span><span class='hljl-t'> </span><span class='hljl-nf'>f</span><span class='hljl-p'>(</span><span class='hljl-n'>du</span><span class='hljl-p'>,</span><span class='hljl-n'>u</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-n'>t</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dx</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dy</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>3</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>4</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-k'>end</span><span class='hljl-t'>
</span><span class='hljl-n'>u0</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>;</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>tspan</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-p'>(</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>10.0</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ones</span><span class='hljl-p'>(</span><span class='hljl-ni'>4</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span>
</pre>
<img src="data:image/png;base64,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" />
<p>Here I took all of the parametrs to be <code>1</code>, since my only guess is their relative order of magnitude which should be about correct &#40;maybe?&#41;.</p>
<p>To get some parameter values, I then need do some parameter fitting. Let&#39;s define a cost function as a difference of our result against the data sources we have:</p>
<pre class='hljl'>
<span class='hljl-k'>using</span><span class='hljl-t'> </span><span class='hljl-n'>LinearAlgebra</span><span class='hljl-t'>
</span><span class='hljl-k'>function</span><span class='hljl-t'> </span><span class='hljl-nf'>cost</span><span class='hljl-p'>(</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-cs'># Needed for the optimizer to reject parameters out of the domain</span><span class='hljl-t'>
</span><span class='hljl-nf'>any</span><span class='hljl-p'>(</span><span class='hljl-n'>x</span><span class='hljl-oB'>-&gt;</span><span class='hljl-n'>x</span><span class='hljl-oB'>&lt;</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>&amp;&amp;</span><span class='hljl-t'> </span><span class='hljl-k'>return</span><span class='hljl-t'> </span><span class='hljl-n'>Inf</span><span class='hljl-t'>
</span><span class='hljl-cs'># Solve the ODE with current parameters `p`</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>(),</span><span class='hljl-n'>abstol</span><span class='hljl-oB'>=</span><span class='hljl-nfB'>1e-8</span><span class='hljl-p'>,</span><span class='hljl-n'>reltol</span><span class='hljl-oB'>=</span><span class='hljl-nfB'>1e-8</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-cs'># Check the difference from the data</span><span class='hljl-t'>
</span><span class='hljl-nf'>norm</span><span class='hljl-p'>(</span><span class='hljl-nf'>sol</span><span class='hljl-p'>(</span><span class='hljl-ni'>0</span><span class='hljl-oB'>:</span><span class='hljl-ni'>1</span><span class='hljl-oB'>:</span><span class='hljl-ni'>10</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-nf'>norm</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-nf'>sol</span><span class='hljl-p'>(</span><span class='hljl-ni'>0</span><span class='hljl-oB'>:</span><span class='hljl-nfB'>0.1</span><span class='hljl-oB'>:</span><span class='hljl-ni'>2</span><span class='hljl-p'>;</span><span class='hljl-n'>idxs</span><span class='hljl-oB'>=</span><span class='hljl-ni'>2</span><span class='hljl-p'>))</span><span class='hljl-t'>
</span><span class='hljl-k'>end</span><span class='hljl-t'>
</span><span class='hljl-nf'>cost</span><span class='hljl-p'>(</span><span class='hljl-nf'>ones</span><span class='hljl-p'>(</span><span class='hljl-ni'>4</span><span class='hljl-p'>))</span>
</pre>
<pre class="output">
10.917779941345977
</pre>
<p>Yeah, those original parameters are pretty bad. But now let&#39;s optimize them:</p>
<pre class='hljl'>
<span class='hljl-k'>using</span><span class='hljl-t'> </span><span class='hljl-n'>Optim</span><span class='hljl-t'>
</span><span class='hljl-n'>opt</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>optimize</span><span class='hljl-p'>(</span><span class='hljl-n'>cost</span><span class='hljl-p'>,</span><span class='hljl-nf'>ones</span><span class='hljl-p'>(</span><span class='hljl-ni'>4</span><span class='hljl-p'>),</span><span class='hljl-nf'>BFGS</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>Optim</span><span class='hljl-oB'>.</span><span class='hljl-nf'>minimizer</span><span class='hljl-p'>(</span><span class='hljl-n'>opt</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<p>Oh wow, that fit is pretty bad&#33; Well generally, for large models &#40;the models are usually &gt;200 lines long&#41;, this is pretty standard for a local optimizer. So okay, we need to use a global optimizer.</p>
<pre class='hljl'>
<span class='hljl-k'>using</span><span class='hljl-t'> </span><span class='hljl-n'>BlackBoxOptim</span><span class='hljl-t'>
</span><span class='hljl-n'>bound</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>Tuple</span><span class='hljl-p'>{</span><span class='hljl-n'>Float64</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-n'>Float64</span><span class='hljl-p'>}[(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>)]</span><span class='hljl-t'>
</span><span class='hljl-n'>result</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>bboptimize</span><span class='hljl-p'>(</span><span class='hljl-n'>cost</span><span class='hljl-p'>;</span><span class='hljl-n'>SearchRange</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>bound</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-n'>MaxSteps</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nfB'>21e3</span><span class='hljl-p'>)</span>
</pre>
<pre class="output">
Starting optimization with optimizer BlackBoxOptim.DiffEvoOpt&#123;BlackBoxOptim
.FitPopulation&#123;Float64&#125;,BlackBoxOptim.RadiusLimitedSelector,BlackBoxOptim.A
daptiveDiffEvoRandBin&#123;3&#125;,BlackBoxOptim.RandomBound&#123;BlackBoxOptim.Continuous
RectSearchSpace&#125;&#125;
0.00 secs, 0 evals, 0 steps
0.50 secs, 942 evals, 848 steps, improv/step: 0.259 &#40;last &#61; 0.2594&#41;, fitnes
s&#61;3.317135922
1.00 secs, 1894 evals, 1800 steps, improv/step: 0.198 &#40;last &#61; 0.1439&#41;, fitn
ess&#61;3.023363462
1.50 secs, 3060 evals, 2966 steps, improv/step: 0.183 &#40;last &#61; 0.1595&#41;, fitn
ess&#61;2.962818427
2.00 secs, 3962 evals, 3868 steps, improv/step: 0.180 &#40;last &#61; 0.1707&#41;, fitn
ess&#61;2.940117187
2.52 secs, 5128 evals, 5034 steps, improv/step: 0.177 &#40;last &#61; 0.1664&#41;, fitn
ess&#61;2.936803328
3.02 secs, 6190 evals, 6096 steps, improv/step: 0.177 &#40;last &#61; 0.1742&#41;, fitn
ess&#61;2.936688386
3.53 secs, 7538 evals, 7444 steps, improv/step: 0.181 &#40;last &#61; 0.2010&#41;, fitn
ess&#61;2.936640663
4.03 secs, 8692 evals, 8599 steps, improv/step: 0.179 &#40;last &#61; 0.1662&#41;, fitn
ess&#61;2.936639336
4.53 secs, 9864 evals, 9771 steps, improv/step: 0.175 &#40;last &#61; 0.1468&#41;, fitn
ess&#61;2.936639323
5.03 secs, 10967 evals, 10874 steps, improv/step: 0.175 &#40;last &#61; 0.1741&#41;, fi
tness&#61;2.936639322
5.53 secs, 11951 evals, 11858 steps, improv/step: 0.177 &#40;last &#61; 0.2043&#41;, fi
tness&#61;2.936639322
6.03 secs, 13041 evals, 12948 steps, improv/step: 0.176 &#40;last &#61; 0.1661&#41;, fi
tness&#61;2.936639322
6.53 secs, 14214 evals, 14123 steps, improv/step: 0.176 &#40;last &#61; 0.1719&#41;, fi
tness&#61;2.936639322
7.03 secs, 15501 evals, 15410 steps, improv/step: 0.174 &#40;last &#61; 0.1453&#41;, fi
tness&#61;2.936639322
7.54 secs, 16720 evals, 16629 steps, improv/step: 0.165 &#40;last &#61; 0.0509&#41;, fi
tness&#61;2.936639322
8.04 secs, 17918 evals, 17827 steps, improv/step: 0.156 &#40;last &#61; 0.0359&#41;, fi
tness&#61;2.936639322
8.54 secs, 19245 evals, 19154 steps, improv/step: 0.147 &#40;last &#61; 0.0249&#41;, fi
tness&#61;2.936639322
9.05 secs, 20566 evals, 20475 steps, improv/step: 0.139 &#40;last &#61; 0.0220&#41;, fi
tness&#61;2.936639322
Optimization stopped after 21001 steps and 9.28 seconds
Termination reason: Max number of steps &#40;21000&#41; reached
Steps per second &#61; 2264.01
Function evals per second &#61; 2273.82
Improvements/step &#61; 0.13557
Total function evaluations &#61; 21092
Best candidate found: &#91;0.766198, 1.31019, 2.92441, 1.12677&#93;
Fitness: 2.936639322
</pre>
<pre class='hljl'>
<span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>result</span><span class='hljl-oB'>.</span><span class='hljl-n'>archive_output</span><span class='hljl-oB'>.</span><span class='hljl-n'>best_candidate</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<p>Oh dang, still no good. This means our model is misspecified. We see that we overshoot over time, so there&#39;s some kind of decay missing. Thus we go and talk to our collegues a bit more and find out that there&#39;s this weird bunny disease that is huge problem every few years: that may be an effect that is required to produce the data&#33;</p>
<p>So then we change our model. What if this disease is just old age related? Then we would have decay of rabbits unrelated to wolves, so the model would be like:</p>
<pre class='hljl'>
<span class='hljl-k'>function</span><span class='hljl-t'> </span><span class='hljl-nf'>f2</span><span class='hljl-p'>(</span><span class='hljl-n'>du</span><span class='hljl-p'>,</span><span class='hljl-n'>u</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-n'>t</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dx</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>5</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dy</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>3</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>4</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-k'>end</span>
</pre>
<pre class="output">
f2 &#40;generic function with 1 method&#41;
</pre>
<p>So now let&#39;s optimize with this:</p>
<pre class='hljl'>
<span class='hljl-k'>function</span><span class='hljl-t'> </span><span class='hljl-nf'>cost2</span><span class='hljl-p'>(</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-cs'># Needed for the optimizer to reject parameters out of the domain</span><span class='hljl-t'>
</span><span class='hljl-nf'>any</span><span class='hljl-p'>(</span><span class='hljl-n'>x</span><span class='hljl-oB'>-&gt;</span><span class='hljl-n'>x</span><span class='hljl-oB'>&lt;</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>&amp;&amp;</span><span class='hljl-t'> </span><span class='hljl-k'>return</span><span class='hljl-t'> </span><span class='hljl-n'>Inf</span><span class='hljl-t'>
</span><span class='hljl-cs'># Solve the ODE with current parameters `p`</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f2</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>(),</span><span class='hljl-n'>abstol</span><span class='hljl-oB'>=</span><span class='hljl-nfB'>1e-8</span><span class='hljl-p'>,</span><span class='hljl-n'>reltol</span><span class='hljl-oB'>=</span><span class='hljl-nfB'>1e-8</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-cs'># Check the difference from the data</span><span class='hljl-t'>
</span><span class='hljl-nf'>norm</span><span class='hljl-p'>(</span><span class='hljl-nf'>sol</span><span class='hljl-p'>(</span><span class='hljl-ni'>0</span><span class='hljl-oB'>:</span><span class='hljl-ni'>1</span><span class='hljl-oB'>:</span><span class='hljl-ni'>10</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-nf'>norm</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-nf'>sol</span><span class='hljl-p'>(</span><span class='hljl-ni'>0</span><span class='hljl-oB'>:</span><span class='hljl-nfB'>0.1</span><span class='hljl-oB'>:</span><span class='hljl-ni'>2</span><span class='hljl-p'>;</span><span class='hljl-n'>idxs</span><span class='hljl-oB'>=</span><span class='hljl-ni'>2</span><span class='hljl-p'>))</span><span class='hljl-t'>
</span><span class='hljl-k'>end</span><span class='hljl-t'>
</span><span class='hljl-n'>bound</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>Tuple</span><span class='hljl-p'>{</span><span class='hljl-n'>Float64</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-n'>Float64</span><span class='hljl-p'>}[(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>)]</span><span class='hljl-t'>
</span><span class='hljl-n'>result</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>bboptimize</span><span class='hljl-p'>(</span><span class='hljl-n'>cost2</span><span class='hljl-p'>;</span><span class='hljl-n'>SearchRange</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>bound</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-n'>MaxSteps</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nfB'>21e3</span><span class='hljl-p'>)</span>
</pre>
<pre class="output">
Starting optimization with optimizer BlackBoxOptim.DiffEvoOpt&#123;BlackBoxOptim
.FitPopulation&#123;Float64&#125;,BlackBoxOptim.RadiusLimitedSelector,BlackBoxOptim.A
daptiveDiffEvoRandBin&#123;3&#125;,BlackBoxOptim.RandomBound&#123;BlackBoxOptim.Continuous
RectSearchSpace&#125;&#125;
0.00 secs, 0 evals, 0 steps
0.50 secs, 740 evals, 612 steps, improv/step: 0.252 &#40;last &#61; 0.2516&#41;, fitnes
s&#61;5.269508848
1.00 secs, 1385 evals, 1252 steps, improv/step: 0.175 &#40;last &#61; 0.1016&#41;, fitn
ess&#61;4.380580433
1.50 secs, 2006 evals, 1873 steps, improv/step: 0.146 &#40;last &#61; 0.0870&#41;, fitn
ess&#61;4.136444391
2.00 secs, 2791 evals, 2659 steps, improv/step: 0.140 &#40;last &#61; 0.1247&#41;, fitn
ess&#61;3.503409075
2.51 secs, 3675 evals, 3543 steps, improv/step: 0.140 &#40;last &#61; 0.1403&#41;, fitn
ess&#61;3.224799080
3.02 secs, 4657 evals, 4525 steps, improv/step: 0.139 &#40;last &#61; 0.1385&#41;, fitn
ess&#61;2.972947845
3.52 secs, 5697 evals, 5565 steps, improv/step: 0.141 &#40;last &#61; 0.1471&#41;, fitn
ess&#61;2.940026109
4.02 secs, 6788 evals, 6656 steps, improv/step: 0.144 &#40;last &#61; 0.1622&#41;, fitn
ess&#61;2.936773525
4.52 secs, 8059 evals, 7927 steps, improv/step: 0.144 &#40;last &#61; 0.1432&#41;, fitn
ess&#61;2.936654026
5.02 secs, 9410 evals, 9280 steps, improv/step: 0.145 &#40;last &#61; 0.1515&#41;, fitn
ess&#61;2.936639903
5.52 secs, 10848 evals, 10718 steps, improv/step: 0.144 &#40;last &#61; 0.1370&#41;, fi
tness&#61;2.936639336
6.03 secs, 12051 evals, 11922 steps, improv/step: 0.141 &#40;last &#61; 0.1163&#41;, fi
tness&#61;2.936639327
6.53 secs, 13156 evals, 13027 steps, improv/step: 0.143 &#40;last &#61; 0.1593&#41;, fi
tness&#61;2.936639322
7.03 secs, 14131 evals, 14004 steps, improv/step: 0.144 &#40;last &#61; 0.1638&#41;, fi
tness&#61;2.936639322
7.53 secs, 14953 evals, 14826 steps, improv/step: 0.145 &#40;last &#61; 0.1521&#41;, fi
tness&#61;2.936639322
8.03 secs, 16116 evals, 15989 steps, improv/step: 0.145 &#40;last &#61; 0.1470&#41;, fi
tness&#61;2.936639322
8.53 secs, 17517 evals, 17390 steps, improv/step: 0.144 &#40;last &#61; 0.1292&#41;, fi
tness&#61;2.936639322
9.03 secs, 18811 evals, 18684 steps, improv/step: 0.141 &#40;last &#61; 0.1036&#41;, fi
tness&#61;2.936639322
9.53 secs, 20128 evals, 20003 steps, improv/step: 0.135 &#40;last &#61; 0.0546&#41;, fi
tness&#61;2.936639322
Optimization stopped after 21001 steps and 9.93 seconds
Termination reason: Max number of steps &#40;21000&#41; reached
Steps per second &#61; 2114.05
Function evals per second &#61; 2126.64
Improvements/step &#61; 0.12981
Total function evaluations &#61; 21126
Best candidate found: &#91;6.53541, 1.31019, 2.92441, 1.12677, 5.76921&#93;
Fitness: 2.936639322
</pre>
<pre class='hljl'>
<span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>result</span><span class='hljl-oB'>.</span><span class='hljl-n'>archive_output</span><span class='hljl-oB'>.</span><span class='hljl-n'>best_candidate</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f2</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-p'>)</span>
</pre>
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" />
<p>Okay, that model is not right yet, but it&#39;s better. Let&#39;s try the local one and see what we get:</p>
<pre class='hljl'>
<span class='hljl-n'>opt</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>optimize</span><span class='hljl-p'>(</span><span class='hljl-n'>cost2</span><span class='hljl-p'>,</span><span class='hljl-nf'>ones</span><span class='hljl-p'>(</span><span class='hljl-ni'>5</span><span class='hljl-p'>),</span><span class='hljl-nf'>BFGS</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>Optim</span><span class='hljl-oB'>.</span><span class='hljl-nf'>minimizer</span><span class='hljl-p'>(</span><span class='hljl-n'>opt</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f2</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<p>So we go back to our collegues who know the local ecology and tell them, that model is giving me junk. Then you learn it&#39;s population dependent, so this death is only going to occur when the population is higher&#33; So you need to add an interaction between bunnies to bunnies. A simple model for this is to assume that two bunnies always have to die together, so:</p>
<pre class='hljl'>
<span class='hljl-k'>function</span><span class='hljl-t'> </span><span class='hljl-nf'>f3</span><span class='hljl-p'>(</span><span class='hljl-n'>du</span><span class='hljl-p'>,</span><span class='hljl-n'>u</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-n'>t</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dx</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>5</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>^</span><span class='hljl-ni'>2</span><span class='hljl-t'>
</span><span class='hljl-n'>du</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>dy</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>3</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-p'>[</span><span class='hljl-ni'>4</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>1</span><span class='hljl-p'>]</span><span class='hljl-oB'>*</span><span class='hljl-n'>u</span><span class='hljl-p'>[</span><span class='hljl-ni'>2</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-k'>end</span><span class='hljl-t'>
</span><span class='hljl-k'>function</span><span class='hljl-t'> </span><span class='hljl-nf'>cost3</span><span class='hljl-p'>(</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-cs'># Needed for the optimizer to reject parameters out of the domain</span><span class='hljl-t'>
</span><span class='hljl-nf'>any</span><span class='hljl-p'>(</span><span class='hljl-n'>x</span><span class='hljl-oB'>-&gt;</span><span class='hljl-n'>x</span><span class='hljl-oB'>&lt;</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>&amp;&amp;</span><span class='hljl-t'> </span><span class='hljl-k'>return</span><span class='hljl-t'> </span><span class='hljl-n'>Inf</span><span class='hljl-t'>
</span><span class='hljl-cs'># Solve the ODE with current parameters `p`</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f3</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>(),</span><span class='hljl-n'>abstol</span><span class='hljl-oB'>=</span><span class='hljl-nfB'>1e-8</span><span class='hljl-p'>,</span><span class='hljl-n'>reltol</span><span class='hljl-oB'>=</span><span class='hljl-nfB'>1e-8</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-cs'># Check the difference from the data</span><span class='hljl-t'>
</span><span class='hljl-nf'>norm</span><span class='hljl-p'>(</span><span class='hljl-nf'>sol</span><span class='hljl-p'>(</span><span class='hljl-ni'>0</span><span class='hljl-oB'>:</span><span class='hljl-ni'>1</span><span class='hljl-oB'>:</span><span class='hljl-ni'>10</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-nf'>norm</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-nf'>sol</span><span class='hljl-p'>(</span><span class='hljl-ni'>0</span><span class='hljl-oB'>:</span><span class='hljl-nfB'>0.1</span><span class='hljl-oB'>:</span><span class='hljl-ni'>2</span><span class='hljl-p'>;</span><span class='hljl-n'>idxs</span><span class='hljl-oB'>=</span><span class='hljl-ni'>2</span><span class='hljl-p'>))</span><span class='hljl-t'>
</span><span class='hljl-k'>end</span><span class='hljl-t'>
</span><span class='hljl-n'>opt</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>optimize</span><span class='hljl-p'>(</span><span class='hljl-n'>cost3</span><span class='hljl-p'>,</span><span class='hljl-nf'>ones</span><span class='hljl-p'>(</span><span class='hljl-ni'>5</span><span class='hljl-p'>),</span><span class='hljl-nf'>BFGS</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>Optim</span><span class='hljl-oB'>.</span><span class='hljl-nf'>minimizer</span><span class='hljl-p'>(</span><span class='hljl-n'>opt</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f2</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<p>That might just be an optimization issue? So let&#39;s run our big model with global optimization on the cluster:</p>
<pre class='hljl'>
<span class='hljl-n'>bound</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>Tuple</span><span class='hljl-p'>{</span><span class='hljl-n'>Float64</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-n'>Float64</span><span class='hljl-p'>}[(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>),(</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-ni'>10</span><span class='hljl-p'>)]</span><span class='hljl-t'>
</span><span class='hljl-n'>result</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>bboptimize</span><span class='hljl-p'>(</span><span class='hljl-n'>cost3</span><span class='hljl-p'>;</span><span class='hljl-n'>SearchRange</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>bound</span><span class='hljl-p'>,</span><span class='hljl-t'> </span><span class='hljl-n'>MaxSteps</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nfB'>21e3</span><span class='hljl-p'>)</span>
</pre>
<pre class="output">
Starting optimization with optimizer BlackBoxOptim.DiffEvoOpt&#123;BlackBoxOptim
.FitPopulation&#123;Float64&#125;,BlackBoxOptim.RadiusLimitedSelector,BlackBoxOptim.A
daptiveDiffEvoRandBin&#123;3&#125;,BlackBoxOptim.RandomBound&#123;BlackBoxOptim.Continuous
RectSearchSpace&#125;&#125;
0.00 secs, 0 evals, 0 steps
0.50 secs, 1427 evals, 1325 steps, improv/step: 0.267 &#40;last &#61; 0.2672&#41;, fitn
ess&#61;3.659818646
1.00 secs, 3162 evals, 3062 steps, improv/step: 0.194 &#40;last &#61; 0.1376&#41;, fitn
ess&#61;2.236392570
1.50 secs, 4556 evals, 4456 steps, improv/step: 0.180 &#40;last &#61; 0.1506&#41;, fitn
ess&#61;1.053944784
2.00 secs, 5627 evals, 5528 steps, improv/step: 0.180 &#40;last &#61; 0.1782&#41;, fitn
ess&#61;0.433969616
2.50 secs, 6614 evals, 6516 steps, improv/step: 0.177 &#40;last &#61; 0.1619&#41;, fitn
ess&#61;0.159514518
3.01 secs, 8011 evals, 7913 steps, improv/step: 0.174 &#40;last &#61; 0.1589&#41;, fitn
ess&#61;0.057836419
3.51 secs, 9013 evals, 8915 steps, improv/step: 0.171 &#40;last &#61; 0.1467&#41;, fitn
ess&#61;0.020524079
4.01 secs, 9754 evals, 9656 steps, improv/step: 0.169 &#40;last &#61; 0.1525&#41;, fitn
ess&#61;0.016040864
4.51 secs, 11169 evals, 11071 steps, improv/step: 0.168 &#40;last &#61; 0.1618&#41;, fi
tness&#61;0.005913857
5.01 secs, 12885 evals, 12787 steps, improv/step: 0.166 &#40;last &#61; 0.1474&#41;, fi
tness&#61;0.002874341
5.51 secs, 14017 evals, 13919 steps, improv/step: 0.166 &#40;last &#61; 0.1714&#41;, fi
tness&#61;0.002487151
6.02 secs, 15310 evals, 15212 steps, improv/step: 0.166 &#40;last &#61; 0.1609&#41;, fi
tness&#61;0.002450532
6.52 secs, 16441 evals, 16343 steps, improv/step: 0.165 &#40;last &#61; 0.1618&#41;, fi
tness&#61;0.002449064
7.02 secs, 17621 evals, 17523 steps, improv/step: 0.166 &#40;last &#61; 0.1763&#41;, fi
tness&#61;0.002448736
7.54 secs, 19167 evals, 19069 steps, improv/step: 0.168 &#40;last &#61; 0.1953&#41;, fi
tness&#61;0.002448716
8.05 secs, 20881 evals, 20784 steps, improv/step: 0.170 &#40;last &#61; 0.1878&#41;, fi
tness&#61;0.002448716
Optimization stopped after 21001 steps and 8.10 seconds
Termination reason: Max number of steps &#40;21000&#41; reached
Steps per second &#61; 2591.44
Function evals per second &#61; 2603.41
Improvements/step &#61; 0.17048
Total function evaluations &#61; 21098
Best candidate found: &#91;0.999909, 1.00034, 3.00008, 1.00015, 0.0999369&#93;
Fitness: 0.002448716
</pre>
<pre class='hljl'>
<span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>result</span><span class='hljl-oB'>.</span><span class='hljl-n'>archive_output</span><span class='hljl-oB'>.</span><span class='hljl-n'>best_candidate</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f3</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data1</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-nf'>scatter!</span><span class='hljl-p'>(</span><span class='hljl-n'>data2</span><span class='hljl-p'>)</span>
</pre>
<img src="data:image/png;base64,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" />
<p>Oh bingo&#33; That looks good&#33; So okay, is it safe to reduce the rabbit birth rate, and how much would we need to target it by to get it under 4?</p>
<pre class='hljl'>
<span class='hljl-n'>test_p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>0.5</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f3</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>test_p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span>
</pre>
<img 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vtwdBheGWPUAOtLsZq2VXbs2DF37txevXrde++9VP87qlwjBBgAXKvdBeKRrXx9TlV0dYli/+onj0hAdFUj+p5n1C2gcjsVIcRHH3104MCBmTNnJiYmeg82wI4q1wIBBgC1V+ikZ3/lcw4qnooLk2NN9HIveWp7SUZ4BbBLt1PZvXv31q1b33nnHVmW7XY7EZnN5jrcUaU+IMAAoDYUQR8fUp7ewfMqFl3VS/RQJ+n5HnJEQ2/DAn67dDuVjIyMrKyscePGVZ6TlpZWVzuq1BMEGAD47Zdz4qGf+C/nbZc8shn7d3+5I9bU0IhLt1OZMmXKlClTLjqtrnZUqSeYhQgAfihw0rTNvN9yT2V6JYeyJSPlH27QIb2CTwPvqOIvtMAAoEYE0SeHlL/9UtVnaNbRk13lGV0lMz5IglcD76jiF/zeAUD1dheIP23hW85W9Rne0lJ6qx+WkA9+Db+jSs0hwADgaso99MKv/K19VfMMk0LZv/tLN7fAAASoDAEGAFe0/ITy8FblZJmv4WWUaXoX6ZlUGX2GEAjwawgAl3HaRtM38cWZSuWREQnsvYEyltWAwIEAA4ALKILmHjO8sk8qqdg1Oc5M/+wrT2qDPkMILAgwAKiyt1Dcv4lvzTV6bzKi+9pLr/eRI43q1gVwGQgwACAicnJ6dReflaG4KnoNO0awOYPkwU3QZwgBCgEGAPTTWTF1U9XOk0aZnugsZvbUG7EBSp3q0aNHSkoKa4Dl5wNJUVGRd3vMOocAA2jUytz0zA7+7v6qzScHxrM3upZ1b2JGetW5ZcuWFRUVqV2FCiIjI+vjYRFgAI1XWra4fzOv3MErVE+zessPdJSKCpWrfyPUjtVqtVqtalcRPBBgAI1RsYum/8w/PlTZ7qIbm7MPBsnNLY2rdws0DQEG0OisOiWmbeZZ5b7wijbSW/0xSx60BwEG0IgUueiv2/i8w1U9hLcnSe8OkOPMKhYFUEsIMIDG4rtT4v7zGl7xZnpvgHxbEhpeoFUIMIDgV+Kmx7ddMOI1obX0zgA5Gpcng5YhwACC3NrT4o8b+YmKBXnjzPTBQPnWVmh4geYhwACCls1Df/uFv7uvquE1Pll6b4AcY1KzKoC6ggADCE4/54opG/jhYl94xZjovQHy+GQ0vCB4IMAAgo1boZfS+ayMqi0ob2kpfThIjsdUQwguCDCAoHKgSExez3/N8zW8wvT07/7yPe3Q8IIghAADCBKC6N19ypO/cLvHd2RoU/bf6+SWViyuAcEJAQYQDHJsdM8Gzw/ZvoaXSaZXe8uPdJYkhBcELwQYgOZ9c1yZtpnnO303u0ezz4bKnSORXRDkEGAAGlbmpke28k8qloaSGT3RVXqxp2zAmBc0AggwAK36OVdMWs+Plvi6DVta2adD5SHYQBkaDQQYgPZwQbMylBd3cnfFRPlJbaR3B8jhBlXLAmhYCDAAjTlVLiav5xtyfA2vCAO9P1Ce0BqdhtDoIMAAtOR/x5X7N/PCivkag5uwz4Ziojw0UggwAG2weejRbfyjg75OQ51Ez3WXn06VZIQXNFYIMAAN2F0g7lzLDxT5ug2TQtmCYXL/OGQXNGoIMICAJoje369M/5k7uO/IhNbSfwbJYXpVywIIAAgwgMBV4KT7NvKlJ3zdhlY9vYOFDQEqIMAAAtSWs2LiOn6yYiPK7tFs4XC5XTi6DQF8EGAAAUcRNCtDeX4n9+6Hwoj+kiK91ls2ympXBhBIEGAAgeWsnSat96ypWJY32kjzrpNvboFuQ4CLIcAAAsiPp8WkdZ4zdt/NIU3YgmFyogXdhgCXgQADCAhc0Es7+d93KYogIpIYPZMqPddd1qHpBXAFCDAA9eXY6K51nnUVq0M1MdPnw3QjEtDwArgaBBiAyn48Le5a5zlb0W04IoEtGKaLN6taE4AWIMAAVKMIejldeTmdc0FEJDN6trs8sztWhwKoEQQYgDpy7XTXebMNm5jpi+G6YU2RXQA1hQADUMGmM+LOtfy0zZdewxPYgmG6Jug2BPAHZjgBNChB9PpuZfgqjze9JEbPdZd+uAHpBeA3tMAAGk6hk+7ZyJdXrG0Ya6LPh+lGNUO3IUBtIMAAGsjOPHH7j/xYqa/bcGA8WzgcFykD1B4CDKAhfHRQ+ctW35YojOixLtKs3rIeXfgA1wABBlC/bB760xY+/4iv2zDcQPOGyONaIbsArhUCDKAeHS0Rf1jDMwp83YbdotjXI+S22BIFoC74HWDbt2+fM2dOfn5+dHT0gw8+2KtXr/ooCyAILD+hTNnAi12+m/e0k94fIJvxRyNAHfGvH4Nz/uqrrz700EOLFy++++6733jjjXoqC0DTuKCnf+Fj03zpZZLpo8HyvCFIL4C65N/7iXP+1FNPde/e3W636/V6i8VST2UBaNc5B01Y6/nxtK/bMCmUfT1C7hmDbkOAOuZfgBkMhr59+9rt9jFjxhDRW2+9ddnTduzY0axZs0uPz5s3LzU1tRZVNiqc88LCQrWr0La8vDwhhCSpMFEivUj3x+2W0w7fU4+Id7/fwxahKLm5DV9L7RUVFdlsNoPBoHYhWlVWVsYYs9lsaheiVU6nMyYmRq/XX/202vRomM3m5cuXL1my5P3333/vvfcuPSElJeWTTz659Hh8fLzRaKzFMzYqnHMiio6OVrsQDfN4PNHR0Q0fYB8eEo/9LJyciEhiNLMbm5lqlJj2fucZYxaLBe/WWjMYDIwxq9WqdiFa5XA4ZFmu9jT/AiwnJ2flypX/93//Zzabb7jhhi+//PKyp5lMpqSkJL8eGc4ny3JNfnhwJd4XsCEDzMHpT1v4vMO+bsMoI30+VHdDc612G8oV1C5Eq2RZZozhBaw17wtY7Wn+vcOjo6O//fbbPXv2CCHWr1/fpk2b2pYHEDwyS8XAFZ55h31XenWPZjvGaji9ALTC7zGwF1988f333z9z5kzz5s2nT59eT2UBaEVatpiw1pPv9N28u630wUDMNgRoCH6/z7p16/bBBx/URykA2iKIXstQZu7wbUdpkOit/vKDHbHEBkADwR+KALVR6qZ7N/Jvjvu6DZtZ2Ncj5P5x6DYEaDgIMAC/HS4W49L4/iLflI0hTdhXI3Tx2NALoGEhwAD8s+KkMnl91QJRj6RIs/tgXXkAFSDAAGpKEL24k7+criiCiChERx8Oku9qg+wCUAcCDKBGil00eT1fcdI36JUUyhZfL6dGY9ALQDUIMIDqHSgS49L4oWLfoNeoZuyL4bporFMBoCoEGEA1lp5QpqznpW4iIkY0o5v0Si9ZRtMLQG0IMIArUgS9sJP/Pd075kVWPX0yRL49CYNeAAEBAQZwecUumrTes/Kkr9uwTRhbMlJOiUTLCyBQIMAALuNgkRh73qDX6ET2xTBdJAa9AAIJAgzgYstPKJPX85KKQa8nu0l/x6AXQOBBgAFUEUQvpysv7uTeUS+LjuZdh0EvgACFAAPwKXXTlPV86QnflV7JoWzpSLlLFFpeAAEKAQZARHSkWIw9b3nDkc3YwuG6KAx6AQQwBBgAfZ8lJqz1FFUsbzi9izSrDwa9AAIdAgwaNUH0eobyTMWeXmYdzR0sT2yNQS8ADUCAQeNl89B9m/jC33yDXi2sbMn1co8YtLwAtAEBBo3UiTIxLo2n51ft6fX1CF0c9vQC0A4EGDRGG3LE7T96zjl8N//USXqrH/b0AtAYBBg0Ou/tVx7bxt0KEZFRpncHyFPbI7sAtAcBBo2Ik9Off+JzD/kGvZqG0P9G6AbEY9ALQJMQYNBYnLHTbWs8P531DXr1iWWLr5ebWZBeAFqFAING4Zdz4tY1PKvcl15T2kpzBskmWd2iAOCaIMAg+H12VLl/E3dwIiKdRLP7yI+mYNALQPMQYBDMuKAZ2/mbe3yDXlFGWjRcd30zdBsCBAMEGAStQifdudbzQ7av2zAlki0dKbcOQ3oBBAkEGASnfYXi1h89R0t86TWulfTpdbJVr25RAFCXEGAQhL4/o394l1JasSPlcz2k53tgbV6AYIMAg6Di3ZHyhV9DvS0vq54+vU4e1wpTNgCCEAIMgkeZm+7ewBdn+qZstA5jS0fKKZFoegEEJwQYBIljpWJsGt9T4Bv0GpFAX43AjpQAwQxdKxAMfjwt+iz1VKbXtGTHqlEy0gsguKEFBpr3773K9O3coxARmWSaM0j+XZhNJ1nUrgsA6hcCDDTMyenBLXzeYd+gVzMLW3y93CeWnT2rbl0A0BAQYKBVp23i1jX851xft2H/OPbN9bqmIeoWBQANBwEGmrQtV9y2hp+2+dLrj+2k9wfKRizOC9CYIMBAe+YdVh7cwp0Vi/O+2Vd+uDOmIwE0Oggw0BKPQn/9mb+zzzfoFWOir0bohjXFlV4AjRECDDQjz0Hjf/Ssy/F1G3aLYktGykmhSC+ARgoBBtqwK1+MW8MzS33pdXuSNO862YLfX4BGDB8AoAGLjil/3MhtHiIiidHLPeWnUiW0vAAaOQQYBDRF0DM7+GsZirflFW6gBcN0NzZHeAEAAgwCWJGL7lrnWXXK123YIYItHSm3D0d6AQARAgwC1oEiMSaNHyn2pddNLdjnQ3XhBnWLAoAAggCDQLTshDJ5Pa/ckfLpVOmlnjJGvQDgfAgwCCyC6MWd/KWdSuWOlP8dIt+WhOuUAeBiCDAIICVumryeLz9RtSPlkuvlLlFoeQHAZSDAIFAcKhZj0/jBIt+g16hm7Mvh2JESAK4IAQYBYcVJZfJ6XuwiImJET3SVXu0ty2h6AcCVIcBAZYLopZ3KS+ncO+pl0dHHQ+Q7kjHoBQDVQICBmi4a9EoKZUtGyt0w6AUANYAAA9UcLBLj1lQNeo1sxr4crovGoBcA1AwCDNSx9IRy93peUnGl1/Su0j8w6AUA/kCAQUNTBD2/k7+S7rvSC4NeAFA7CDBoUIVOmrjO832Wr9sQV3oBQK0hwKDhZBSI29bw30p86XVDc7ZgqC4Sg14AUCsIMGggC44q92/27emF5Q0B4NohwKDeuRV6Yjv/917fXPkwPX06VB7TEoNeAHBNEGBQv87YafyPnk1nfN2GHSPY4uvlDhFoeQHAtUKAQT3aclbc/qMnx+a7eVuSNG+IHKpXtSYACBYIMKgv7+xTHv+ZuxUiIpnRK73kGd0w5gUAdcbvANu0adP8+fPz8vKSkpIef/zxxMTE+igLNM3mof/bxL/4zTfoFWOihcN1IxIQXgBQl/wbSM/JyZk9e/b06dMXLVrUv3//2bNn11NZoF2Hi0W/5Z7K9Oody3aOQ3oBQN3zO8CGDx/eoUMHo9E4atSoU6dO1VNZoFFLTyh9lnn2FPimbEzrIG26SdfcgvQCgLrnXxdijx49evToQUSc8/nz5w8dOvSypx0+fHjixImXHn/88cfbtGnjf5GNC+e8pKTEaNTY9b0ehV7aq3/nkN6bXSZZvNnDPbGVx1FGjgYvpqSkxGAwSBJm6tdSSUmJx+PR3C9h4CgrK2OMcc7VLkSrHA5HeHi4Xl/NjK/aTOLYsWPH3Llze/Xqde+99172hPDw8MtmW0xMTLUFgSRJer1eWy/UWQe7e7O0KdcXGElWWjCYd4tkROr8L7wvIAKs1vQV1C5Eq7wvHV7AWuOcM1Z9z41/ASaE+Oijjw4cODBz5syrTN+Ij4+///77/XpkqMQ5t9vtISEhahdSU5vOiDvWVs2Vv6kF+/Q6XaRRzbeu2WwOCQlBgNWaw+EICQlBC6zWvJ+/GnoXBxpJkmry/vUvwHbv3r1169Z33nlHlmW73U5EZrO5lgWC9gmiN3YrT+/gnoq58i/2lJ9OxVx5AGgI/gVYRkZGVlbWuHHjKo+kpaXVdUmgDUUuuncDX1qxmXKcmb4YhtmGANBw/AuwKVOmTJkypZ5KAQ3ZmSfGr61aV35APFs0XE7EbEMAaEBYiQP8Nueg8uhW7uBERIzokRTp9T6yHuNNANCwEGDghzI3PbCFLzhata78x0PkPyQhuwBABQgwqKl9heL2H/mBIl+3YWo0+2q43DYc3YYAoD6/32sAAB5ZSURBVA4EGNTIfw8rD/3k246SiKa2l97uL5vx6wMA6sEnEFSj3EMPbeHzj/i6DS06+mCQPLkNug0BQGUIMLiafYVi/I98f0W3YedI9tUIuRO2owSAAIAAgyv65LDy8Hndhne3ld4bKFvwKwMAgQGfRnAZpW568LzZhhYdvTtAvqcdug0BIIAgwOBi6fnizrX8cLGv2zAlki1CtyEABB4EGFQRRO/uU57Yzp0Vu0BgtiEABCx8MoFPvpPu28iXnai6SPmDQfLE1ug2BIAAhQADIqKNZ8SkdfxUua/bsGcMWzhcbhOGbkMACFwIsMbOo9Dfd/G/pytcEFWsbTirt2yU1a4MAOCqEGCN2okyMWk933zG1/CKNdG863Q3NkfDCwA0AAHWeH11TJm2mRe5fDdHJLBPh8oJIUgvANAGBFhjVOamv2zl8w775mvoJXqxp/xkVwlbKQOAhiDAGp3t58Rd6/jRir0ok0PZF8PkvnHILgDQGARYI8IFzcpQXtzJ3b6mF01uI707UA7Tq1oWAECtIMAai8xSMWk933LW1/AKN9AHA+UJuMwLADQLAdYofHpEefgnXuL23RzchH02VG5pRbchAGgYAizI5Tvpgc38f8er5mu80EN+spskI7wAQOMQYMHs+yxx30Z+2ubrNmwfzj4bKveORXYBQDBAgAWncg9N/5nPOaB4s4sRPdBReqOvHIIfOAAEC3yeBaGfzoq7N1RNlG9ipo+H6H6P9TUAILggwIKKk9PzO/kbu30LGxLRbUnSfwbKMSZVywIAqAcIsOCxM0/cvYHvLfRlV4SB3h4gT26DifIAEJwQYMHArdAru/iru5TKK5RHNmMfD5GbW9BtCABBCwGmeRkF4p4NfFe+r+Fl0dHrfeQHO2FdQwAIcggwDXMr9Oou5ZVdVUtDDW7C5g2RW2MjSgBoBBBgWrUzT/xxI88o8DW8zDp6tZf8l85YUR4AGgsEmPY4Ob2Uzl/frXgqGl4D49knQ+R24cguAGhEEGAa89NZMXUTP1Dka3iF6OjVXvLDaHgBQOODANOMMjc9vYO/t19RKq7xGtqUzR2MES8AaKQQYNqw6pR4cAs/WebLrjA9zeojP9AR7S4AaLwQYIHurJ0e28a//E2pPHJjc/bBIFzjBQCNHQIscAmiTw4pM7bzAqfvSKyJ3uovT8QulAAACLCAdaBIPLCZbzwjKo9MaSv9sy9WNQQA8EGABRy7h/5xwPT+bx5XRa9h6zD2wUB5ZDP0GQIAVEGABZbvTomHt4rfSszem3qJnugqzUyVzfhBAQBcCJ+LgeJUuXh0q7I4s2qyxsB4NmeQ3DkSDS8AgMtAgKnPpdCbe5S/p/Nyj+9IpF6Z3U//x/aYJQ8AcEUIMJX9kC0e2coPVqyswYjuactmtC7tkBijbmEAAAEOAaaa46Xir9uUpSeq+gy7RbH3B8p9Y5T8fOUq3wgAAIQAU0W5h2Zl8Dd2Kw7uOxJhoJd6yn/qJMmMOL/qNwMAABEhwBqYIPryN+XJ7UpWua/PUGJ0T1vpH73lOLO6pQEAaAwCrOH8nCse3ca35VZdm9w7lr07QO4Ti7kaAAB+Q4A1hJNl4qlflC9/q1xHnpqY6dXe8t1tsQ0KAEAtIcDqV7GL/pHB/723arjLKNNjKdLTqXKoXtXKAAA0DgFWX9wKfXBAeTmd5zmqDt6eJL3WR0oKRbMLAOBaIcDqniD66pjyzA7lt5Kq4a6+ceyffeWB8YguAIC6gQCrY6uzxNM7+M68quhKDmWv9pbGJ2O0CwCgLiHA6sxPZ8XTO/iGnKroijbSM93lhzpJBmzgBQBQ1xBgdeDXPPH8r/zbU1XRFaKjR1OkGV3lcIOKdQEABDME2DXJKBAv/KosO1E1P14v0dT20rPd5aYhahYGABD0EGC1tCtfvJSuLM2sii6Z0cTW0gs9pWRMMgQAqH8IML9tPyde2aWsOK/VJTH6Q5L0Qg+pYwSiCwCggSDA/LAuR/xjF0/LrhrrYkS3JknPd5e6RCG6AAAaFAKseoqgZSeU13YrP5+3jKHE6LZW0rOILgAAlSDArsbuoU+PKm/uUQ4XV0WXTqIJydLfUqVO6DAEAFAPAuzycmz0/gH+nwPK+QtBmWS6p530RFdM0wAAUB8C7GLbcsU7+5T/HVdc5+2KHGmkBzpIj6TI8di1CwAgMCDAfGweWnhMeX+/8ut5q0ARUVIoezRF+mM7yYrF4wEAAkltAoxzPnXq1Hnz5tV5NarYUyA+OqR8dkQpcl1wfHAT9khnaWwrSUZ/IQBA4PE7wBYvXrx27dqsrKyrnyaIAvxjv8hFC39T5h1Wtp+7oMll1tGEZOnPnaXu0QH+PwAAaNT8DrDk5OSEhIRnn332KuectLYf987GQeZTEWQ///jIkSNjY2P9rrFOuRRKO80WZsqrslnlJpNebcPoj635pNYiyiCIyGZTp0LOud1ut6n19EHB+wJKEhZRriW73c4Y45xXfypcjt1uJyL8Btaaw+GwWCzVnuZ3gKWmplZ7zqyWtpaZ7w5q/W7K4S9bnt1Webx79+4RERH+PmOd4II2n5OXnJKXZcmFrguaViaZbmrGpyR5Bsdx7x1utyo1+nDO3W63W90iNM77AuLjo9bwAl4jt9vNGMO7uNbcbrcQotrT6mUSh1ESUa6S6+z7V6b8KWz0Q2/2k9W6ZMrBaU22WHpCWXbiggnxXr1i2N3tpLtaS5HGAJqhwTn3eDzh4eFqF6JhDocjPDwcn7+1xjm3WCxGo1HtQrRKkiTGmNVqVbsQrTIajbIsV3tavQSYyZZHOppYuHpl+MDVWaLrN55JbaSnUqX24Q0UY5ml4vss8V2WWJOt2DwX39vSyia2ZpPa4kpkAAANq5cAkz120tGg8l1J7jPH9U24oPlHlM+OKqMT2f0dpBua18sGj9nlYuMZsT5HrMsRR4ov0/ZMtLDbktj4JKl/PENwAQBoXb0EWKGHWhIxIVbHrvmLdfL3WYKIFEGrTolVp3iUkd/UQrohkQ1NkJpcw3XBeQ7KKBDp+eKXc2JbrjhZdvkO044R7JaWbGxLqW8ccgsAIHjUMsDS0tKucu/mYkq1EhFZdq1e9cKkrfm613YrK08q3g1ICpz06RHl0yNExJNDWc8Y1jGC2oSzllYWa6JoIzPK5N3I2KVQuZvKPKLISbkOOm0TJ8sos1QcLRH7i0Su/YoFWHR0XVM2OlH6fXPWOgyxBQAQhOqlBbanjMmRsbwwVykrsmdsHtBz2LKR8vFS6ZPDyudHRWZpVVPpWKk4Vlr9VJOasOqpbywb0lQa2pT1i2P10UsJAACBo14CTCGyDvh98bf/JaKyzStCeg4joqRQ9nJP+eWetDNPrDwlfsxWfskT9ktmWNScRUedIllqNOsZw/rGspRIpkNoAQA0GvW1FqKl/+iS1QuEx+06vt916oihedvKu3rEsB4x7LnukluhvYVid4E4WCQyyyirXOTaqdApnJxK3EREeomserLqWLiBok3ULIQ1s1ArK2sdxtqFU0srk9A7CADQWNVXgEnWCHP3IbZffiSiso1Lo+564tJz9BJ1j2ZYsQkAAGqhHjvdrEPGeL+w79zASwrq74kAAKARqscAMzRvZ0zuTESCe8o3rai/JwIAgEaofqc9WIfe6v2i7KdvheuSpZwAAABqq34DzJzSXxeTQERKeUn5ttX1+lwAANCo1PPEc0kKHXab98vSdd8Ifg2z5gEAAM5T71dOhfQZKYdGEhEvzLX9uq6+nw4AABqJeg8wpjdYrxvr/bo0bSEpSn0/IwAANAYNsXaFZdDNUoiViDznsm3pGxrgGQEAIOg1RIBJphDrEF8jrOSHL9AIAwCAa9dAqwdarxsrma1E5Dl7CiNhAABw7RoowCSztXIkrGT155iOCAAA16jh1m+3Dr1VsoQRkScvp3zr9w32vAAAEJQaLsAkU0jo9Xd4vy5dvUA4r7wfJQAAQHUadAct66Cb5cg4IuKlhaVrv27IpwYAgCDToAHG9Ibw39/t/bp03Te86FxDPjsAAASTht7DOKTXcO/mlsLlLF7+cQM/OwAABI2GDjBiLHzcNGKMiGzpG5zH9jZ0AQAAEBQaPMCIjMkpId2HEBEJUfT1u6Twhq8BAAC0ToUAI6LwW/6PGc1E5M7JLF2/RJUaAABA09QJMDkiJmz0JO/XJd9/7sk/o0oZAACgXeoEGBGFXjdW3yyZiITLUbjo3ySEWpUAAIAWqRZgJMmRdzxKkkREzsPp5duwNgcAAPhBvQAjMrRoFzr0Vu/XRUs/REciAADUnJoBRkRhN0zRxbcgIuG0Fy6YjZ1WAACghlQOMKY3RE2azmQdETmP7StJ+1LdegAAQCtUDjAiMjRvF/q7u7xfl6xe4Dy6R916AABAE9QPMCIKu/4OY5uuRESKUvDpP3hJodoVAQBAoAuIACNJipr8pGSNICJeUlDw31ew4yUAAFxdYAQYkRweHT3lb75Z9cf2Fi3+QO2KAAAgoAVKgBGRsV1q+I33er8u3/Jt2cZl6tYDAACBLIACjIhCh/8hpOcw79dFS+fY925Ttx4AAAhYgRVgxFjknY8ZWnUk8k3ocB3fp3ZNAAAQiAIswIiY3hAz9QVdTAIRCZcz78Pn3dm/qV0UAAAEnIALMCKSrOExD7wih0USkWIvO/fB0+6cTJVrAgCAABOIAUZEupimMdNekUKsRKSUFZ9770n36eNqFwUAAAEkQAOMiPTNkmMeeEUyWcibYe/OcJ04qHZRAAAQKAI3wIjI0KJ9zIMV7TBb6bn3/uY48IvaRQEAQEAI6AAjIkPLDrF/ek2yhhORcDnyPnqh/KdVahcFAAD1xXXioH3LypqcqavvUq6dPrF13CNv5v3nGU/+GVJ44Vdvu3MyI8ZNI0lWuzQAAKgbvLTQtmOt7efV7jMnSZLMqUP00XFX/xYNBBgR6WKbxT7yr/y5z7tOHiaisk3L3dnHou5+Sg6PVrs0AACoPcE9jn3bbdt/sO//hRTuO6ooorSQgiPAiEgOi4z98+yCL/9pT99IRM5je8/Ofijqrummjr3ULg0AAPzmOnnI9suPtp3rlfKS848zo9nYdaAUEVPtI2gmwIiIGYzRU54qTWxT/O1/SVGUsqK8D5+1Dr4l/KY/MoNR7eoAAKB6noKzth1rbb+u9Zw9dcEdjBmTUyx9R5m7DXIKJsnVDxJpKcCIiBgLHTHe0LJjwWezeHE+CVG2cZlj/y+Rdz7q21EMAAACDy8ttGdstv26zpV5gIQ4/y5dVHxI7xEhvUfqYpr6DjkcNXlMrQUYEREZ23SJn/FB4cK37Ht+IiJP3ulz7z1p6X19+C33eTcVAwCAQKCUl9h3b7Hv2uQ4sosU5fy7mNEckjo4pPf1xtZdiLFaPLgmA4yIJEtY9H3PlW9PK14yR7GXkRDl29Psu38KHTXBOmQM0+nVLhAAoPHiJYWOPT/Zd29xHMmomppBRERM1hk79AzpOczcZQDTG67lWbQaYF6WPiNNHXoWLf7AvmsTESmO8uLlc8s2Lw8bPdnSazjm2QMANCTPuWz7nq32PVtdmfsv6ickxoytU0K6DzWnDpYsYXXydNoOMCKSw6Ki73nGcfDXoiX/8Q4J8oLcwi/+WZq2MPT6O0J6DWey5v+PAAABS3CP67e9jv3b7ft+9pzLvvhuxoxJncypQ8zdBtX5hU9B8uFu6tAzfsYH5Vu/K/l+gVJWRESec9mFX75Zsmq+dcgYS7/RdRX4AABARJ5z2Y5D6c6DOxxHMoTTfvHdkmRs3cXcdaC568D6u2A3SAKMiJissw662dL7+tKNS8vWLVZspUTEi/OLV3xS8v3n5u7XWfuPNiR1VrtMAACt4sX5ziMZziMZjiPpvCD30hOYwWTq0NOc0s/UuW8DNBuCJ8C8mNEcNnJC6JCxZZtXlm1cyovziUi4Xbbtabbtabq4xJBeI0J6DtVFN632oQAAGjshPLlZzsz9rt/2Oo/t9eTlXPYsXUyCqVNvU6c+xjZdG3IOXbAFmBczmkNH3G4dOs6+c33ZxmWuU0e8xz25WSWr5pesmm9o3tbcbZAppb++SQt1SwUACChKeYnr5GHXyUOuE4dcJw5etExGJckUYmzT1dihp6lDT11MQgMX6RWcAebFZF1I7+tDel/vOnW4fOv39p0bFEe59y7XqSOuU0eKV87TRTcxdexlbN/T2Lard+8xAIBGhRfmunMyXdm/ubN+c5864ik4e6UzmcFoaNXJ2LarqW2qoUU71Wd6B3OAVTI0b2do3i5i3AP2PT/Z0zc4DuwQHrf3Lk/+mbLNK8s2ryRJMiS2MSanGJJTDK06ymGR6tYMAFAfeHG+J/eU++wpd06m58xJd85xxVZ2lfMlS5gxqZMhOcWY3FnfvG1AzesOoFLqG9MbQnoMDekxVHGUO/b/Yt/zk/PADsVh892tKK6Th10nD9P6xUQkR8YZWrQ3NG+jT2yjT0hGngGA5vDSQp5/xpOf4zl32nMu25Ob7TmXXdkRdSVMb9AnJBtatjc0b2do1UEX26xhqq2FRhRglSSTxZtkgntcx/Y5Du10Hk53ZR09f5kTXphrL8y1Z2zyfYslTJ+QpI9rrotvrotL1MUk6KLiVG8+AwAIt4sXnePFBbzoHC86xwvPeQpzecFZT8EZ4XLW5BGkEKs+IUmfkKxv1tqQ2FrftJVWPtwaY4BVYrLO2LabsW03onsVR7nr2D7nsX2uY/tcWUcu+sEr5SXeyaPnf68cGStHNdFFxcuRcbrIWDkiVgqP0kXEMqO5wf8rABCchMuhlJXwsiKlrFgpL+ZlxUpxPi8v5sUFSkkBLynwXjJUc5LZqotP1Me31MU31zdtpW/aSq7BxiWBqVEH2Pkkk8XUqY+pUx8iIoW7c064Th1xZx1xZR93nz526WV6gns8eTmevJxL/8JhBpMcFimFRsnWcMkaLlsjJGuYFBImWcKkEKsUEiqFWJnZGlBdyQDQMBSHTbicwmlTHDbhKFccduEoV+zlir1c2MsUe7liL1VspYqtTCkvUWylwu2q9XNJZqsupqkc3UQXk6CLTdDFJOjjmwfTiud+f4aWlpa+9tpr+/btS0lJmTFjRmhoaH2UpTJJ1jdL1jdLJvodEZEQnsJcz5mT7jMnPOeyPeeyPXmneVHelb5buByevBy6wgUTlZjeIJktzGCWzBZmskhGEzOavf+4010aHcP0RqbTM7OFSZJkthIxZrYQkRRiJSLJaCZJx2QZDT6AOiecdsE5EQmXQ3A3EQl7uRCCuEe4HEIIYS8nIsVpI86F2yk8bu+3CIdNCMVVUkic27lbuBzC4xJ2m3A7hMtV7fhTLTBZJ4VHyeGxuogYOSJGjoyTo+J1kbFyVLxkttb50wUUvwNs0aJF8fHxzz333Jw5c7766qv77ruvPsoKLIzpouJ1UfGmTr0rjwm3y5N/hhec9RSe5YW+rmdeUsCL82rY7yzcLu52ERVe9t5if2vUG7zrOjO9kekMRESyLFVkG9MbSOdb9Znp9Ofv/8n0xosWhGYG06WtQ2YwMd3lf1u8QVt9hQZT7a9wlCTJFFLz00VhoasogtVqg4ZGTiiKcNh4WZnTaFT0tfx5CZejcqJvNWe6nVc5U3g8wnXZfaGEYr8kCbhHubCnRLgcwuOpuumwkfCNcwvuEU5HxbO4hNv3nlXs5RcvQas2pjdIljDJEi6HRkiWcMkaLodFyqGRUmikHBEjWcPl0MY7xczvANu8efNLL71kMBjGjBnz3HPPXTbAnE7niRMnLj0eFxdnMFzT4vkBRJKl2GZSbLNL3+LCaedFeYqtRCkt4qVFSnmxsJUq5SWKrUyxlQp7mWIvE/ZywT2XedjaEm5XRVfD1WbENh5XbCBDzdTorzDwHzOYJKOZGU3MZGEmi2QyM1OIZLJIZgsZQ6SQUMlskUJCpZBQFmKVQsKq3W6ec371E7SIcy5JUrWn+R1g+fn58fHxRBQfH19QUHDZc3bv3t2/f/9Lj8+bN6979+7+PqMm6UIoLITCmlx0mBExIt+Pxe0STjs5bcJlZ067cDnI7SKXg9vLHWWlIXqZXA6hcHKUk6IIp52EYC67EAo57EQknDZGQnBOl/8TFQCugd7o63LQGUjWExGZzIxJgklkMBERM1mIEdMbhawjnZ7pDKQ3kKwjg5lJkoMkJutMYRGk0wtZz8wWkvWkN7BLVkvwNgkvH0GcqLSscf5J6nQ6Y2Kqn1rid4AJIbw9M0II5cLtNSv17t37u+++8/eRwYtznp+fHxcX59d3VfaWCLdTeFxERB6PUpFtwu2kio6a89pqld94QR+O4nLQJa3DyiGByzz1VXuBrvJEflCUqiv2asDlcun1enQh1gKTJGYKcblcOp2uJn8CX/5BLumXvtqZV+5YZjodM5gue9dlRndknXThePBF/d7MaK6cHc4kmZkqOth1BqY3VjyspXZbA1+ktLSUMWa1BvkQVP1xOByyXP1Ufr8DLDo6Ojc3NzExMS8vryYJCQ2DGUzM94mB9wydPXs2Jja21p+/UFBQYLFYjMZqOq8A1OX3O7xfv36rV68WQqxevXrAgAH1URMAAEC1/A6wyZMnHzt2bMKECZmZmXfdddelJ+Tl5V1pbAxqwm63r1ixQu0qtG3FihUOB4YGa2/Tpk2nT59WuwoN27Nnz969e9WuQsOysrI2bNhQ7Wl+B5jVan3llVcWLlz48ssvWyyXWb792LFjx48f9/dhoVJhYeEzzzyjdhXa9vTTTxcVFaldhYa99957GRkZ1Z8HV7B8+fKVK1eqXYWGpaenv/3229WehkECAADQJAQYAABoEgIMAAA0iYm6Xjdl2bJl999/v8tV+wUoGzkhhMPhMJuxwmHt2e12k8mE68Bqzel06nS6mlyIA5fldrsZY7orrL4G1eKcP/74488///zVT6v7ACOi0tJSj6cu10kCAIBGJSwsrNo/oeolwAAAAOobxsAAAECTEGAAAKBJCDAAANCkugyw0tLSmTNnjhs37tlnny0tLa3DR24kNm3aNHXq1LFjxz722GNZWVlql6NVx48fv+mmm9SuQpM452+//fZtt932yCOP5OVhSzW/ZWRkTJs27eabb542bdru3bvVLkdjOOf33nuv9+sapkldBph3s+ZFixbFxcV99dVXdfjIjUFOTs7s2bOnT5++aNGi/v37z549W+2KNKmsrOz11193OrEdY21888035eXlCxYs6Ny58/z589UuR3tmzZo1ceLEJUuWTJgwYdasWWqXoyWLFy9+5JFHKv9wr2Ga1GWAbd68ecyYMd7Nmjdt2lSHj9wY5OTkDB8+vEOHDkajcdSoUadOnVK7Iu1RFOX111+fOHGi2oVo1dq1a8ePH28ymSZNmnTzzTerXY72hISElJeX2+12u92OSzn9kpycPGnSpMqbNUyTurzOriabNcOV9OjRo0ePHkTEOZ8/f/7QoUPVrkh7vvzyy8TExMGDB6tdiFbl5uauW7du+vTpTZs2feKJJ9QuR3tmzJjx5z//+V//+hcRvfvuu2qXoyWpqann36xhmtRlC6wmmzXD1e3YseOhhx6yWCwPPfSQ2rVozM6dO9PT0++77z61C9Gw8vJyIcTcuXN79+795ptvql2O9sydO3f8+PELFy68/fbbP/74Y7XL0bAapkldBph3s2YiwmbNtSCE+PDDDxcsWDBz5sypU6diFR9/7dy5MyMjY/To0SNHjiSikSNHYkMmf0VERNx6663R0dFjxozJzMxUuxztOXjw4G233RYdHX3nnXceOHBA7XI0rIZpUpcBhs2ar8Xu3bu3bt368ssvR0dHe/vQ1a5IY6ZOnZpWgYjS0tJSUlLULkpjevXq9cMPP7hcrm+//bZdu3Zql6M9SUlJ3333nd1uT0tLa926tdrlaFgN06QuA6zazZrhKjIyMrKyssaNG3dLBbUrgkbnvvvuS09PHz9+fHp6+l//+le1y9Ge6dOnb9++ffz48Rs3bsQLeC1qmCZYCxEAADQJK3EAAIAmIcAAAECTEGAAAKBJCDAAANAkBBgAAGgSAgwAADQJAQYAAJqEAANoUKtXry4vL1e7CoBggAADaFBvvPFGfn6+2lUABAMEGAAAaBKWkgJoON6V8r28iw4DQK0hwAAazpkzZyZPnvzaa68lJCQ0adJE7XIAtA1diAANxxtaMTExSC+Aa4cAAwAATUKAAQCAJiHAAABAkxBgAACgSQgwgAYly/KmTZv27dundiEAmodp9AAN6qOPPlq+fLlOp1uyZInatQBoGwIMAAA0CV2IAACgSQgwAADQJAQYAABoEgIMAAA0CQEGAACahAADAABNQoABAIAmIcAAAECTEGAAAKBJ/w9RnWVJg6e6wwAAAABJRU5ErkJggg==" />
<pre class='hljl'>
<span class='hljl-n'>test_p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>0.58</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f3</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>test_p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<pre class='hljl'>
<span class='hljl-n'>test_p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>-</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>0.7</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f3</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>test_p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<p>Ouch. We see that effecting the birth rate, we would have to hit a reduction range of &#91;0.55,0.7&#93; to get the effect we want without introducing population collapse. What about effecting wolf population growth?</p>
<pre class='hljl'>
<span class='hljl-n'>test_p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.25</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f3</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>test_p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<pre class='hljl'>
<span class='hljl-n'>test_p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.5</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f3</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>test_p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<pre class='hljl'>
<span class='hljl-n'>test_p</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-n'>p</span><span class='hljl-t'> </span><span class='hljl-oB'>+</span><span class='hljl-t'> </span><span class='hljl-p'>[</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>1.5</span><span class='hljl-p'>,</span><span class='hljl-nfB'>2.0</span><span class='hljl-p'>,</span><span class='hljl-ni'>0</span><span class='hljl-p'>]</span><span class='hljl-t'>
</span><span class='hljl-n'>prob</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>ODEProblem</span><span class='hljl-p'>(</span><span class='hljl-n'>f3</span><span class='hljl-p'>,</span><span class='hljl-n'>u0</span><span class='hljl-p'>,</span><span class='hljl-n'>tspan</span><span class='hljl-p'>,</span><span class='hljl-n'>test_p</span><span class='hljl-p'>)</span><span class='hljl-t'>
</span><span class='hljl-n'>sol</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>solve</span><span class='hljl-p'>(</span><span class='hljl-n'>prob</span><span class='hljl-p'>,</span><span class='hljl-nf'>Tsit5</span><span class='hljl-p'>())</span><span class='hljl-t'>
</span><span class='hljl-nf'>plot</span><span class='hljl-p'>(</span><span class='hljl-n'>sol</span><span class='hljl-p'>)</span>
</pre>
<img 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" />
<p>Wow, it&#39;s very easy to intervene this way and get the rabbit population below 4 million, and not have a population collapse&#33;</p>
<h2>Board Meeting Recommendations</h2>
<p>From these results you go to your board meeting and recommend:</p>
<ul>
<li><p>Do not attempt to decrease the rabbit population by killing baby rabbits. This seems like the obvious approach, but the models show that it can easily lead to population collapse.</p>
</li>
<li><p>However, making it easier for wolves to feast on rabbits is a robust change to the ecosystem that gives the people what they want.</p>
</li>
<li><p>We recommend clearing a lot of bushes to give rabbits a harder chance of hiding, along with long-term investment in research for wolf binoculars.</p>
</li>
<li><p>As we go through our results, we tell our collegues to never use a local optimizer.</p>
</li>
<li><p>During our talk, we tell our collegues that the global optimization takes for ever, so we should probably parallelize it, or do other things, like change our models into Julia to use their faster tools.</p>
</li>
</ul>
<h2>Translating This Example to Systems Pharmacology</h2>
<p>We have a cancer pathway and our team is synthesizing molecules to target different aspects of the pathway. Our goal as the modeler is to help the guide the choice of which part of the pathway we should target. So we:</p>
<ol>
<li><p>Talk to biologists and consult the literature to learn about the pathway</p>
</li>
<li><p>Build a model</p>
</li>
<li><p>Find some data in the literature about how the pathway should generally act</p>
</li>
<li><p>Try to fit the data</p>
</li>
<li><p>If we don&#39;t fit well, go back to &#40;1&#41;</p>
</li>
<li><p>Great, we now have a good enough model. Investigate what happens to the cancer patient if we effect X vs Y. Does X introduce toxic effects? Can we know if it only produces toxic effects in men?</p>
</li>
<li><p>Gather these plots to showcase that yes, the model gives a reliable fit, and the analysis shows that targetting X will cause ...</p>
</li>
</ol>
<h2>Possible Improvements for Tooling</h2>
<p>Given this process, the possible improvements to tooling are:</p>