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A Live SEIR Model for Covid-19 with Error Bars in Julia
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## A Live [SEIR](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model) Model for Covid-19 with Error Bars in Julia\n", | |
| "\n", | |
| "#### Author: Dan Segal (@[djsegal](https://github.com/djsegal/))\n", | |
| "\n", | |
| "as requested by Prof. Alan Edelman, MIT\n", | |
| "\n", | |
| "----\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "using Measurements\n", | |
| "\n", | |
| "param_error = 0.05\n", | |
| "\n", | |
| "α = 0.2 ± param_error\n", | |
| "γ = 0.5 ± param_error\n", | |
| "\n", | |
| "# β = f(social distancing, masks, etc.)\n", | |
| "\n", | |
| "E₀ = 1e-4\n", | |
| "u₀ = [ 1 - E₀ ; E₀ ; 0 ; 0 ]\n", | |
| "\n", | |
| "tspan = (0.0, 200.0); # 200 days\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "using DifferentialEquations\n", | |
| "\n", | |
| "function seir!(du,u,p,t)\n", | |
| " S,E,I,_ = u\n", | |
| " α,β,γ = p\n", | |
| "\n", | |
| " dS = ( -β*I*S )\n", | |
| " dE = ( +β*I*S ) - α*E\n", | |
| " dI = ( -γ*I ) + α*E\n", | |
| " dR = ( +γ*I )\n", | |
| "\n", | |
| " du .= (dS, dE, dI, dR)\n", | |
| "end\n", | |
| "\n", | |
| "labels = [\n", | |
| " \"Susceptible\", \"Exposed\", \n", | |
| " \"Infected\", \"Recovered\"\n", | |
| "];\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": { | |
| "scrolled": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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| " <script type=\"text/javascript\" class=\"js-plotly-script\">\n", | |
| " globalComms = {};\n", | |
| " demoData = {};\n", | |
| "\n", | |
| " $(\".js-plotly-script\").parent().css('padding', 0);\n", | |
| "\n", | |
| " function customPlotlyReact(curPlot, curData, curLayout, curConfig) {\n", | |
| " for (var i = 0; i < curData.length; i++) {\n", | |
| " curData[i][\"visible\"] = true;\n", | |
| " for (var j = 0; j < curPlot.data.length; j++) {\n", | |
| " if ( curData[i].name !== curPlot.data[j].name ) { continue; }\n", | |
| " if ( curPlot.data[j].visible !== \"legendonly\" ) { continue; }\n", | |
| "\n", | |
| " curData[i][\"visible\"] = \"legendonly\";\n", | |
| " }\n", | |
| " }\n", | |
| "\n", | |
| " Plotly.react(curPlot, curData, curLayout, curConfig);\n", | |
| " }\n", | |
| "\n", | |
| " function customPlotLoader(curCallback) {\n", | |
| " if ( $(\".js-nouislider-css\").length == 0 ) {\n", | |
| " $(\"head\").append(\n", | |
| " '<link class=\"js-nouislider-css\" href=\"https://cdn.jsdelivr.net/gh/djsegal/SimplePlots.jl/dist/nouislider.min.css\" rel=\"stylesheet\">'\n", | |
| " );\n", | |
| " }\n", | |
| "\n", | |
| " if ( $(\".js-custom-css\").length == 0 ) {\n", | |
| " $(\"head\").append(\n", | |
| " '<link class=\"js-custom-css\" href=\"https://cdn.jsdelivr.net/gh/djsegal/SimplePlots.jl/dist/custom.min.css\" rel=\"stylesheet\">'\n", | |
| " );\n", | |
| " }\n", | |
| "\n", | |
| " if ( typeof Plotly !== \"undefined\" ) {\n", | |
| " if ( typeof curCallback !== \"undefined\" ) {\n", | |
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| " scriptParent.style.margin = \"0\";\n", | |
| " scriptParent.style.padding = \"0\";\n", | |
| " }\n", | |
| "\n", | |
| " require.config({\n", | |
| " paths: {\n", | |
| " Plotly: \"https://cdn.plot.ly/plotly-1.53.0.min\",\n", | |
| " noUiSlider: \"https://cdn.jsdelivr.net/gh/djsegal/SimplePlots.jl/dist/nouislider.min\",\n", | |
| " wNumb: \"https://cdn.jsdelivr.net/gh/djsegal/SimplePlots.jl/dist/wnumb.min\"\n", | |
| " }\n", | |
| " });\n", | |
| "\n", | |
| " require([\"Plotly\", \"noUiSlider\", \"wNumb\"], function(Plotly, noUiSlider, wNumb){\n", | |
| " window.Plotly = Plotly;\n", | |
| " window.noUiSlider = noUiSlider;\n", | |
| " window.wNumb = wNumb;\n", | |
| "\n", | |
| " if ( typeof curCallback !== \"undefined\" ) {\n", | |
| " curCallback();\n", | |
| " }\n", | |
| "\n", | |
| " $(\"head\").append($(\".js-plotly-script\"));\n", | |
| " $(\"head .js-plotly-script:not(:first)\").remove();\n", | |
| " $(\"body .js-plotly-script\").remove();\n", | |
| " });\n", | |
| " }\n", | |
| "\n", | |
| " $(document).ready(customPlotLoader);\n", | |
| " customPlotLoader();\n", | |
| " </script>\n" | |
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| " <h3> Sliding the β value reduces/increases infectivity </h3>\n", | |
| " <p style=\"margin-top: 0.4em\">(social distancing, immunity, vaccines reduce β)</p>\n" | |
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| " if ( typeof workPlot === \"undefined\" ) { alert(\"Could not find plotly plot!\"); }\n", | |
| "\n", | |
| " var workJson = msg.content.data.json.plot;\n", | |
| " customPlotlyReact(workPlot, workJson.data, workJson.layout, workJson.config);\n", | |
| "\n", | |
| " $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673 .js-new-plot-script\").replaceWith(msg.content.data.json.script);\n", | |
| " } else {\n", | |
| " if ( \"html\" in msg.content.data ) {\n", | |
| " var tmpDisplay = $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673 .js-display\");\n", | |
| " tmpDisplay.html(msg.content.data.html);\n", | |
| " } else {\n", | |
| " if ( \"text\" in msg.content.data ) {\n", | |
| " console.log(msg.content.data.text);\n", | |
| " } else {\n", | |
| " alert(\"Unrecognized interact content type!\");\n", | |
| " }\n", | |
| " }\n", | |
| " }\n", | |
| " });\n", | |
| "\n", | |
| " comm.on_close(function(msg) { console.log(\"Julia close message: \" + msg); });\n", | |
| " $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673\").trigger(\"interact\");\n", | |
| " })\n", | |
| "\n", | |
| " var curCommand = 'Main.SimplePlots.interact_comms[\"interact-4a4e53eb-56fd-4403-a0eb-c48916e51673\"][] += 10';\n", | |
| " Jupyter.notebook.kernel.execute(curCommand, {\"iopub\": {\"output\": function(tmpMessage) {\n", | |
| " console.log(tmpMessage)\n", | |
| " }}});\n", | |
| "\n", | |
| " if ( typeof curCallback !== \"undefined\" ) { curCallback(); }\n", | |
| " }\n", | |
| "\n", | |
| " if ( typeof Jupyter === \"undefined\" ) {\n", | |
| " customPlotLoader(function() {\n", | |
| " $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673\").trigger(\"interact\");\n", | |
| " });\n", | |
| " } else {\n", | |
| " if (Jupyter.notebook.kernel) {\n", | |
| " _guiBootup()\n", | |
| " } else {\n", | |
| " Jupyter.notebook.events.one('kernel_ready.Kernel', (e) => {\n", | |
| " _guiBootup(function() {\n", | |
| " customPlotLoader(function() {\n", | |
| " $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673\").trigger(\"interact\");\n", | |
| " });\n", | |
| " });\n", | |
| " });\n", | |
| " }\n", | |
| " }\n" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "application/javascript": [ | |
| "demoData['interact-4a4e53eb-56fd-4403-a0eb-c48916e51673'] = 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(Days)\",\"type\":\"linear\"},\"annotations\":[],\"title\":\"Covid-19 SEIR Model with Error Bars\",\"yaxis\":{\"autorange\":false,\"range\":[0,100],\"title\":\"%\",\"type\":\"linear\"},\"shapes\":[],\"legend\":{}}}}\n", | |
| " $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673\").trigger(\"interact\");\n" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "using SimplePlots\n", | |
| "\n", | |
| "display(html\"\"\"\n", | |
| " <h3> Sliding the β value reduces/increases infectivity </h3>\n", | |
| " <p style=\"margin-top: 0.4em\">(social distancing, immunity, vaccines reduce β)</p>\n", | |
| "\"\"\")\n", | |
| "\n", | |
| "beta_slider = slider(0.25:0.25:2, value=1, label=\"β\") \n", | |
| "\n", | |
| "@demo for β in beta_slider\n", | |
| " title!(\"Covid-19 SEIR Model with Error Bars\") ;\n", | |
| " xlabel!(\"Time (Days)\") ; ylabel!(\"%\") \n", | |
| " \n", | |
| " soln = solve(ODEProblem(\n", | |
| " seir!, u₀, tspan, [α, β ± param_error, γ]\n", | |
| " ), saveat=0.5)\n", | |
| " \n", | |
| " x, y = soln.t, 100*Array(soln)\n", | |
| " ylims!(0, 100) # using percentages\n", | |
| " \n", | |
| " for (index, label) in enumerate(labels)\n", | |
| " plot!(\n", | |
| " x, y[index,:], label=label, \n", | |
| " alpha=0.8, fillalpha=0.1\n", | |
| " )\n", | |
| " end\n", | |
| "end\n" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "@webio": { | |
| "lastCommId": null, | |
| "lastKernelId": null | |
| }, | |
| "kernelspec": { | |
| "display_name": "Julia 1.4.0", | |
| "language": "julia", | |
| "name": "julia-1.4" | |
| }, | |
| "language_info": { | |
| "file_extension": ".jl", | |
| "mimetype": "application/julia", | |
| "name": "julia", | |
| "version": "1.4.0" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 4 | |
| } |
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