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@germannp
Last active July 20, 2021 12:19
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "proved-table",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"from scipy.integrate import odeint"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "about-chapter",
"metadata": {},
"outputs": [],
"source": [
"%load_ext blackcellmagic\n",
"\n",
"plt.rcParams['figure.figsize'] = [10, 7]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "accomplished-aside",
"metadata": {},
"outputs": [],
"source": [
"variable_names = [\n",
" \"Susceptible\",\n",
" \"Infectious\",\n",
" \"Recovered\",\n",
" \"Vaccinated\",\n",
" \"Vacc. & infect.\",\n",
" \"Vacc. & rec.\",\n",
"]\n",
"\n",
"# From https://www.covid19.admin.ch\n",
"R_e = 1.53\n",
"\n",
"# 40% vaccinated, 30% recovered\n",
"S_0 = 0.3\n",
"V_0 = 0.4\n",
"\n",
"# Pop. of 8e6, 800 cases/day, 5 days infectious before test, and 50% reported\n",
"I_0 = (800 * 2 * 5) / 8e6 * (S_0 / (S_0 + V_0 / 2))\n",
"VI_0 = (800 * 2 * 5) / 8e6 * (V_0 / 2 / (S_0 + V_0 / 2))\n",
"\n",
"# Neglect initial recovered and vaccinated, I don't know any data to estimate that 🤷\n",
"VR_0 = 0\n",
"\n",
"# Assume that currently exclusively unvaccinated people are infected\n",
"R_0 = R_e / S_0\n",
"\n",
"# 1 / Avg. time being infectious; chosen to match current doubling time\n",
"gamma = 1 / 0.3\n",
"beta = R_0 * gamma\n",
"\n",
"\n",
"def dXdt(X, t):\n",
" \"\"\"See https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology\"\"\"\n",
" S, I, R, V, VI, VR = X\n",
"\n",
" # Assume vaccination makes you half as infectious\n",
" dSdt = -beta * (I + VI / 2) * S\n",
" dIdt = beta * (I + VI / 2) * S - gamma * I\n",
" dRdt = gamma * I\n",
" # Assume vaccination makes you half as likely to get infected\n",
" dVdt = -beta * (I + VI / 2) * V / 2\n",
" dVIdt = beta * (I + VI / 2) * V / 2 - gamma * VI\n",
" dVRdt = gamma * VI\n",
"\n",
" return [dSdt, dIdt, dRdt, dVdt, dVIdt, dVRdt]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "weighted-mozambique",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x504 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def simulate():\n",
" fig, ax = plt.subplots(2, 1, sharex=True)\n",
" time_points = np.linspace(0, 4, 200)\n",
" solution = odeint(dXdt, [S_0, I_0, 1 - S_0 - I_0 - V_0, V_0, VI_0, VR_0], time_points)\n",
" solution = pd.DataFrame(solution, columns=variable_names, index=time_points)\n",
"\n",
" ax[0].set_title(\"SIRV Model with partial protection\")\n",
" solution[[\"Susceptible\", \"Infectious\", \"Recovered\"]].plot(\n",
" ax=ax[0], color=[\"C1\", \"C3\", \"C0\", \"C2\"]\n",
" )\n",
" solution[[\"Vaccinated\", \"Vacc. & infect.\", \"Vacc. & rec.\"]].plot(\n",
" ax=ax[0], color=[\"C1\", \"C3\", \"C0\", \"C2\"], ls=\":\"\n",
" )\n",
" ax[0].set_ylabel(\"Proportion in Population\")\n",
" ax[0].legend(frameon=False, loc=\"center right\")\n",
"\n",
" ax[1].set_title(\"Daily cases\")\n",
" solution[\"cases\"] = -(solution[\"Susceptible\"] + solution[\"Vaccinated\"]).diff()\n",
" # Assuming currently only 50% reported\n",
" solution[\"cases\"] = solution[\"cases\"] * 1600 / solution[\"cases\"].iloc[1]\n",
" solution[\"cases\"].plot(ax=ax[1], color=\"k\", label=\"Cases\")\n",
"\n",
" # Smoothly limiting cases due to false negatives, the proper way would be stats 🤷\n",
" max_reported_cases = 17_500\n",
" K = (max_reported_cases * 1_600 - 800 * 1_600) / 800\n",
" solution[\"Reported cases\"] = max_reported_cases * solution[\"cases\"] / (solution[\"cases\"] + K)\n",
" solution[\"Reported cases\"].plot(ax=ax[1], color=\"k\", ls=\":\")\n",
"\n",
" ax[1].vlines([1.5], ymin=0, ymax=solution[\"cases\"].max(), color=\"r\", ls=\":\")\n",
" ax[1].set_xlabel(\"Time [months]\")\n",
" ax[1].legend(frameon=False)\n",
"\n",
" sns.despine()\n",
" plt.show()\n",
" \n",
" return solution\n",
"\n",
"\n",
"solution = simulate()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "turkish-external",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(9.299999999999999, 1.8235294117647054)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Avg. days being infectious, avg. time between infect. contacts\n",
"31 / gamma, 31 / beta"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "found-above",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.14522348776944577"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The chance of not getting covid if you are not yet vaccinated\n",
"solution[\"Susceptible\"].min() / solution[\"Susceptible\"].max()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "binding-shoulder",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.17095530244611085"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The chance of not getting long covid if you are not yet vaccinated\n",
"(1 - _) * 0.2"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "killing-ghost",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.000000 NaN\n",
"0.020101 800.000000\n",
"0.040201 854.656499\n",
"0.060302 912.625924\n",
"0.080402 974.615094\n",
"0.100503 1040.356548\n",
"0.120603 1110.163279\n",
"0.140704 1184.207750\n",
"0.160804 1262.719691\n",
"0.180905 1345.895089\n",
"0.201005 1433.975156\n",
"0.221106 1527.145818\n",
"0.241206 1625.628652\n",
"0.261307 1729.623116\n",
"0.281407 1839.288534\n",
"0.301508 1954.828619\n",
"0.321608 2076.436955\n",
"0.341709 2204.253494\n",
"0.361809 2338.465306\n",
"0.381910 2479.166863\n",
"0.402010 2626.525788\n",
"0.422111 2780.565548\n",
"0.442211 2941.331639\n",
"0.462312 3108.894791\n",
"0.482412 3283.276087\n",
"0.502513 3464.458899\n",
"0.522613 3652.367877\n",
"0.542714 3846.813075\n",
"0.562814 4047.685480\n",
"0.582915 4254.797740\n",
"Name: Reported cases, dtype: float64"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Supposed to start with 800 and double every 0.25 month\n",
"solution[\"Reported cases\"].iloc[:30]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "oriented-enclosure",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x504 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Assuming infection of vaccinated people alrady contributes proportionally to new cases\n",
"# and choosing gamma accordingly\n",
"R_0 = R_e / (S_0 + V_0 / 2)\n",
"gamma = 1 / 0.06\n",
"beta = R_0 * gamma\n",
"\n",
"solution = simulate()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "bright-rouge",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1.8599999999999999, 0.6078431372549019)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Avg. days being infectious, avg. time between infect. contacts\n",
"31 / gamma, 31 / beta"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "marked-tumor",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.6094534305972884"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The chance of not getting covid if you are not yet vaccinated\n",
"solution[\"Susceptible\"].min() / solution[\"Susceptible\"].max()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "based-bailey",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.07810931388054232"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The chance of not getting long covid if you are not yet vaccinated\n",
"(1 - _) * 0.2"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "younger-perception",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.000000 NaN\n",
"0.020101 800.000000\n",
"0.040201 858.365735\n",
"0.060302 920.542568\n",
"0.080402 986.558579\n",
"0.100503 1056.547265\n",
"0.120603 1130.647009\n",
"0.140704 1208.978608\n",
"0.160804 1291.660127\n",
"0.180905 1378.759265\n",
"0.201005 1470.371503\n",
"0.221106 1566.502801\n",
"0.241206 1667.169086\n",
"0.261307 1772.338650\n",
"0.281407 1881.971842\n",
"0.301508 1995.944510\n",
"0.321608 2114.147365\n",
"0.341709 2236.359692\n",
"0.361809 2362.376495\n",
"0.381910 2491.883312\n",
"0.402010 2624.577128\n",
"0.422111 2760.045328\n",
"0.442211 2897.864350\n",
"0.462312 3037.550800\n",
"0.482412 3178.550864\n",
"0.502513 3320.324234\n",
"0.522613 3462.203502\n",
"0.542714 3603.597454\n",
"0.562814 3743.763003\n",
"0.582915 3882.059498\n",
"Name: Reported cases, dtype: float64"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Supposed to start with 800 and double every 0.25 month\n",
"solution[\"Reported cases\"].iloc[:30]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "legislative-grove",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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