{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-08-31T16:28:35.316574Z", "start_time": "2021-08-31T16:28:35.300597Z" } }, "outputs": [], "source": [ "%display typeset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Usando Modelos Populacionais Logísticos para Epidemias\n", "Nesta aula vamos conhecer o modelo logístico de Richards, e estuda sua aplicabilidade no estudo de epidemias. Este notebook se baseia [neste artigo](https://userweb.ucs.louisiana.edu/~xxw6637/papers/JTB2012.pdf)\n", "\n", "O modelo de Richards se baseia em um modelo proposto por Verhulst em 1838.\n", "\n", "$$\\frac{dN(t)}{dt}=r N(t)\\left[1-\\frac{N(t)}{K}\\right]$$\n", "\n", "Richards generalizou este modelo em 1959, adicionando o parâmetro $a$ permitindo o desvio da dependência estrita da densidade." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-08-30T12:09:51.582016Z", "start_time": "2021-08-30T12:09:51.571761Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial t}C\\left(t\\right) = r_{1} C\\left(-\\left(\\frac{C\\left(t\\right)}{K}\\right)^{a} + 1\\right)$$" ], "text/plain": [ "diff(C(t), t) == r1*C(-(C(t)/K)^a + 1)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('C r1 K a t')\n", "C = function('C')(t)\n", "dcdt = diff(C,t)==r1*C(1-(C/K)^a)\n", "dcdt" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2021-08-30T12:12:03.274132Z", "start_time": "2021-08-30T12:12:03.097801Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\int \\frac{\\frac{\\partial}{\\partial t}C\\left(t\\right)}{C\\left(-\\left(\\frac{C\\left(t\\right)}{K}\\right)^{a} + 1\\right)}\\,{d t}}{r_{1}} = C + t$$" ], "text/plain": [ "integrate(1/C(-(C(t)/K)^a + 1), C(t))/r1 == _C + t" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "desolve(dcdt, C, ivar=t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O modelo de Richards admite uma solução explícita:\n", "\n", "$$C(t)=K\\left[1+a e^{-a r1(t-t_c)}\\right]^{-1/a},$$\n", "\n", "onde $t_c$ é o ponto no tempo em que a segunda derivada de $C(t)$ se torna 0, ou seja, quando $C(t)=K(1+a)^{-1/a}$. Seja $r=a r1$, então a equação acima se torna:\n", "$$C(t)=K\\left[1+a e^{-r(t-t_c)}\\right]^{-1/a}.$$\n", "\n", "## Relação com o modelo SIR\n", "Seja o modelo SIR,\n", "$$\n", "\\frac{dS}{dt} = -\\beta S I/N \\label{dsdt}\n", "$$\n", "$$\\frac{dI}{dt} = \\beta S I/N -\\gamma I$$\n", "$$\\frac{dR}{dt} = \\gamma I$$\n", "\n", "Onde podemos considerar que $N=S+I$. A partir das equações acima temos que\n", "\n", "$$\\frac{d(S+I)}{ds}=\\frac{\\gamma (S+I)}{\\beta S}$$\n", "\n", "cuja solução é:\n", "\n", "$$S(t)+I(t) = cS(t)^{\\gamma/\\beta} \\label{eq10}$$\n", "\n", "onde\n", "\n", "$$c:=[S(0)+I(0)]S(0)^{\\gamma/\\beta}$$\n", "\n", "combinando (\\ref{dsdt}) e (\\ref{eq10}) obtemos:\n", "\n", "$$\\frac{dS}{dt}=-\\beta S[1-(S/L)^\\alpha] \\label{eq12}$$\n", "\n", "onde $\\alpha:= 1-\\gamma/\\beta$ e $L:=c^{1/(1-\\gamma/\\beta)}$.\n", "\n", "Como a equação (\\ref{eq12}) tem a mesma forma que a equação (\\ref{dsdt}), pode ser resolvida como:\n", "\n", "$$S(t)=L[1+\\alpha e^{b(t-t_j)}]^{-1/\\alpha}$$\n", "\n", "onde $b=\\alpha\\beta$ e $t_j$ o tempo finito em que a segunda derivada de $S(t)$ é $0$.\n", "\n", "Como estamos interessados no numero acumulado de de casos, podemos definir:\n", "\n", "\\begin{align}\n", "J(t) :=& I(t)+R(t)\\nonumber\\\\\n", "=& N-S(t)\\nonumber\\\\\n", "=& N-L[1+\\alpha e^{b(t-t_j)}]^{-1/\\alpha}\n", "\\end{align}\n", "\n", "Sendo $N=S(0)+I(0)$ então $N \\approx L$. Como $I(0)/S(0)\\rightarrow 0$,\n", "\n", "$$J(t)\\approx L-L[1+\\alpha e^{b(t-t_j)}]^{-1/\\alpha}.$$\n", "\n", "Esta última equação nos dá uma forma eficiente de mapear uma curva de casos acumulados ao modelo SIR sem utilizar equações diferenciais.\n", "\n", "Na prática podemos igualar $L$ ao tamanho final da epidemia, e $t_j$ ao ponto de inflexão da curva. Temos ainda que $\\alpha=1-1/{\\cal R}_0$, e $b=\\beta -\\gamma$ a taxa de geração de infeções.\n", "\n", "### Instante do pico, $t_i$\n", "O pico da epidemia ocorre quando $\\dot{I}(t_i)=0$ o que implica que \n", "$$\\frac{\\beta S(t_i)}{S(t_i)+I(t_i)}=\\gamma$$\n", "\n", "Considerando as equações (\\ref{eq10}) e $\\alpha:= 1-\\gamma/\\beta$ e $L:=c^{1/(1-\\gamma/\\beta)}$, podemos obter\n", "\n", "$$S(t_i)=L (\\beta/\\gamma)^{-1/\\alpha}$$\n", "\n", "combinando as duas equações acima temos\n", "\n", "$$I(t_i)=L{\\cal R}_0^{-{\\cal R}_0/({\\cal R}_0-1)}({\\cal R}_0-1)$$\n", "\n", "com \n", "\n", "$${\\cal R}_0=e^{b(t_i-t_j)}$$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ajustando o modelo de Richards a Dados\n", "Agora vamos ver como o modelo de Richards se presta para representar uma epidemia com múltiplas ondas. Vamos utilizar os dados da Epidemia da COVID-19 em 2020 e 21" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2021-08-31T22:16:09.589023Z", "start_time": "2021-08-31T22:16:09.575167Z" } }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-08-31T16:39:21.134371Z", "start_time": "2021-08-31T16:39:21.100928Z" } }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
total_casesnew_caseslocationtotal_deathsnew_deathstotal_vaccinationsnew_vaccinationsstringency_indexpopulation
date
2020-01-3122United KingdomNaNNaNNaNNaN8.3368207114
2020-02-0120United KingdomNaNNaNNaNNaN8.3368207114
2020-02-0220United KingdomNaNNaNNaNNaN11.1168207114
2020-02-0386United KingdomNaNNaNNaNNaN11.1168207114
2020-02-0480United KingdomNaNNaNNaNNaN11.1168207114
..............................
2021-08-24658618130762United Kingdom132174.0174.089865264.0186086.043.9868207114
2021-08-25662179935618United Kingdom132323.0149.090095045.0229781.043.9868207114
2021-08-26665991638117United Kingdom132465.0142.090295121.0200076.043.9868207114
2021-08-27669777037854United Kingdom132566.0101.090466529.0171408.043.9868207114
2021-08-28672991232142United Kingdom132699.0133.0NaNNaNNaN68207114
\n", "

576 rows × 9 columns

\n", "
" ], "text/plain": [ " total_cases new_cases location total_deaths new_deaths \\\n", "date \n", "2020-01-31 2 2 United Kingdom NaN NaN \n", "2020-02-01 2 0 United Kingdom NaN NaN \n", "2020-02-02 2 0 United Kingdom NaN NaN \n", "2020-02-03 8 6 United Kingdom NaN NaN \n", "2020-02-04 8 0 United Kingdom NaN NaN \n", "... ... ... ... ... ... \n", "2021-08-24 6586181 30762 United Kingdom 132174.0 174.0 \n", "2021-08-25 6621799 35618 United Kingdom 132323.0 149.0 \n", "2021-08-26 6659916 38117 United Kingdom 132465.0 142.0 \n", "2021-08-27 6697770 37854 United Kingdom 132566.0 101.0 \n", "2021-08-28 6729912 32142 United Kingdom 132699.0 133.0 \n", "\n", " total_vaccinations new_vaccinations stringency_index population \n", "date \n", "2020-01-31 NaN NaN 8.33 68207114 \n", "2020-02-01 NaN NaN 8.33 68207114 \n", "2020-02-02 NaN NaN 11.11 68207114 \n", "2020-02-03 NaN NaN 11.11 68207114 \n", "2020-02-04 NaN NaN 11.11 68207114 \n", "... ... ... ... ... \n", "2021-08-24 89865264.0 186086.0 43.98 68207114 \n", "2021-08-25 90095045.0 229781.0 43.98 68207114 \n", "2021-08-26 90295121.0 200076.0 43.98 68207114 \n", "2021-08-27 90466529.0 171408.0 43.98 68207114 \n", "2021-08-28 NaN NaN NaN 68207114 \n", "\n", "[576 rows x 9 columns]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ukd = pd.read_csv('UK_covid.csv')\n", "ukd['date'] = pd.to_datetime(ukd.date)\n", "ukd.set_index('date', inplace=True)\n", "ukd" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2021-08-31T16:51:29.358024Z", "start_time": "2021-08-31T16:51:29.073625Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig , [a1,a2] = plt.subplots(2,1, figsize=[15,6], sharex=True)\n", "ukd.total_cases.plot(ax=a1);\n", "ukd.new_cases.plot(ax=a2);" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "ExecuteTime": { "end_time": "2021-08-31T22:53:56.405590Z", "start_time": "2021-08-31T22:53:56.050035Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "2083fe183edf437ba71865abeb57eaf3", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 15 widgets\n", " w1: TransformIntRangeSlider(…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def rich(L,a,b,t,tj):\n", " j=L-L*(1+a*np.exp(b*(t-tj)))**(-1/a)\n", " return j\n", "df = ukd.reset_index()\n", "@interact\n", "def plot_richards(w1=range_slider(1,180,step_size=1,default=(1,160)), \n", " tp1=(86,(10,150)),L1=(.3e6,(.1e6,1.5e6)),a1=(0.1,(0.1,1)),b1=(0.2,(0.001,.2,.01)),\n", " w2=range_slider(180,350,step_size=1,default=(210,300)), \n", " tp2=(277,(230,350)),L2=(1e6,(.9e6,3.5e6)),a2=(0.1,(0.1,1)),b2=(0.2,(0.001,.2,.01)),\n", " w3=range_slider(220,400,step_size=1,default=(300,400)), \n", " tp3=(329,(220,400)),L3=(2e6,(1e6,4.5e6)),a3=(0.1,(0.1,1)),b3=(0.2,(0.001,.2,.01)),\n", " ):\n", " fig,ax = plt.subplots(1,1, figsize=(15,8))\n", " df.total_cases.plot(ax=ax, label='Total cases',style='+')\n", " plt.plot(range(w1[0],w1[1]), [rich(L1,a1,b1,t,tp1) for t in range(w1[0],w1[1])], label='onda 1')\n", " plt.plot(range(w2[0],w2[1]), [L1+rich(L2,a2,b2,t,tp2) for t in range(w2[0],w2[1])], label='onda 2')\n", " plt.plot(range(w3[0],w3[1]), [L2+rich(L3,a3,b3,t,tp3) for t in range(w3[0],w3[1])], label='onda 3')\n", " plt.grid()\n", " plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Encontrando os Parâmetros por otimização" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T12:09:57.464266Z", "start_time": "2021-09-01T12:09:56.584737Z" } }, "outputs": [], "source": [ "import sherpa" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T14:03:09.081814Z", "start_time": "2021-09-01T14:03:05.163633Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied: gpyopt in /home/fccoelho/Downloads/SageMath/local/lib/python3.9/site-packages (1.2.6)\n", "Requirement already satisfied: numpy>=1.7 in /home/fccoelho/Downloads/SageMath/local/lib/python3.9/site-packages (from gpyopt) (1.19.5)\n", "Requirement already satisfied: scipy>=0.16 in /home/fccoelho/Downloads/SageMath/local/lib/python3.9/site-packages (from gpyopt) (1.5.4)\n", "Requirement already satisfied: GPy>=1.8 in /home/fccoelho/Downloads/SageMath/local/lib/python3.9/site-packages (from gpyopt) (1.10.0)\n", "Requirement already satisfied: cython>=0.29 in /home/fccoelho/Downloads/SageMath/local/lib/python3.9/site-packages (from GPy>=1.8->gpyopt) (0.29.21)\n", "Requirement already satisfied: paramz>=0.9.0 in /home/fccoelho/Downloads/SageMath/local/lib/python3.9/site-packages (from GPy>=1.8->gpyopt) (0.9.5)\n", "Requirement already satisfied: six in /home/fccoelho/Downloads/SageMath/local/lib/python3.9/site-packages (from GPy>=1.8->gpyopt) (1.15.0)\n", "Requirement already satisfied: decorator>=4.0.10 in /home/fccoelho/Downloads/SageMath/local/lib/python3.9/site-packages (from paramz>=0.9.0->GPy>=1.8->gpyopt) (4.4.2)\n", "\u001b[33mWARNING: You are using pip version 21.0.1; however, version 21.2.4 is available.\n", "You should consider upgrading via the '/home/fccoelho/Downloads/SageMath/local/bin/python3 -m pip install --upgrade pip' command.\u001b[0m\n" ] } ], "source": [ "!pip install gpyopt" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T13:43:49.736948Z", "start_time": "2021-09-01T13:43:49.720732Z" } }, "outputs": [], "source": [ "parameters = [\n", " sherpa.Discrete(name='L1', range=[.1e6,1e6]),\n", " sherpa.Discrete(name='tp1', range=[10,150]),\n", "# sherpa.Discrete(name='s1', range=[1,180]), #inicio da onda\n", "# sherpa.Discrete(name='d1', range=[10,180]), # duração da onda \n", " sherpa.Continuous(name='a1', range=[0,1]),\n", " sherpa.Continuous(name='b1', range=[0,1]),\n", "]" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T14:17:05.238576Z", "start_time": "2021-09-01T14:17:05.230472Z" } }, "outputs": [], "source": [ "# algorithm = sherpa.algorithms.RandomSearch(max_num_trials=2000)\n", "algorithm = sherpa.algorithms.SuccessiveHalving(max_finished_configs=500)\n", "study = sherpa.Study(parameters=parameters,\n", " algorithm=algorithm,\n", " lower_is_better=True,\n", " disable_dashboard=True)" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T14:17:06.816280Z", "start_time": "2021-09-01T14:17:06.804213Z" } }, "outputs": [ { "data": { "text/plain": [ "{'L1': 257465,\n", " 'tp1': 116,\n", " 'a1': 0.3479896982752564,\n", " 'b1': 0.06494139156730783,\n", " 'resource': 1,\n", " 'rung': 0,\n", " 'load_from': '',\n", " 'save_to': '1'}" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "trial = study.get_suggestion()\n", "trial.parameters" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T14:21:20.061010Z", "start_time": "2021-09-01T14:17:08.111442Z" } }, "outputs": [], "source": [ "s=1\n", "e=160\n", "for trial in study:\n", " L = trial.parameters['L1']\n", " tp = trial.parameters['tp1']\n", " a = trial.parameters['a1']\n", " b = trial.parameters['b1']\n", " dado = df.loc[s:e].total_cases.values\n", " sig = [rich(L,a,b,t,tp) for t in range(s,e)]\n", " \n", " loss = sum((dado[s:e]-sig)**2)/(e-s)\n", " study.add_observation(trial=trial,\n", " objective=loss,\n", " )\n", " study.finalize(trial)" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T14:26:52.048413Z", "start_time": "2021-09-01T14:26:52.042214Z" } }, "outputs": [ { "data": { "text/plain": [ "{'Trial-ID': 5801,\n", " 'Iteration': 1,\n", " 'L1': 280608,\n", " 'a1': 0.298767528283268,\n", " 'b1': 0.056357823970169973,\n", " 'load_from': '',\n", " 'resource': 1,\n", " 'rung': 0,\n", " 'save_to': '5801',\n", " 'tp1': 91,\n", " 'Objective': 152888426.20476854}" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res = study.get_best_result()\n", "res" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T14:26:59.570261Z", "start_time": "2021-09-01T14:26:59.564723Z" } }, "outputs": [], "source": [ "sig = [rich(res['L1'],res['a1'],res['b1'],t,res['tp1']) for t in range(s,e+1)]" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "ExecuteTime": { "end_time": "2021-09-01T14:27:01.992946Z", "start_time": "2021-09-01T14:27:01.741164Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(s,e+1),dado,label='dados')\n", "plt.plot(range(s,e+1),sig, label='richards')\n", "plt.grid()\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.3", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.2" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }