{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Epidemics on networks" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On this lab we will consider an implementation of disease spreading over a network. We will start from SIS model and slightly modify it to SIR model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SIS model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just to recall from the lecture how it looks like:\n", "\\begin{equation}\n", " \\begin{cases}\n", " \\cfrac{ds_i(t)}{dt} = -\\beta s_i(t)\\sum\\limits_j A_{ij}x_j(t) + \\gamma x_i(t)\\\\\n", " \\cfrac{dx_i(t)}{dt} = \\beta s_i(t)\\sum\\limits_j A_{ij}x_j(t) - \\gamma x_i(t)\n", " \\end{cases}\n", " \\\\\n", " x_i(t) + s_i(t) = 1\n", "\\end{equation}\n", "where $x_i(t)$ and $s_i(t)$ are probabilities for a node $v_i$ to be infected or susceptable." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "from numpy.linalg import eig\n", "from scipy.integrate import odeint\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Let's start from a complete graph\n", "n = 50\n", "G = nx.watts_strogatz_graph(n, 5, 0.4)\n", "\n", "# Get adj. matrix\n", "A = np.array(nx.adjacency_matrix(G).todense())\n", "\n", "# Spreading\\restoring coefficient\n", "beta, gamma = 0.03, 0.2\n", "\n", "# Time domain\n", "t = np.arange(0,5,0.05)\n", "\n", "# Initial state\n", "idx = np.random.choice(range(n), 5)\n", "i0 = np.zeros((n,))\n", "i0[idx] = 1\n", "# i0 = np.random.random_integers(0,1,[n,])\n", "z0 = np.concatenate((1-i0,i0))\n", "\n", "# System of differential equations..\n", "def sis(z, t, A, n, beta, gamma):\n", " return np.concatenate((\n", " -beta * z[0:n] * A.dot(z[n:2*n]) + gamma * z[n:2*n],\n", " beta * z[0:n] * A.dot(z[n:2*n]) - gamma * z[n:2*n]))\n", " \n", "\n", "# ..Solved\n", "z = odeint(sis, z0, t, (A, n, beta, gamma))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(20, 100)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# It's a bit messy, so let's see what we have got here\n", "z.shape" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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BNk9Dhvh2XkIIIUQdRcJMsKT36NHAgQNcbt8eWLEC6NvXt/MSQggh6hgK/hfs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\niISN3mblB8XFDGRmHLKEBOAPfwBmzGA4ExERkfBSMBOUlgIXXeSO1B8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot probs for some node\n", "nId = 6\n", "s = z[:,0:n]\n", "x = z[:,n:2*n]\n", "\n", "\n", "fig, ax = plt.subplots(1,1,figsize=(10,6))\n", "ax.plot(s,color = 'blue')\n", "ax.plot(x,color = 'red')\n", "ax.set_xlabel('$t$')\n", "ax.set_ylabel('prob')\n", "ax.set_title('Probability for all nodes', fontsize = 15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hope that you remember that stuff about the correspondence between largest eigenvalue and $\\frac{\\gamma}{\\beta}$ ratio:
\n", "* if $\\lambda_1 > \\frac{\\gamma}{\\beta}$ - GROWTH\n", "* if $\\lambda_1 < \\frac{\\gamma}{\\beta}$ - NOPE
\n", "Check it" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.47087231 0.666666666667\n" ] } ], "source": [ "w,v = eig(A)\n", "print max(w), gamma/beta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Play with $\\gamma$, $\\beta$ parameters and try out SIS model for other graphs\n", "2. Does it matter how many nodes are initially infected?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SIR model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In SIR model healed population gain immunity to the infection\n", "\\begin{equation}\n", " \\begin{cases}\n", " \\cfrac{ds_i(t)}{dt} = -\\beta s_i(t)\\sum\\limits_j A_{ij} x_j(t)\\\\\n", " \\cfrac{dx_i(t)}{dt} = \\beta s_i(t)\\sum\\limits_j A_{ij} x_j(t) - \\gamma x_i(t)\\\\\n", " \\cfrac{dr_i(t)}{dt} = \\gamma x_i(t)\n", " \\end{cases}\n", " \\\\\n", " x_i(t) + s_i(t) + r_i(t) = 1\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adapt the code above to produce SIR model" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Let's start from a complete graph\n", "n = 50\n", "G = nx.barabasi_albert_graph(n, 5)\n", "\n", "# Get adj. matrix\n", "A = np.array(nx.adj_matrix(G))\n", "\n", "# Spreading\\restoring coefficient\n", "beta, gamma = 0.3, 0.2\n", "\n", "# Time domain\n", "t = np.arange(0,5,0.05)\n", "\n", "# Initial state\n", "idx = np.random.choice(range(n), 30)\n", "i0 = np.zeros((n,))\n", "i0[idx] = 1\n", "# i0 = np.random.random_integers(0,1,[n,])\n", "z0 = np.concatenate((1-i0,i0,np.zeros((n,))))\n", "\n", "# System of differential equations..\n", "def sir(z, t, A, n, beta, gamma):\n", " return np.concatenate((\n", " -beta * z[0:n] * A.dot(z[n:2*n]),\n", " beta * z[0:n] * A.dot(z[n:2*n]) - gamma * z[n:2*n],\n", " gamma * z[n:2*n]\n", " ))\n", " \n", "\n", "# ..Solved\n", "z = odeint(sir, z0, t, (A, n, beta, gamma))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(20, 150)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "z.shape" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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R+HiqaHd3bh8VxZTfLl04+Nu20axqNNKCFxjIh6F3b16T9FIVBEEQHgJPunBr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\ndr6Mt1LeYsOpDVS3VANgrjJnhMsIHhr3EGMHjiWhIIENORtIPZOKhYkF7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olOTxrXHV/H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eyU7sxf8PmL5oetnB7f+MfrXzHeeJzY9l6+mtJBQmMNx5OAv8FzDfbz5e/b16rG3ubCa+IJ6t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\n0MY3OKXthubi+bL1Th+joiJhw5QUAZYTJyoG1ZbXihXiFJ0/Lz9/+01O6+/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Pyk0qnQpN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\nhTtWl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RfX4u2jb6OgsQALByzEggEL0MWnCwBgW+E2PL/1eeTV50GChB6BPfCXrL/AITvw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\nKb/P5GSjOTAdXZf2p4mToabBJtZwxNu0D8jJk80n9rIr9PQknJ6c0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot probs for some node\n", "nId = 6\n", "s = z[:,0:n]\n", "x = z[:,n:2*n]\n", "r = z[:,2*n:3*n]\n", "\n", "\n", "fig, ax = plt.subplots(1,1,figsize=(10,6))\n", "ax.plot(s,color = 'blue')\n", "ax.plot(x,color = 'red')\n", "ax.plot(r,color = 'green')\n", "ax.set_xlabel('$t$')\n", "ax.set_ylabel('prob')\n", "ax.set_title('Probability for all nodes', fontsize = 15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stochastic Modelling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The stuff that you will see below is kind of simulation model of infection spreading on graph. The description of the model is the following:
\n", "\n", "* The infection has some vital period, the node is diseased for that period\n", "* At the end of this period node become susceptible without immunity system's reinforcement\n", "* Each infected node can spread disease within its neigbours with a sertain probability" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Dhw/RuHFjiEQinDlzBuXKlRM6Ur6qV6+Obdu24fz583j06BEqV66MGTNmIJ5XSmJawsWX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\nUYMpU6bw3Xff4evrS7NmzXjppZc4cuSIq0sjOzubN954g0G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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "size = 4\n", "# Create Grid Graph\n", "G = nx.grid_2d_graph(size,size)\n", "\n", "# Make node relabelling\n", "f = {}\n", "for v in G.nodes_iter():\n", " f[v] = v[0]*size+v[1]\n", "\n", "G = nx.relabel_nodes(G, f)\n", "nx.draw_spectral(G)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def simulSIS(A, timePeriod, modelParams):\n", " # init params\n", " initInfected = modelParams.get('initInfected', None)\n", " p = modelParams.get('probInfect', 0.5)\n", " upd = modelParams.get('updateInfection', True)\n", " maxRecTime = modelParams.get('t2Recover', 2)\n", " \n", " # init output\n", " n = A.shape[0]\n", " states = np.zeros([n, timePeriod+1]) # 1 = infected, 0 = susceptable\n", " recTime = np.zeros(n,)\n", " # set initially infected nodes\n", " if initInfected is None:\n", " initInfected = np.random.choice(range(n), n/2)\n", " states[initInfected,0] = 1\n", " else:\n", " states[initInfected,0] = 1\n", " recTime[initInfected] = maxRecTime + 1\n", " \n", " # Start simulation\n", " for t in xrange(1, timePeriod+1):\n", " recTime = np.maximum(recTime-1,0)\n", " states[recTime>0, t] = 1\n", " states[recTime==0, t] = 0\n", " \n", " curInf = np.nonzero(states[:,t])[0]\n", " states[curInf, t] = 1\n", " for i in curInf:\n", " #NN = np.setdiff1d(np.nonzero(A[i,])[0], curInf)\n", " NN = np.nonzero(A[i,])[0]\n", " infNN = NN[np.random.rand(len(NN))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plotting inferction spread\n", "\n", "pos = nx.spectral_layout(G)\n", "fig = plt.figure(figsize=(15,10))\n", "for t in xrange(0,timePeriod+1):\n", " plt.subplot(3,4,t+1)\n", " nx.draw_spectral(G,\n", " nodelist=np.nonzero(states[:,t])[0].tolist(),\n", " node_color = 'r')\n", " nx.draw_spectral(G,\n", " nodelist=np.nonzero(1-states[:,t])[0].tolist(),\n", " node_color = 'b')\n", " plt.title('t = {0}'.format(t+1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The branching process" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In simple branchin process (tree of depth $h$ with $k$ leaths per each parent and probability $p$ to infect a neigbour) we are considerring $R_0=pk$ - the basic reproductive number of the infection.
\n", "* If $R_0 < 1$ infection will stop without reaching the bottom of the tree\n", "* If $R_0 > 1$ infertion will corrupt all population" ] }, { "cell_type": "code", "execution_count": 159, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1., 3., 5., 6., 5., 2., 0., 0., 0., 0., 0.])" ] }, "execution_count": 159, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## Checking of branching branching process\n", "\n", "G=nx.balanced_tree(3,7, create_using=nx.DiGraph())\n", "sp = nx.shortest_path_length(G,0)\n", "\n", "timePeriod = 10\n", "modelParams = {}\n", "modelParams['t2Recover'] = 1\n", "modelParams['initInfected'] = [0]\n", "modelParams['probInfect'] = 0.2\n", "modelParams['updateInfection'] = False\n", "\n", "A = np.array(nx.adj_matrix(G))\n", "\n", "states = simulSIS(A, timePeriod, modelParams)\n", "sum(states)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }