{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Schistosomiasis Vaccine - A Python Notebook" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "In this notebook we are going to try and reproduce results from this recent [paper]( https://parasitesandvectors.biomedcentral.com/articles/10.1186/s13071-017-2227-0) by *Stylianou et al. (2017)*, which models the effect of a partially efficacious schistosomiasis vaccine.\n", "\n", "## Recap:\n", "\n", "Recall from last time we produced a model for the mean worm burden M, and density of juvenile worms in the environement:\n", "\n", "$$\\frac{dM}{d t} = \\beta L(t)\\,d_1 - (\\mu+\\mu_1)M(t)$$ \n", "\n", "$$\\frac{dL}{d t} = sNd_2\\lambda M(t) - (\\mu_2 + \\beta N) L(t)$$\n", "\n", "where,\n", "\n", "* $d_1$ is the death rate of worms in hosts before maturity\n", "* $\\mu$ is the death rate of human hosts\n", "* $\\mu_1$ is the death rate of adult worms\n", "* $\\mu_2$ is the death rate of juvenile worms in the environment\n", "* $\\beta$ is the rate of infection\n", "* $s$ is the proportion of female worms in worm population\n", "* $N$ is the size of the human population\n", "* and $\\lambda = \\lambda(M)$ is the egg output per female worm\n", "\n", "By assuming the density of juvenile worms in the environement is close to its local equilibrium, and that the fecundity and worm mating probabilities are density dependent\n", "\n", "$$\\frac{dM}{d t} =(\\mu+\\mu_1)(R_0 F(M) - 1)M(t)$$\n", "\n", "where $F(M) = f(M)\\phi(M,k)$ with $f(M) = \\left(1+ M(1-z)/k\\right)^{-(k+1)}$ and $\\phi(M,k) = 1 - \\pi M^{1-k}\\left(1 - M/(M+k)\\right)^{1+k}$.\n" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Dynamics without vaccine " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "First lets use Python's handy libraries to solve and plot a few trajectories. We'll use numpy, scipy to integrate the ODE, and pyplot for plotting. Importing seaborn improves the appearance of pyplots plots." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Import the required modules\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "import seaborn as sns\n", "# This makes the plots appear inside the notebook\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "To demonstrate how these functions work, here is a simple example where we are using the libraries to solve the ODE $dy/dx = x - y$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# This defines a function which calculates the derivative\n", "def dy_dx(y, x):\n", " return x - y\n", "\n", "xs = np.linspace(0,5,100)\n", "y0 = 1.0 # the initial condition\n", "ys = odeint(dy_dx, y0, xs) # This function integrates the ODE\n", "ys = np.array(ys).flatten()\n", "\n", "z0 = 2.0 # a different initial condition\n", "zs = odeint(dy_dx, z0, xs) # This function integrates the ODE\n", "zs = np.array(zs).flatten()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the numerical solution\n", "plt.rcParams.update({'font.size': 14}) # increase the font size\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.plot(xs, ys,xs,zs);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "
Question: Can you plot a few trajectories of solutions to the density dependent model above, given the following set of parameters? Can you find (roughly) the critical worm burden under which the worm population dies out?
\n", "\n", "N.B. in Python to raise to the power use ** " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "k = 0.24 # negative binomial aggregation parameter\n", "mu = 1.0/50.0 # human per capita death rate per year\n", "gamma = 0.0007 # density dependent fecundity parameter\n", "beta = 0.63 # rate of contact between human and infective stages\n", "mu1 = 1.0/4.0 # parasite mortality rate\n", "r0 = 3.0 " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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WP4t5JXPdLkcIR0gQXIfdR+UkMq8719tAc6SVBaXzyPIH3S5HCEdIEFyHXbqZ\ngN/HopmlbpciHCJDTotMIEEwSvWtvdS19LJwRgm52eO5z12Mp+qm/QR8ARaWznO7FCEcI0EwStIt\n5H2NvU2c621gfslccgI5bpcjhGMkCEZpp27G7zNYOqfM7VKEQ/Yku4WWydhCwuMkCEahpTPC6YZu\n5k0rJj9HdiB6VXXTPvyGn0VlN7hdihCOkiAYhV1yEpnntURaOdNzDlUym7xgrtvlCOEoCYJR2Hmk\nCcOA5RIEnrWnKXElMukWEplAguAatXX1c+JcF/OmFlOYn+V2OcIhe5r34zN8LC5b4HYpQjhOguAa\n7TzSBMDKeXKBeq9q62/ndNcZ5kyYSUFWvtvlCOE4CYJrtEMnuoVk/4B3DZ5EtqxcuoVEZpAguAZt\nXf2cqOtCVU2QbiEP2924FwODJXI2scgQEgTXYLBbaJV0C3lWa6Sdmq5a5hbPojArs658JTKXBME1\nGOwWWq4kCLxqd9NeAFaUL3G5EiHGjwTBVRraLVQk3UKetbtpHz7Dx5Jy6RYSmUOC4CpJt5D3Nfe1\nUtt9lnnFcygIytFCInNIEFylbYcb8RkGK6RbyLMGu4WWV0i3kMgsEgRXobG9j5r6bm6YLieRedmu\npr0EDD9L5CQykWEkCK7CtkONAKy5ocLlSoRTGnubqOupZ37pXBlbSGQcCYIrsG2btw42Egz4ZGwh\nD9s12C0kRwuJDOTopbWUUmuA/9Bar1dKzQaeBmzgAPCY1tpSSj0B3A/Egce11tudrOla1Tb20NDW\nx0oVliuReZRt2+xo2EPQF2SxDDktMpBjWwRKqc8ATwGDl3b6MvB5rfWtgAE8qJRaDqwD1gCPAF9z\nqp7R2nZ4sFuo0uVKhFNOdZ2hKdLCkvACuRKZyEhOdg2dAN4z5P4K4I3k9IvAXcBaYKPW2tZa1wIB\npVLn2o+WbbPtUCO52QEWzypxuxzhkO0NuwFYXbnc5UqEcIdjfR1a618ppaYPmWVore3kdDdQBBQC\nrUPWGZzffLnnLi7OIxDwj7q2cPjqhg44cKKF9u4B7l49lUkTJ4z69VLB1bbZS66mzXEzzp7mvRTl\nFHLr3OX4faP/vUoF8j57nxPtHc9Ob2vIdAjoALqS05fOv6z29r5RFxEOh2hu7r6qdV/cUgPA4pkl\nV/2YVHQtbfaKq23zvuaDdEd7ub1qLW2to/+9SgXyPnvf9bZ3pBAZz6OG9iil1ien7wM2A1uADUop\nn1JqKuC6Udk1AAAPDUlEQVTTWreMY00jGoiZbD/cSHEom/lTi90uRzhEuoWEGN8tgn8AvqOUygIO\nA89qrU2l1GZgK4lQemwc67ms3bqZ/qjJXSun4PMZbpcjHNAXi7C/9TCV+RVUFUx2uxwhXONoEGit\nTwE3JqePkjhC6NJ1ngSedLKO0di87xwAtyya6HIlwil7mvYRt+KsqViOYUjYi8wlJ5QNo7kjwpHa\nDuZWTaCiOM/tcoRDttbvxMBgZeVSt0sRwlUSBMPYsr8egLWyNeBZ53oaqOk6zfySuZTkyD4gkdkk\nCC5h2TZb9jeQHfSzcl7KnNIgxtib5xInsN8yabXLlQjhPgmCS+jT7bR29bNqXjk5WTKkhBfFzBjb\nGnYRyipgkQwpIYQEwaU27Ut2Cy2WbiGv2tO8n754hJsmrkr7E8iEGAsSBEN09kbZeaSJSWX5zJlS\n5HY5wiFbzm0D4OaJ0i0kBEgQXGRTdR2mZXPH8slyOKFHNfY2cbyjBlU8m3BeqdvlCJESJAiSTMvi\n9epz5GT5uWmBjDTqVVtkJ7EQbyNBkLTnaGKAuVsWTpTrDnhUf3yAN+t3EAoWsDi80O1yhEgZEgRJ\nf9p9FoDbl8tQA171VsNOIvEIt065iaBPwl6IQRIEQF1zD0dqO5g/rZhJZflulyMcYNkWr535MwFf\ngNsm3+R2OUKkFAkC4NXddQDcsXyKy5UIp+xvOUxLpJXVFcsIZRW4XY4QKSXjg6CzZ4A/76unrCiH\npXPkKBKv+tOZTQDcXnWry5UIkXoyPgg27jxD3LS478Zp+H0Z/8/hSbVdZzneUcP8krlMKpAjwoS4\nVEZ/8vX2x3htdx1F+VmsXSQfEF71anJr4A7ZGhBiWBkdBH/adZb+qMk9q6sIXsc1kEXqauhtYlfj\nXiblVzK/ZK7b5QiRkjI2CAaiJi/vPEtedoD1S+WQUa968dQr2NjcP/MeOVtciBFkbBC8sfccPZEY\nd62cIieQedS5ngZ2Ne6lqmASS8oWuF2OECkrI4MgMhDnD2+dJjvo566VVW6XIxzyB9kaEOKqZGQQ\n/HF7LV29UTasrqIgN+h2OcIBpzvOsqdpH1NDU1hYOt/tcoRIaRkXBK2dEV7aXktRfhb3rpnqdjnC\nIb848DwA75StASGuaNw7x5VSu4Gu5N0a4FvA/wPiwEat9T87+fo/+aMmGrN45M4ZcgUyjzrSdowd\ndXuZWTSNG0qU2+UIkfLG9ZNQKZUDGFrr9UPmVQPvBU4CLyillmmt9zjx+nXNPbyy/TQTS/O4Va5A\n5kmmZfLLo7/FwODhuQ/K1oAQV2G8vxIvAfKUUhuTr/0kkK21PgGglPojcBfgSBD8bsspLBsevn22\nnEXsUa+f3UJDXxN3z7qVqSEZO0qIqzHeQdAHfBF4CpgDvAh0DFneDcy80pMUF+cRGMUJYPNmlFJR\nms9dN07PuG+K4XDI7RIc1x7p5MVTr1CQlc8ji95FKDvzBpfLhPf5UpnWZifaO95BcBQ4rrW2gaNK\nqU6gZMjyEBcHw7Da2/tG9eK3L5lIOByiubl7VI9PV5nS5qcP/oJIvJ9H1EOEsgsyos1DZcr7PFSm\ntfl62ztSiIx3/8jHgS8BKKUmAXlAr1JqllLKADYAm8e5JuEBe5sPsKNxN1WhydwyaY3b5QiRVsZ7\ni+C7wNNKqT8DNolgsIBnAD+Jo4a2jXNNIs11DnTxzJFnCfgCfHj+X+AzZP+PENdiXINAax0FPjjM\nohvHsw7hHbZt8+PDv6Q31sf75rxLhpkWYhTkq5NIa5vqtnKoTTO/ZC7rptzsdjlCpCUJApG2ajpP\n8+vjz5MfzOPR+Q9Ll5AQoyR/OSIttUba+Na+H2BaJh+54QNMyC5yuyQh0pYEgUg7kXg/39z3NN2x\nHh6e+yALSmUYCSGuhwSBSCtxK873DjzDud4G1k25RfYLCDEGZNQ1kTZiZoynDvyIQ22aBaXzeO/s\nd7pdkhCeIEEg0kLUjPLt/T/kcNtR5pfM5RMLH8Xvk+tMCzEWJAhEyuuL9fHt/T/kWMdJFpbO5xML\nHyXolwsKCTFWJAhESqvrqefb+39IS6SVpeGFfGzBBwn45NdWiLEkf1EiZe1q3MuPD/+CqBVjw7Q7\neOfMe+RcASEcIEEgUk5PtJdnj/2eHY27yfZn8VeLPszS8EK3yxLCsyQIRMqwbZtdjdX88tjv6In1\nMjU0hY/c8BdU5le4XZoQniZBIFLC0fYT/O7ES9R0nSboC/LQ7Pu5fcpaOTJIiHEgQSBcY9s2R9tP\n8HLt6xxuOwrAkrIFPDT7nYTzSl2uTojMIUEgxl0k3s/OxmreOLuF+t5GAOYVz+GBWRuYXjjV5eqE\nyDwSBGJcRM0oh1o1OxqrOdB6mLgVx2f4WFmxlHVTbmFm0TS3SxQiY0kQCEdYtkV9byO6/TiHWjXH\nOk4St+IAVOaVs7JiGTdNWimjhgqRAiQIxHWzbZvOaBdnuus4013Hqa4znOw8TSQeOb/O5IKJLCid\nx4ryJUwumIhhGC5WLIQYSoJAXLX++ACt/W20RFppibTR2NdMQ28TDX2N9Mb6Llo3nFvKkrIFzJ4w\ng/mlc+WbvxApTIIgg9m2TcyK0Rvroy8eoTvaQ0+sl55oL13Rbrqi3XRGu+jo76R9oPOib/iDDAzC\nuaXMLppBVWhy8mcKRdkhF1okhBgNCYIUZdkWpm1hWnHitolpmcSteOLHNolZMWJm4n7UiiXvx4ha\nMaJmlKgZZcCKMmBG8Z2w6eztIWIOMBAfIGJGiMT6icQjxG3zirXk+HMoziliRuFUSnImUJZbSji3\nlHBeGeW5ZTIAnBBpLiWCQCnlA74OLAEGgE9orY+P9esc76jh5fqT9PYOYA/+ZyduscHChuQ8a3CZ\nffF6lm1jYw1Zxzo/z7JtLDu5zLawhsxLzE98uA/eN20z8WFvm1jW4H3z/DpOCPoC5ARyyAvmUpJb\nTH4gj7xgLnmBPAqCeRRkFVAQzKcwK0RRdojCrEJyAtmO1CKESA0pEQTAu4EcrfVNSqkbgS8BD471\ni9T86DtUHqrHNkj8ALZhXLhvgGUAGOenE/ONi5YP95jBeW9b7jOS9w3wGTDk1vb5wDAwfD7w+ZLz\nfRh+H4YRxPD5MPx+DJ8Pn8+P4fPj8/vx+fz4/AH8fj8+XwC/P4A/eRvwBwkEggR8QYLBIEF/FiXF\nhfRHbLL92fj8/guvaSRfb7Auw8CwfRA3wDQw+mNgtBM1SKxnGGCQWJchj3nbvESXEYM7hAcfx5D1\nh12emH/RjuSrmJYdz0Jcn1QJgrXASwBa67eUUiudeJHFs26kp20rZtwC2wbLwrAB2wLLTsxLzse2\nwbQTy2wb2xqcb11YbttOlDlm4smfOrcLccHRwYmRQmKkgBnBmIXN9T7PZR5/nMSXm0xy3DCwU/zv\ncCydCoWY/JnPESwtG9PnTZUgKAQ6h9w3lVIBrXV8uJWLi/MIBK59DJrwR/4SPvKXoyzx7exkaNiD\nP6Z1/j720PnmReuN9JhLlw07bQ6zzB46z04G18XrMdjNZZrnQ+zi+RaJ/rHkfC6EX+IPbXCaZAAm\nl2NfCMpkF9v55UOmE6tdbh0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# DEFINE A FUNCTION THAT CALCULATES THE DERIVATIVE\n", "\n", "def f(m):\n", " return (1.0 + m*(1.0-np.exp(-1.0*gamma))/k)**(-k-1.0)\n", "\n", "def phi(m):\n", " return 1.0 - (1.0-(m/(m+k))**(1.0+k))*(np.pi * m**0.75)\n", "\n", "def dm_dt(m,t):\n", " # YOUR CODE HERE\n", " return (mu+mu1)*(r0*phi(m)*f(m) - 1.0)*m\n", "\n", "\n", "# SOLVE THE ODE WITH DIFFERENT INITIAL CONDITIONS AND PLOT THE RESULTS\n", "\n", "ts = np.linspace(0,100,100)\n", "m0 = 50.0 # the initial condition\n", "ms1 = odeint(dm_dt, m0,ts)\n", "ms1 = np.array(ms1).flatten()\n", "\n", "m0 = 3.0 # the initial condition\n", "ms2 = odeint(dm_dt, m0,ts)\n", "ms2 = np.array(ms2).flatten()\n", "\n", "m0 = 2.0 # the initial condition\n", "ms3 = odeint(dm_dt, m0,ts)\n", "ms3 = np.array(ms3).flatten()\n", "\n", "# Plot the numerical solution\n", "plt.rcParams.update({'font.size': 14}) # increase the font size\n", "plt.xlabel(\"t\")\n", "plt.ylabel(\"M\")\n", "plt.plot(ts, ms1,ts,ms2,ts,ms3);" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Great, now lets consider how a vaccine will work" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "A vaccine for schistosomiasis has the potential to work in 3 different ways.\n", "\n", "1. It could increase the per capital mortility rate of the adult worms $\\sigma$.\n", "\n", "2. It may decrease the number of eggs produced by female worms $\\lambda$.\n", "\n", "3. It could decrease the rate at which juvenile worms are able to infect hosts $\\beta$.\n", "\n", "Lets denote the efficacy of tha vaccine of doing these three things $\\nu_1$, $\\nu_2$ and $\\nu_3\\in[0,1]$, so that once a vaccine has been administered the rates $\\sigma$, $\\lambda$ and $\\beta$ become\n", "\n", "$$\\sigma' = \\left(\\dfrac{1}{1-\\nu_1}\\right)\\sigma$$\n", "\n", "$$\\lambda' = (1-\\nu_2)\\,\\lambda$$\n", "\n", "$$\\beta' = (1-\\nu_3)\\,\\beta$$\n", "\n", "Individuals in the population will either be vaccinated, or not vaccinated. Lets denote the number of people in the vaccinated population $N_v$ and the number in the non-vaccinated group $N_u$, so that $N_u +N_v = N$.\n", "\n", "Lets now suppose that we vaccinate non-vaccinated people with per capita rate $q$ per year.\n", "The protection from a vaccine will eventually wear off, so lets say that immunity is lost with rate $\\omega$. Therefore\n", "\n", "$$\\dfrac{dN_u}{dt} = -qN_u + \\omega N_v -\\mu N_u $$\n", "\n", "$$\\dfrac{dN_v}{dt} = qN_u - \\omega N_v - \\mu N_v$$\n", "\n", "With the initial conditions,$N_v(0) = p$, $N_u(0) = 1 - p$, can you solve the system?\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": true, "editable": true }, "source": [ "In their paper, Stylianou et al looked at two vaccination frameworks.\n", "\n", "#### 1. Vaccination of a proportion p of infants\n", "\n", "$q=0$, $N_v(0) = p>0$\n", "\n", "#### 2. Vaccination of the general public at a per capita rate q\n", "\n", "$p=0$, $q>0$\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": true, "editable": true }, "source": [ "## Model without density dependence\n", "\n", "We are following the Stylianou [paper]( https://parasitesandvectors.biomedcentral.com/articles/10.1186/s13071-017-2227-0), so lets go along with their model and terminology. This means $\\mu_1\\rightarrow\\sigma$, $sNd_2\\rightarrow\\psi$ and $\\beta N$ is now small enough to ignore.\n", "\n", "The dynamics of the worm burden within the unvaccinated and unvaccinated groups, and size of the environmental reservoir of worms are given by\n", "\n", "$$\\frac{dM_u}{d t} = \\beta_u L(t) - (\\mu+\\sigma)M_u(t) - qM_u(t)+\\omega M_v(t)$$\n", "\n", "$$\\frac{dM_u}{d t} = \\beta_v L(t) - (\\mu+\\sigma')M_u(t) + qM_v(t)-\\omega M_u(t)$$\n", "\n", "$$\\frac{dL}{d t} = \\psi\\left(\\lambda M_u(t)+\\lambda'M_v(t)\\right) - \n", "\\mu_2 L(t)$$\n", "\n", "where $\\beta_u = \\int\\limits_{t=0}^{\\infty}\\beta N_u(t)\\, dt=\\dfrac{\\beta(\\mu+\\omega-p\\mu)}{\\mu(\\omega+q+\\mu)}$ is the average contact of the unvaccinated population\n", "\n", "and $\\beta_v = \\int\\limits_{t=0}^{\\infty}\\beta' N_v(t)\\, dt=\\dfrac{\\beta'(q+p\\mu)}{\\mu(\\omega+q+\\mu)}$ is the average contact of the vaccinated population" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "deletable": true, "editable": true }, "source": [ "## Effective reproduction number\n", "\n", "Recall from the first lecture that $R_0$, which is the number of female offspring produced per female worm that survives to reproductive immunity, determines the long term behaviour of the model without density dependence (and vaccination) and is given by\n", "\n", "$$R_0 = \\dfrac{\\psi\\lambda\\beta}{\\mu_2(\\mu+\\sigma)}$$.\n", "\n", "\n", "
Questions:
\n", "\n", "We will now see how the vaccination model affects this.

\n", "\n", "1. If we put $n$ worms into the environment, how many will establish? And what proportion go into the vaccinated/unvaccinated popuation?

\n", "\n", "2. Now we're going to consider the eggs produced worms during their life time, which depends on the vaccination status of the hosts. During their lifetime, the number of worms status of host will be given by the equation
\n", "
\n", "$$\\frac{d}{d t}\\left(\\begin{array}{c}M_u\\\\M_v\\end{array} \\right) = \\begin{pmatrix} -\\mu_u & \\omega \\\\ q & -\\mu_v \\end{pmatrix}\\left(\\begin{array}{c}M_u\\\\M_v\\end{array} \\right) = \\boldsymbol{M}\\left(\\begin{array}{c}M_u\\\\M_v\\end{array} \\right)$$
\n", "\n", "where $\\mu_u = (\\mu+\\sigma+q)$, $\\mu_v =(\\mu+\\sigma'+\\omega)$.\n", "Find the eigenvalues and eigenvectors of $\\textbf{M}$ and express it using its eigen-decomposition.

\n", "\n", "3. If the egg production of a female worm during its two states is $\\Lambda = (\\lambda_u,\\lambda_v)$, the contribution off eggs from an infected worm durings its life, Q, will be

\n", "\n", "$$ Q = \\psi\\int\\limits_{t=0}^{\\infty}\\Lambda\\cdot\\left(\\begin{array}{c}M_u\\\\M_v\\end{array} \\right)(t)\\,dt$$

\n", "\n", "Show that $$Q = -\\psi\\Lambda \\boldsymbol{M}^{-1}\\Pi$$

\n", "\n", "where $\\Pi$ are the initial conditions of $(M_u,M_v)$, and hence show

\n", "\n", "$$R_e = -\\frac{\\psi}{\\mu_2}\\lambda\\boldsymbol{M}^{-1}\\boldsymbol{b}$$\n", "\n", "where $\\boldsymbol{b}=(\\beta_u,\\beta_v)$\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Model with density dependence\n", "\n", "As in the previous lecture, we'll now consider the effect of the density dependent fecundity, and mating probabilities when the underlying distribution of worms is a negative-binomial with mean $M$ and aggregation $k$.\n", "\n", "This means that female worm fecundity is replaced by $\\lambda\\rightarrow\\lambda F(M)$, with $F(M) = f(M)\\,\\phi(M,k)$ where\n", "\n", "$$f(M) = \\left(1+ M(1-z)/k\\right)^{-(k+1)}$$\n", "\n", "$$\\phi(M,k) = 1 - \\pi M^{1-k}\\left(1 - M/(M+k)\\right)^{1+k}$$\n", "\n", "Because the timescales determining dynamics of worms in the environment are a lot smaller than those of adult worms, we can set $L$ to be at its local equilibrium.\n", "\n", "$$L(t) = \\psi\\left(\\lambda F(M_u) M_u(t) + \\lambda'F(M_v)M_v\\right)/\\mu_2$$\n", "\n", "which we sub into\n", "\n", "$$\\frac{dM_u}{d t} = \\beta_u L(t) - (\\mu+\\sigma)M_u(t) - qM_u(t)+\\omega M_v(t)$$\n", "\n", "$$\\frac{dM_v}{d t} = \\beta_v L(t) - (\\mu+\\sigma')M_v(t) + qM_v(t)-\\omega M_u(t)$$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "In this workbook we are just going to focus on **Strategy 1**, vaccinating infants ($q=0$, $p\\in[0,1]$). These are the model parameters which have been found from emperical data\n", " " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "mu = 1.0/50.0 \n", "sigma = 1.0/4.0\n", "mu2 = 365.0/7.0\n", "lamb = 0.14\n", "beta = 0.63\n", "k = 0.24\n", "gamma = 0.0006" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We get to choose R0, which sets the parameter $\\psi$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "R0 = 3.0\n", "psi = R0*mu2*(mu+sigma)/(lamb*beta) " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Here we define the parameters that set the vaccine performance:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "omega = 0.0 # rate that vaccine wears off, average protection duration is 1/omega\n", "p = 0.8 # proportion of people receiving vaccination at birth\n", "q = 0.0 # rate of general public being vaccinated \n", "\n", "n1 = 0.0 # vaccine death rate efficacy \n", "n2 = 0.0 # vaccine anti-fecundity efficacy\n", "n3 = 0.9 # vaccine infection protection efficacy\n", "\n", "sigma2 = sigma * 1.0/(1.0-n1)\n", "lamb2 = lamb*(1-n2)\n", "beta2 = beta*(1.0-n3)\n", "\n", "beta_u = beta*(mu+omega-p*mu)/((omega+q+mu))\n", "beta_v = beta2*(q+p*mu)/((omega+q+mu))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "
Question:
\n", " Can you plot a trajectories of the overall mean prevalence $M$?\n", "
\n", "[Hint: $M = \\left(1-p\\right)M_u + pM_v$]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "#Here are the density dependent function all set up \n", "\n", "def f(m):\n", " return (1.0 + m*(1.0-np.exp(-1.0*gamma))/k)**(-k-1.0)\n", "\n", "def phi(m):\n", " return 1.0- 2.0*np.pi*m*(1.0 - m/(m+k))**(1.0+k)\n", "\n", "def phi(m):\n", " return 1.0 - (1.0-(m/(m+k))**(1.0+k))*(np.pi * m**0.75)\n", "\n", "# YOUR CODE HERE\n", "\n", "def derivative(M, t, r0,p,omega):\n", " \n", " beta_u = beta*(mu+omega-p*mu)/(omega+q+mu)\n", " beta_v = beta2*(q+p*mu)/(omega+q+mu)\n", " psi = r0*mu2*(mu+sigma)/(lamb*beta) \n", " M_u, M_v = M\n", " L = psi*(lamb*f(M_u)*phi(M_u)*M_u + lamb2*f(M_v)*phi(M_v)*M_v )/mu2\n", " dMdt = [beta_u*L - (mu+sigma)*M_u - q*M_u + omega*M_v, beta_v*L - (mu+sigma2)*M_v + q*M_u - omega*M_v]\n", " return dMdt" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "M0 = [100.0,100.0]\n", "t = np.linspace(0, 100, 1000)\n", "sol = odeint(derivative, M0, t,args=(3.0,p,0.0))\n", "m = (1.0-p)*sol[:, 0] + p*sol[:, 1]\n", "\n", "plt.plot(t,m)\n", "plt.ylim((-1,101))\n", "plt.xlim((-3,50))\n", "plt.xlabel('Years')\n", "plt.ylabel('Mean worm burden')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "If you experiment a bit with varying the proportion of infants vaccinated, you will find that for low levels of vaccine coverage $p$, M will reach a lower equilibrium mean worm burden $M^*>0$, and for higher levels of coverage the mean worm burden decays to zero. This suggests that there will be a critical level of coverage $p_c$ that above which, the disease is eliminated." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "
Question:
\n", " Write some code that finds this critical level of coverage for a given basic reproduction number $R_0$, and plot $R_0$ against $p_c$.\n", "
" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "def find_critical_p(r0):\n", " # YOUR CODE HERE\n", " end = 100\n", " p = 0.0\n", " while ((end > 0.001)&(p<1)):\n", " p+=0.01\n", " sol = odeint(derivative, M0, t,args=(r0,p,0.00))\n", " m = (1.0-p)*sol[:, 0] + p*sol[:, 1]\n", " end = m[-1]\n", " return p\n", " " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/Ben/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:10: RuntimeWarning: invalid value encountered in double_scalars\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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TXZCyQrDyBikrBCtvkLKCN3m9LIBmIDFxZt/Ov4+Zfc05903gF865jWa2ZaA3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\nACIiaUoFICKSplQAIiJp6v8DCOGkNPhpf1EAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rs = np.linspace(1, 8, 50)\n", "ps = [find_critical_p(r) for r in rs]\n", "plt.plot(rs,ps)\n", "plt.xlabel('R_0')\n", "plt.ylabel('p_c')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "
Question:
\n", " Real vaccines do not give a life-long protection, can you find the critical coverage as both a function of $R_0$ and $\\omega$?, and plot this as a surface?\n", "
" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Hint: here is an example some python code that produces a 3D surface plot" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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HmUAc38d4MsVRcMd9TCKLdV+05gUQmU6/81YiER9HfhCvOgqappJKJUmlkrdt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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits import mplot3d\n", "\n", "def g(x, y):\n", " return np.sin(np.sqrt(x ** 2 + y ** 2))\n", "\n", "xs = np.linspace(-6, 6, 50)\n", "ys = np.linspace(-6, 6, 30)\n", "\n", "X, Y = np.meshgrid(xs, ys)\n", "Z = [[g(x,y) for x in xs] for y in ys]\n", "\n", "fig = plt.figure()\n", "ax = plt.axes(projection='3d')\n", "ax.plot_surface(X, Y, Z, lw=0.5, rstride=1, cstride=1)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')\n", "ax.set_zlabel('z');\n", "ax.view_init(60, 235)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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9OiOSo+MTzIqJRx64Tvgg0pXgF9AsibHjBD6vi6DfgySJfOO5xa4t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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rs = np.linspace(1, 3, 10)\n", "taus = np.linspace(10,20,10) # Duration of vaccine tau = 1/omega\n", "\n", "def find_critical_p(r0,w):\n", " # YOUR CODE HERE\n", " end = 100\n", " p = 0.0\n", " while ((end > 0.001)&(p<1.0)):\n", " p+=0.01\n", " sol = odeint(derivative, M0, t,args=(r0,p,w))\n", " m = (1.0-p)*sol[:, 0] + p*sol[:, 1]\n", " end = m[-1]\n", " return p\n", " \n", "Rs, Taus = np.meshgrid(rs, taus)\n", "Ps = [[find_critical_p(r,1.0/tau) for r in rs] for tau in taus]\n", "\n", "fig = plt.figure()\n", "ax = plt.axes(projection='3d')\n", "ax.plot_surface(Rs, Taus, Ps, lw=0.5, rstride=1, cstride=1)\n", "ax.view_init(30, 235)\n", "ax.set_xlabel('R0')\n", "ax.set_ylabel('Tau')\n", "ax.set_zlabel('p_c');" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 2 }