ch05/complete_cross_immunity/Complete cross-immunity.ipynb

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    "| **Chapter**                   | 5:  Multi-pathogen dynamics                           |\n",
    "| ----------------------------- | ----------------------------------------------------- |\n",
    "| **Computational Note**        | 5.x: Complete cross-immunity                          |\n",
    "| **Package prerequisites**     | None                                                  |\n",
    "\n",
    "\n",
    "# Complete cross-immunity"
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   "source": [
    "## Two-pathogen cross-immunity\n",
    "\n",
    "The two-pathogen model is governed by the following system of ODEs:"
   ],
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    "\\begin{equation}\n",
    "        \\frac{dS}{dt} =    - \\beta_a S I_a - \\beta_b S I_b + \\nu\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "        \\frac{dI_a}{dt} =    \\beta_a S I_a - \\gamma_a I_a - \\mu I_a\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "        \\frac{dI_b}{dt} =    \\beta_b S I_b - \\gamma_b I_b - \\mu I_b\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "        \\frac{dR}{dt} =    \\gamma_a I_a + \\gamma_b I_b - \\mu R\n",
    "\\end{equation}"
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    "We assume a constant population with a turnover rate of $\\mu = \\nu = 10^{-4}$ persons per day and the following pathogenic parameters:\n",
    "\n",
    "|  | $\\beta$      | $\\gamma$       | $\\mathfrak{R}_0$ |\n",
    "|----------|-----------|-----------|----|\n",
    "| $a$  | 1.5 | 1 | 1.5 |\n",
    "| $b$  | 0.4 | 0.2 | 2 |"
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   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "COLORS = {\"S\": \"#2f4b7c\",\n",
    "          \"E\": \"#ffa600\",\n",
    "          \"I\": \"#f95d6a\",\n",
    "          \"R\": \"#a05195\",\n",
    "          \"D\": \"#003f5c\",\n",
    "          \"C\": \"#ff7c43\",\n",
    "          \"X\": \"#665191\",\n",
    "          \"Y\": \"#d45087\"}"
   ],
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   "source": [
    "def deriv(t, y, beta, gamma, mu, nu):\n",
    "\n",
    "    S = y[0]\n",
    "    I = y[1:].T.flatten()\n",
    "\n",
    "    dSdt  = - (beta * S).dot(I) + nu\n",
    "    dIdt = beta * S * I - gamma * I - mu * I\n",
    "\n",
    "    return dSdt, *dIdt"
   ],
   "execution_count": 2,
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   "source": [
    "I_0 = np.array([1e-6, 1e-6])\n",
    "S_0 = 1 - I_0.sum()\n",
    "\n",
    "y_0 = np.array([S_0, *I_0])\n",
    "\n",
    "beta = np.array([1.5, 0.4])\n",
    "gamma = np.array([1.0, 0.2])\n",
    "\n",
    "mu, nu = 1e-4, 1e-4"
   ],
   "execution_count": 3,
   "outputs": [],
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   "source": [
    "res = solve_ivp(fun=deriv, t_span = (0, 100), y0=y_0, args=(beta, gamma, mu, nu), max_step=1)"
   ],
   "execution_count": 4,
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    "_, Ia, Ib = res.y\n",
    "\n",
    "fig = plt.figure(facecolor=\"w\", figsize=(6, 4), dpi=600)\n",
    "ax = fig.add_subplot(111, axisbelow=True)\n",
    "\n",
    "ax.plot(res.t, Ia, color=COLORS[\"D\"], alpha=0.5, lw=2, linestyle=\":\", label=\"Pathogen 1 ($\\mathfrak{R}_0 = 1.5$)\")\n",
    "ax.plot(res.t, Ib, color=COLORS[\"I\"], alpha=0.5, lw=2, label=\"Pathogen 2 ($\\mathfrak{R}_0 = 2.0$)\")\n",
    "\n",
    "\n",
    "# ax.fill_between(res.t, 0, S, color=COLORS[\"S\"], alpha=0.15)\n",
    "# ax.fill_between(res.t, 0, I, color=COLORS[\"I\"], alpha=0.15)\n",
    "# ax.fill_between(res.t, D, R + D, color=COLORS[\"R\"], alpha=0.15, label=\"Recovered\")\n",
    "# ax.fill_between(res.t, 0, D, color=COLORS[\"D\"], alpha=0.15, label=\"Deceased\")\n",
    "\n",
    "ax.set_xlabel('Time (days)')\n",
    "ax.set_ylabel(\"Fraction of infectious population\")\n",
    "# ax.set_ylim(0, 1.0)\n",
    "ax.set_yscale(\"log\")\n",
    "ax.grid(b=True, which='major', c='w', lw=2, ls='-')\n",
    "\n",
    "for spine in (\"top\", \"right\"):\n",
    "    ax.spines[spine].set_visible(False)\n",
    "\n",
    "legend = ax.legend()\n",
    "legend.get_frame().set_alpha(0.5)\n",
    "plt.legend(title='', bbox_to_anchor=(0.5, -0.3), loc=\"lower center\", ncol=2, frameon=False)\n",
    "\n",
    "fig.subplots_adjust(bottom=0.25)\n",
    "\n",
    "plt.savefig(\"complete_cross_immunity.pdf\")\n",
    "plt.show()"
   ],
   "execution_count": 6,
   "outputs": [
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      "/var/folders/1d/97x3559931s0_6hkz64q4zth0000gn/T/ipykernel_26308/324275890.py:19: MatplotlibDeprecationWarning: The 'b' parameter of grid() has been renamed 'visible' since Matplotlib 3.5; support for the old name will be dropped two minor releases later.\n",
      "  ax.grid(b=True, which='major', c='w', lw=2, ls='-')\n"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "metadata": {
    "datalore": {
     "type": "CODE",
     "hide_input_from_viewers": false,
     "hide_output_from_viewers": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
 ],
 "metadata": {
  "datalore": {
   "version": 1,
   "computation_mode": "JUPYTER",
   "package_manager": "pip",
   "base_environment": "default",
   "packages": [
    {
     "name": "sympy",
     "version": "1.8",
     "source": "PIP"
    }
   ]
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}