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   "source": [
    "## SIR model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Author*: Simon Frost\n",
    "\n",
    "*Date*: 2018-07-12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Description\n",
    "\n",
    "The susceptible-infected-recovered (SIR) model in a closed population was proposed by Kermack and McKendrick as a special case of a more general model, and forms the framework of many compartmental models. Susceptible individuals, $S$, are infected by infected individuals, $I$, at a per-capita rate $\\beta I$, and infected individuals recover at a per-capita rate $\\gamma$ to become recovered individuals, $R$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{dS(t)}{dt}  = -\\beta S(t) I(t)\\\\\n",
    "\\frac{dI(t)}{dt}  = \\beta S(t) I(t)- \\gamma I(t)\\\\\n",
    "\\frac{dR(t)}{dt}  = \\gamma I(t)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "1. [Kermack WO, McKendrick AG (August 1, 1927). \"A Contribution to the Mathematical Theory of Epidemics\". Proceedings of the Royal Society A. 115 (772): 700–721](https://doi.org/10.1098/rspa.1927.0118)\n",
    "1. [https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology)"
   ]
  }
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