Interactive_SIR_model.ipynb

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    "The graphic below allows you to model the spread of COVID-19 using the SIR model.  This is a very simple model but has proven surprisingly effective; see [my series of blog posts on the topic](http://davidketcheson.info).  This graphic is meant for educational purposes only and of course I make no guarantees about its ability to forecast real-world infections.\n",
    "\n",
    "**To start the model, click on the computer code below and hit shift+Enter**.\n",
    "\n",
    "The initial conditions for the model are taken from the [JHU CSSE data set](https://github.com/CSSEGISandData/COVID-19) that is updated daily.  For a description of the parameters $\\beta$ and $\\gamma$, see my blog posts, [starting here](http://www.davidketcheson.info/2020/03/17/SIR_model.html).  The other parameters you can adjust are:\n",
    "\n",
    "  - **% of cases confirmed**: The fraction of actual infected individuals that get tested and reported.\n",
    "  - **% of cases critical**: The fraction of actual infected individuals that require critical medical attention.\n",
    "  - **% of cases fatal**: The fraction of actual infected individuals that die from the infection or secondary infections.\n",
    "  - **Use mitigation**: If checked, the model incorporates attempts to reduce the spread of the disease.  This represents the effect of quarantines, closures, etc.\n",
    "  - **Mitigation factor**: If mitigation is enabled, then during the mitigation period the contact rate $\\beta$ is multiplied by this factor.  Corresponds to $q(t)$ in [this blog post](http://www.davidketcheson.info/2020/03/19/SIR_predictions.html).  For instance, a mitigation factor of 0.5 would mean that human contact has been reduced by half.  Of course, this is a very simplified model for mitigation.  In reality, the measures implemented and their effectiveness will vary significantly over time.\n",
    "  - **Mitigation interval**: The mitigation factor is applied over this time period, measured in days from the start of the model (i.e., today).  For instance, \"0-180\" means that mitigation is applied starting from now and for the next 180 days.\n",
    "  \n",
    "You may find it interesting to compare your predictions with [those of a more detailed model used by researchers at Imperial College](https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf).  Roughly, the estimates there predict the infection peak to occur in early June without mitigation, moving up to 1 month later if substantial mitigation is employed."
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    "%matplotlib inline\n",
    "from SIR import *\n",
    "\n",
    "display(SIR_gui,SIR_output)"
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