### Background

### The First Model

The first model is based on the level of transmission of the virus. Increasing the level of social distancing can lead to a *lower infection rate*. This can greatly improve outcomes in terms of not exceeding the hospital maximal capacities. This model is based on the * SIR (Susceptible, Infected, Recovered)* model of the spread of the virus. This comes from a series of differential equations that –when solved– yield three different graphs, as shown above.

### The Second Model

Knowing around when this max growth rate occurs can help us model when the curve will flatten out.

This model is based on a **Logistic Growth** model, which is often denoted by the equation:
$P(t) = \frac{L}{1 + ae^{-bt}}$.

Here, $L$ is the maximum number of people predicted to be infected. $a$ is a constant that is derived from the initial condition (the number of reported cases on March 1st). The growth rate constant, $b$ can be derived from knowing when the maximum growth rate occurs. $P$ is the total number of reported infected individuals. As of now, we don’t have enough data to exactly know when this inflection point will occur.