The SIR model for infection disease

In the present page we numerically solve the SIR model for infection disease of the form \begin{align*} \frac{dS}{dt} & = -\beta IS, \\ \frac{dI}{dt} & = \beta IS - \gamma I, \\ \frac{dR}{dt} & = \gamma I, \end{align*} where $$S(t)$$, $$I(t)$$ and $$R(t)$$ are real-value unknown functions of $$t \in \mathbb{R}$$, and $$\beta$$ and $$\gamma$$ are positive constants. In mathematical epidemiology, $$t$$ is time, $$S(t)$$ is the number of susceptible people, $$I(t)$$ is the number of people infected, $$R(t)$$s the number of people who have recovered and developed immunity to the infection, $$\beta$$ the infection rate, and $$\gamma$$ is the recovery rate.
By using MATLAB we draw a solution to the initial value problem for the SIR model with some appropriate initial data. See sir_model.m for the detail.