Spread of infectious disease

The SIR (susceptible, infectious, recovered) model is derived analytically and its coupled differential equations are solved both with SciPy’s integrators and with a manual fourth-order Runge–Kutta implementation. The stability of the disease-free and endemic states is determined symbolically with SymPy, and the evolution of the disease through a population is visualized with Matplotlib.

$$\begin{aligned} \frac{dS}{dt} &= -\frac{\beta}{N} S I \\[1ex] \frac{dI}{dt} &= \frac{\beta}{N} S I - \gamma I \\[1ex] \frac{dR}{dt} &= \gamma I \end{aligned}$$

Here $\beta$ is the infection rate, $\gamma$ the recovery rate and $N = S + I + R$ the population size. The interactive note puts $\beta$ and $\gamma$ on sliders.

In the same manner, a model for the spread of HIV infection inside the body is built and compared with publicly available data from an academic journal.