### 2 SIRS infection model

The SIRS model is \begin{align} \dot{S} & =-\beta SI+\mu R\tag{1}\\ \dot{I} & =\beta SI-\upsilon I\nonumber \\ \dot{R} & =\upsilon I-\mu R\nonumber \end{align}

Where \(S=S(t)\) is the population of susceptible individuals, \(I=I(t)\), the infected population, and \(R=R(t)\) the recovered
population. This diagram shows the model where now some of the recovered population can
become susceptible again and become infected. The parameter \(\mu \) indicates how much of the
recovered population could become susceptible again.

The units of \(S,R,I\) are population measured in person. These values can not be negative since they are
population amount. The units of \(\mu \) is \(\frac{1}{\text{time}}\) where time can be day or week or any other unit of time.
The units of \(\upsilon \) is also \(\frac{1}{\text{time}}\). The units of \(\beta \) is \(\frac{1}{\left ( \text{time}\right ) \left ( \text{person}\right ) }\)

Figure 1:SIRS model
The following program allows one to do analysis on this model and it also displays the critical
points.

Figure 2:screen shot
The program is written using Mathematica. Here is the notebook

After downloading the notebook and opening it inside Mathematica, you can now use the sliders
and analyze the system behaviour for diﬀerent parameters.

Source code