Recall the Epidemic problem. Now, consider a new model with two significant improvements:

Suppose that after recovery, there is a loss of immunity that causes recovered individuals to become susceptible. This reinfection mechanism can be modeled as $R,$ where $=$ the reinfection rate $=0\mathrm{.}03\frac{1}{\text{d}\text{a}\text{y}}.$

Suppose that some of the infected people recover and some die. $D$ is the number of dead people. The death mechanism can be modeled as $bI,$ where $b=$ the death rate $=0\mathrm{.}15\frac{1}{\text{d}\text{a}\text{y}}.$ Also consider that there is an influx of susceptible individuals moving to the city at the rate of $S_{in}=0\mathrm{.}2\frac{\text{p}\text{e}\text{o}\text{p}\text{l}\text{e}}{\text{d}\text{a}\text{y}}$ and an influx of infected individuals moving to the city at the rate of $I_{in}=0\mathrm{.}3\frac{\text{p}\text{e}\text{o}\text{p}\text{l}\text{e}}{\text{d}\text{a}\text{y}}.$

The new model can be represented by:

Modify your model to include these mechanisms. Choose a contextually sensible initial value for $D.$ Explore various values for each parameter and physically interpret your results.

$($This is meant to be an open$-$ended question. There is no single correct answer, per se$.$ Rather, the emphasis is on self$-$experimentation and seeing what information you can elicit from jockeying around with your updated model.$)$