Modeling pandemics (1)

The most popular model to model epidemics is the so-called SIR model - or Kermack-McKendrick. Consider a population of size [latex]N[/latex], and assume that [latex]S[/latex] is the number of susceptible, [latex]I[/latex] the number of infectious, and [latex]R[/latex] for the number recovered (or immune) individuals, [latex display="true"]\displaystyle {\begin{aligned}&{\frac {dS}{dt}}=-{\frac {\beta IS}{N}},\\[6pt]&{\frac {dI}{dt}}={\frac {\beta IS}{N}}-\gamma I,\\[6pt]&{\frac {dR}{dt}}=\gam...