More models of infection: It´s epidemic

Previously, we studied a model of an infection´s spread through a hospital ward. The ward was small enough that we could track each patient individually, but when population size grows, this kind of model becomes impractical; accordingly, we turn our attention in this paper to models that study the population as a whole. As before, we divide the population into three groups: at day t, I(t) is the infected proportion of the population, whereas S(t) is the proportion that has never been infected. These quantities satisfy 0 ≤ I(t) ≤ 1 and 0 ≤ S(t) ≤ 1 for t ≥ 0. We derive the third part, R(t) the proportion of the population that was once infected but has now recovered - from the first two: R(t) = I - I(t) - S(t).