The Epidemic Subsidence Model

Abstract

Once the presence of smallpox in a previously disease-free region is recognized, a concerted effort is made to bring the epidemic to an end. It should however be realized that awareness of the disease and effort at its control, no matter how conscientious, do not reduce the basic contagiousness of the disease. What is changed is the rate at which infectives are identified and isolated from further contact with susceptible individuals. The result is that the total number of individuals infected over time will continue to grow, but the removal rate will increase so as to exceed the infection rate, and consequently the epidemic will eventually die out. The purpose of the epidemic subsidence model is to predict the total number of individuals who contract smallpox before the epidemic runs its course. Two versions of the epidemic subsidence model will be presented. Although these models are formally very different, they lead to identical results. It is instructive to see both as they graphically demonstrate that there is not a single “right way” to formulate the mathematical model.