Final Report for Sample Project 1

We develop a simple model for the spread of an infectious disease that is limited in duration and is not fatal. We first assume that when an infected person recovers, (s)he becomes susceptible to being infected again, but we also consider the case where some of the recovering people become immune to the disease. We find in the first case that the prevalence of the disease – the proportion of the population that is infected at a given time – approaches a limiting value between 0 and 1 in the long run, and that the predicted limiting value is very sensitive to errors in data taken when the prevalence is small and growing. In the latter case, we find that the prevalence of the disease reaches a peak and then decays toward zero; in the long run, a certain proportion of the population has become immune and a certain proportion remains susceptible.