Modeling Epidemics: A Primer and Numerus Software Implementation

Wayne M. Getz; Richard Salter; Oliver Muellerklein; Hyun S. Yoon; Krti Tallam

6. The assumption that the transmission rate parameter is time independent. Primary reasons why epidemics subside are that either the proportion of susceptible individuals in the population is reduced to the point where the epidemic can no longer be sustained (so-called threshold effect [20, 45]) or the rate at which susceptible individuals contact infectious individual during the course of an epidemic, as in the recent Ebola outbreak in West Africa [17, 46] , precipitously falls due to behavioral reasons as the epidemic proceeds. One approach is to assume that β has the exponential form β(t) = β 0 e −εt (e.g. as in [47] ). This is a little extreme because we should not expect β not to start to decline precipitously at the start of the epidemic, but only part way into the epidemic, once public awareness of the full potential of the epidemic has become apparent. In this case, a mirror-image, sshaped curve of the form