Modelling the dynamics of nonendemic epidemics

We present two models for an epidemic where the individuals are infective over a fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based on a delay-difference scheme. We show that, as a function of the delay (which corresponds to the period of infectiveness) the percentage of non-infected population varies over a wide range. We present also a variant of our model where the recovery rate follows a Poisson law and obtain a discrete version of the SIR model. We estimate the percentage of non-infected population in the two models, show that they lead to almost the same values and present an explanation of this fact. The second model is based on the assumption that the infection is spread by carriers. Under the hypothesis that the carriers are relatively long-lived, and that the number of the infected ones is a relatively small fraction of the total population of potential carriers, we show that the model reduces to the same version of the discrete SIR obtained by our first model.