Introduction

In small communities there are usually only few infectious individuals. If they contact too few susceptibles, this might lead to local extinction. On the other hand, if they contact too many susceptibles, they give rise to too many secondary infections. This reduces the number of susceptibles, which may eventually also lead to extinction. In order for long term persistence of the infection to be likely, the population must exceed a minimum size. If there is a long infectious period (e.g. for leprosy, tuberculosis and HIV it lasts for years), the infection can persist even in small populations. High contact rates cause a better ‘exploitation’ of the population, but they also bear the risk of causing large epidemics which in turn can cause local extinction. Human birth and death rates define the population turnover and therefore also influence the persistence of infectious diseases. It is the aim of this study to determine the minimum population size that is necessary for the persistence of polio virus infection by using stochastic simulations.

Methods

The computer models are stochastic. The sequence of epidemiological events is generated by a Markov process. The type of the event (birth, death of a susceptible, infection, loss of infectivity) is assigned according to a multinomial distribution which depends on the state of the population (number of susceptible and infectious individuals; see Appendix for details). If the event is a birth, the number of susceptibles is increased by one. If it is an infection, the number of susceptibles is decreased by one and the number of infectives is increased by one.