THE REGULATION OF AN AGE-STRUCTURED POPULATION BY A FATAL DISEASE

A model describing the effect of a fatal disease on an age-structured population which would otherwise grow is presented and analysed. If th e disease is capable of regulating host numbers, there is an endemic s teady age distribution (SAD), for which an analytic expression is obta ined under some simplifying assumptions. The ability of the disease to regulate the population depends on a parameter R(alpha), which is def ined in terms of the given age-dependent birth and death rates, and wh ere alpha is the age-dependent disease-induced death rate. If R(alpha) < 1 the endemic SAD is attained, while R(alpha)> 1 means the disease cannot control the population's size. The number R(0) is the expected number of offspring produced by each individual in the absence of the disease; for a growing population we require R(0) > 1. A stability ana lysis is also performed and it is conjectured that the endemic SAD is locally asymptotically stable whenever it is attained. This is demonst rated explicitly for a very simple example where all rates are taken a s constant.