The dynamics of an infectious disease in a population with birth pulses

Abstract

In most models of population dynamics increases in population due to births are assumed to be time-independent, but many species of wild animal give birth only during a single period of the year. We propose a model for the dynamics of a fatal infectious disease in a wild animal population for which births occur in a single pulse once per time period. Periodic solutions are found and criteria for their stability determined. A simple example applied to tuberculosis in the possum is used to illustrate the effect of the birth pulse on critical population parameters.