The dynamics of an infectious disease in a population with birth pulses. (English) Zbl 0928.92027

Summary: 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.


92D30 Epidemiology
34C25 Periodic solutions to ordinary differential equations
92D25 Population dynamics (general)
34D10 Perturbations of ordinary differential equations
Full Text: DOI


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