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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.

MSC:

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

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