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Disease regulation of age-structured host populations. (English) Zbl 0688.92009
Summary: A lethal, contagious disease can generate a density-dependent regulation of its host, provided the hosts’ contact rate grows with population size. The condition for disease-induced population control is that the expected number of offspring of an infected new-born be less than one. In vertebrates that acquire immunity if they survive infection, the disease changes the age structure of its host population.
The steady-state age structure of a disease-regulated host with age- dependent fecundity is computed. Local stability analysis indicates that the equilibrium age structure is always stable. However, when the usual exponentially distribued duration of the disease is replaced by a constant duration, the population can exhibit oscillations with a long period.

MSC:
92D25 Population dynamics (general)
34C99 Qualitative theory for ordinary differential equations
35Q99 Partial differential equations of mathematical physics and other areas of application
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