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Epidemiological models with varying population size and dose-dependent latent period. (English) Zbl 0832.92023
Summary: Two epidemiological models in a variable-size population are considered. Both have a dose-dependent latent period that depends on the proportion of infectious individuals in the population. In the SEIS model, the proportion of infectious individuals tends to either zero or a stable endemic value. In the SEIRS model, for diseases that confer temporary immunity, periodicity can arise by a Hopf bifurcation.

MSC:
92D30 Epidemiology
34C25 Periodic solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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