Epidemiological models with varying population size and dose-dependent latent period

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.