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An \(S \to{} E \to{} I\) epidemic model with varying population size. (English) Zbl 0735.92022
Differential equations models in biology, epidemiology and ecology, Proc. Conf., Claremont/CA (USA) 1990, Lect. Notes Biomath. 92, 121-138 (1991).
Summary: [For the entire collection see Zbl 0732.00026.]
An \(S\rightarrow E\rightarrow I\) epidemic model with a general shape of density-dependent mortality and incidence rate is studied analytically and numerically.
The combined effect of a latent period and of varying population size can produce oscillations in this ODE model. When fertility of exposed individuals is the same as that of susceptibles, there is a clear threshold. On the contrary, when both exposed and infectives do not contribute to birth rate, there may exist multiple endemic states also below the threshold.
When the contact rate is independent of population size, the global behaviour is established: all trajectories converge to an equilibrium.

MSC:
92D30 Epidemiology
34D99 Stability theory for ordinary differential equations