Convergence results in \(SIR\) epidemic models with varying population sizes.

*(English)*Zbl 0879.34054The authors study an \(SIR\) epidemic model in which the force of infection involves a distributed delay and in which the population is not constant. The model exhibits both a disease-free equilibrium, \(E_0\), which exists for all parameter values, and one in which the infection is endemic, \(E_+\), which exists for certain parameter values. Their main result is that \(E_0\) is globally asymptotically stable when \(E_+\) doesn’t exist and that \(E_+\) is locally asymptotically stable when it exists. The proof involves Lyapunov functionals. They also calculate the radius of a ball contained in the domain of attraction of \(E_+\).

Reviewer: A.Hausrath (Boise)

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\textit{E. Beretta} and \textit{Y. Takeuchi}, Nonlinear Anal., Theory Methods Appl. 28, No. 12, 1909--1921 (1997; Zbl 0879.34054)

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