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Global stability in cyclic epidemic models with disease fatalities. (English) Zbl 0924.92018
Ruan, Shigui (ed.) et al., Differential equations with applications to biology. Proceedings of the international conference, Halifax, Canada, July 25–29, 1997. Providence, RI: American Mathematical Society. Fields Inst. Commun. 21, 459-472 (1999).
From the authors’ abstract: A general disease transmission model of SIRS type is formulated and analyzed. There is constant recruitment into the susceptible class, mass action incidence, and stage age in the removed class. Disease fatalities occur in the infective class and the removed stages. Sufficient conditions are given for the endemic equilibrium to be globally asymptotically stable. For example, if the disease confers permanent immunity then global stability of the endemic equilibrium (for parameter values such that it exists) is assured. Other examples are given that exhibit this same assured behavior.
For the entire collection see [Zbl 0903.00038].

92D30 Epidemiology
45J05 Integro-ordinary differential equations
45M10 Stability theory for integral equations