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On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate. (English) Zbl 1203.92049
Summary: We study an epidemic model for infections with non-permanent acquired immunity (SIRS). The incidence rate is assumed to be a general nonlinear function of the susceptibles and the infectious classes. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability are also obtained. Unlike the recent literature on this subject, here no restrictions are required about the monotonicity and concavity of the incidence rate with respect to the infectious class. Among the applications, the noteworthy case of a convex incidence rate is provided.
MSC:
92C60Medical epidemiology
34D20Stability of ODE
34D23Global stability of ODE
92D30Epidemiology
34D05Asymptotic stability of ODE
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