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Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model. (English) Zbl 1257.34065
Summary: We study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form $\beta S(t)\int^h_0 f(\tau)G(I(t-\tau))d\tau$. Applying Lyapunov functional techniques, we establish sufficient conditions of the rate of immunity loss for the global asymptotic stability of an endemic equilibrium for the model. In particular, we offer a unified construction of Lyapunov functionals for both cases of $R_{0}\le 1$ and $R_{0}>1$, where $R_{0}$ is the basic reproduction number.

MSC:
 34K60 Qualitative investigation and simulation of models 34K20 Stability theory of functional-differential equations 34K21 Stationary solutions of functional-differential equations 92C60 Medical epidemiology 92D30 Epidemiology
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References:
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