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Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays

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  • In this paper, we establish the global asymptotic stability of equilibria for an SIR model of infectious diseases with distributed time delays governed by a wide class of nonlinear incidence rates. We obtain the global properties of the model by proving the permanence and constructing a suitable Lyapunov functional. Under some suitable assumptions on the nonlinear term in the incidence rate, the global dynamics of the model is completely determined by the basic reproduction number $R_0$ and the distributed delays do not influence the global dynamics of the model.
    Mathematics Subject Classification: Primary: 34K20, 34K25; Secondary: 92D30.

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