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Asymptotic Behavior and Stability of Stochastic SIR Model with Variable Diffusion Rates

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Document pages: 14 pages

Abstract: In this paper, we propose random fluctuation on contact and recovery rates indeterministic SIR model with disease deaths in nonparametric manner andderive a new stochastic SIR model with distributed time delay and generaldiffusion coefficients. By analysis of the introduced model, we obtain the sufficientconditions for the regularity, existence and uniqueness of a global solutionby means of Lyapunov function. Moreover, we also investigate the stochasticasymptotic stability of disease free equilibria and endemic equilibria ofthis model. Finally, we illustrate our general results by applications.

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