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Abstract In this paper, we consider a stochastic epidemic model with time delay and general incidence rate. We first prove the existence and uniqueness of the global positive solution. By… Click to show full abstract
Abstract In this paper, we consider a stochastic epidemic model with time delay and general incidence rate. We first prove the existence and uniqueness of the global positive solution. By using the Krylov–Bogoliubov method, we obtain the existence of invariant measures. Furthermore, we study a special case where the incidence rate is bilinear with distributed time delay. When the basic reproduction number R 0 1 , the analysis of the asymptotic behavior around the disease-free equilibrium E 0 is provided while when R 0 > 1 , we prove that the invariant measure is unique and ergodic. The numerical simulations also validate our analytical results.
Journal Title: Physica A: Statistical Mechanics and its Applications
Year Published: 2019
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