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Dynamic behavior of a stochastic SIQS epidemic model with Lévy jumps. (English) Zbl 1398.37096
Summary: In this paper, we propose a stochastic SIQS epidemic model with Lévy jumps and investigate sufficient conditions of the extinction and persistence of the disease. Then, we analyze the asymptotic behavior of the solution of the model around the endemic equilibrium of the corresponding deterministic model. We find that Lévy jumps can suppress the disease outbreak. Numerical simulations are carried out and approve our results.

MSC:
37N25 Dynamical systems in biology
37H10 Generation, random and stochastic difference and differential equations
92D25 Population dynamics (general)
34F05 Ordinary differential equations and systems with randomness
34D05 Asymptotic properties of solutions to ordinary differential equations
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