Mathematical Biosciences and Engineering

2021, Issue 2: 1352-1369. doi: 10.3934/mbe.2021071
Research article

Qualitative analysis of a nonautonomous stochastic $SIS$ epidemic model with L$\acute {e}$vy jumps

• Received: 22 November 2020 Accepted: 11 January 2021 Published: 21 January 2021
• In this paper, we study a nonautonomous stochastic $SIS$ epidemic model with L$\acute {e}$vy jumps. We first establish that this model has a unique global positive solution with the positive initial condition. Then, we investigate the condition for extinction of the disease. Moreover, by constructing suitable stochastic Lyapunov function, sufficient conditions for persistence and existence of Nontrivial T-periodic solution of system are obtained. Finally, numerical simulations are also presented to illustrate the main results.

Citation: Long Lv, Xiao-Juan Yao. Qualitative analysis of a nonautonomous stochastic $SIS$ epidemic model with L$\acute {e}$vy jumps[J]. Mathematical Biosciences and Engineering, 2021, 18(2): 1352-1369. doi: 10.3934/mbe.2021071

Related Papers:

• In this paper, we study a nonautonomous stochastic $SIS$ epidemic model with L$\acute {e}$vy jumps. We first establish that this model has a unique global positive solution with the positive initial condition. Then, we investigate the condition for extinction of the disease. Moreover, by constructing suitable stochastic Lyapunov function, sufficient conditions for persistence and existence of Nontrivial T-periodic solution of system are obtained. Finally, numerical simulations are also presented to illustrate the main results.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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