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
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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