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

Long Lv; Xiao-Juan Yao; Long Lv; Xiao-Juan Yao

doi:10.3934/mbe.2021071

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 2: 1352-1369. doi: 10.3934/mbe.2021071

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Research article

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

Long Lv ^{1
,
,},
Xiao-Juan Yao ²

1.
School of General Education, College of Technology And Engineering, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People's Republic of China
2.
No.1 Middle School of Lanzhou, Lanzhou, Gansu, 730030, People's Republic of China

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.
- nonautonomous stochastic $ SIS $ epidemic model,
- L$ \acute {e} $vy jumps,
- Lyapunov function,
- T-periodic solution,
- Extinction and persistence
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

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Abstract

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.

References

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