A HYBRID SWITCHING S-DI-A EPIDEMIC MODEL WITH STANDARD INCIDENCE: PERSISTENCE, EXTINCTION AND POSITIVE RECURRENCE

Zhenfeng Shi; Daqing Jiang

doi:10.11948/20220145

2023 Volume 13 Issue 2

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Zhenfeng Shi, Daqing Jiang. A HYBRID SWITCHING S-DI-A EPIDEMIC MODEL WITH STANDARD INCIDENCE: PERSISTENCE, EXTINCTION AND POSITIVE RECURRENCE[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 826-844. doi: 10.11948/20220145

Citation:

Zhenfeng Shi, Daqing Jiang. A HYBRID SWITCHING S-DI-A EPIDEMIC MODEL WITH STANDARD INCIDENCE: PERSISTENCE, EXTINCTION AND POSITIVE RECURRENCE[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 826-844. doi: 10.11948/20220145

A HYBRID SWITCHING S-DI-A EPIDEMIC MODEL WITH STANDARD INCIDENCE: PERSISTENCE, EXTINCTION AND POSITIVE RECURRENCE

Zhenfeng Shi^1,2,
Daqing Jiang^1, ,

1.
College of Science, China University of Petroleum, Qingdao 266580, Shandong Province, China
2.
School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, Jilin Province, China

Corresponding author: Email: daqingjiang2010@hotmail.com(D. Jiang)

Abstract

Abstract

In this paper, a stochastic S-DI-A epidemic model with standard incidence under Markovian switching is investigated to study the spread of the HIV virus. For this purpose, we firstly obtain sufficient conditions for persistence in the mean of the disease. In addition, sufficient conditions for exponential extinction of the infectious disease is derived. Furthermore, by constructing a suitable stochastic Lyapunov function with regime switching, we establish sufficient conditions for the existence of positive recurrence of the solutions. Finally, numerical simulations are employed to demonstrate the analytical results.
- S-DI-A model /
- Markovian switching /
- persistence in the mean /
- extinction /
- positive recurrence
MSC: 34F05, 37Hx05, 60J27, 92B05

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References

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