THRESHOLD BEHAVIOR OF A STOCHASTIC SVI EPIDEMIC MODEL WITH JUMP NOISE AND SATURATED INCIDENCE RATE

Haoran Geng; Liang Wang; Daqing Jiang

doi:10.11948/20240455

2025 Volume 15 Issue 5

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Haoran Geng, Liang Wang, Daqing Jiang. THRESHOLD BEHAVIOR OF A STOCHASTIC SVI EPIDEMIC MODEL WITH JUMP NOISE AND SATURATED INCIDENCE RATE[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 3004-3024. doi: 10.11948/20240455

Citation:

Haoran Geng, Liang Wang, Daqing Jiang. THRESHOLD BEHAVIOR OF A STOCHASTIC SVI EPIDEMIC MODEL WITH JUMP NOISE AND SATURATED INCIDENCE RATE[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 3004-3024. doi: 10.11948/20240455

THRESHOLD BEHAVIOR OF A STOCHASTIC SVI EPIDEMIC MODEL WITH JUMP NOISE AND SATURATED INCIDENCE RATE

1.
School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
2.
College of Science, China University of Petroleum (East China), Qingdao 266580, China

Author Bio: Email: ntumacghr@hotmail.com (H. Geng); Email: daqingjiang2010@hotmail.com (D. Jiang)
Corresponding author: Email: ntumacwangl@hotmail.com (L. Wang)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 12001271), Natural Science Foundation of Jiangsu Province (No. BK20200484) and Fundamental Research Funds for the Central Universities (No. 30922010813)

Abstract

Abstract

This paper analyzes a stochastic SVI epidemic model with jump noise and saturated incidence rate. By applying Kunita's inequality, we derive the asymptotic pathwise estimation of the stochastic solution. We then present the basic reproduction number of the model, $ \bar{R_0^{s}} $, which determines the extinction and persistence in the mean of the disease. Additionally, numerical simulations are conducted to verify the theoretical results. Consequently, both theoretical and numerical results indicate that the jump noise can hold off the spread of the disease.
- Stochastic SVI model /
- jump noise /
- Kunita’s inequality /
- threshold behavior /
- extinction
MSC: 34E10, 60G51, 60H10

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