STOCHASTIC SURVIVAL ANALYSIS OF AN EPIDEMIC MODEL WITH INNATE IMMUNITY AND TREATMENT

Lijun Chen; Wenshuang Li; Ruiyang Zhou; Fengying Wei

doi:10.11948/20240180

2025 Volume 15 Issue 4

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Lijun Chen, Wenshuang Li, Ruiyang Zhou, Fengying Wei. STOCHASTIC SURVIVAL ANALYSIS OF AN EPIDEMIC MODEL WITH INNATE IMMUNITY AND TREATMENT[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 1862-1881. doi: 10.11948/20240180

Citation:

Lijun Chen, Wenshuang Li, Ruiyang Zhou, Fengying Wei. STOCHASTIC SURVIVAL ANALYSIS OF AN EPIDEMIC MODEL WITH INNATE IMMUNITY AND TREATMENT[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 1862-1881. doi: 10.11948/20240180

STOCHASTIC SURVIVAL ANALYSIS OF AN EPIDEMIC MODEL WITH INNATE IMMUNITY AND TREATMENT

1.
Jin Shan College, Fujian Agriculture and Forestry University, Fuzhou 350000, China
2.
School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, China
3.
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Sichuan 61173, China
4.
Center for Applied Mathematics of Fujian Province, Fuzhou University, Fuzhou 350116, China

Author Bio: Email: chenlijun101086@163.com(L. Chen); Email: lws1501@163.com(W. Li); Email: ruiyangzhou@outlook.com(R. Zhou)
Corresponding author: Email: weifengying@fzu.edu.cn(F. Wei)
Fund Project: The authors were supported by Special Projects of the Central Government Guiding Local Science and Technology Development (2021L3018), Consultancy Project by the Chinese Academy of Engineering (2023-JB-12), Fujian Research and Training Grants for Young and Middle-Aged Leaders in Healthcare (202501140018), the Science and Technology Project for Young Teachers of Jin Shan College of Fujian Agriculture and Forestry University (KX230301), the Science and Technology Project of Education Department of Fujian Province of China (JAT210662)

Abstract

Abstract

The innate immunity helps the individuals in the exposed compartment return into the ones in the susceptible compartment when a pathogen or virus invades the local population of having four compartments: the susceptible, the exposed, the infected and the recovered. In this study, we propose a stochastic SEIR model with innate immunity and treatment. Here, Holling type Ⅱ functional responses are used to describe the saturated effects of the innate immunity and treatment. Then, we obtain the extinction of the exposed and the infected when the basic reproduction number $ \mathcal{R}_0<1 $ and the exponential decline rate $ \nu<0 $ are valid. Moreover, we conclude that when innate immunity and treatment increase, the time that the exposed and the infected approach zero reduces. We also find that the deterministic SEIR model reaches extinction a bit faster than the stochastic SEIR model. Further, the persistence in the mean and stationary distribution of stochastic SEIR model are obtained under suitable conditions. Finally, the numerical investigations with two methods and a case study of Fuzhou COVID-19 epidemic of 2022 are discussed.
- SEIR epidemic model /
- Holling type Ⅱ functional response /
- innate immunity /
- extinction and persistence /
- COVID-19
MSC: 60H10, 92B05, 92D30

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References

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