Stationary distribution and extinction of an HCV transmission model with protection awareness and environmental fluctuations

Wang, Liangwei and Wei, Fengying and Jin, Zhen and Mao, Xuerong (2025) Stationary distribution and extinction of an HCV transmission model with protection awareness and environmental fluctuations. Applied Mathematics Letters, 160. 109356. ISSN 0893-9659 (https://doi.org/10.1016/j.aml.2024.109356)

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Abstract

We propose a stochastic HCV model with protection awareness and exposed-acute-chronic phases in this study. First of all, we show that the stochastic HCV model admits a unique global positive solution for any given positive initial values. Then, we verify that HCV model has a unique stationary distribution under the sufficient criterion R0s>1, which indicates that HCV transmission undergoes the persistence in the long term. Furthermore, we derive the sufficient conditions for HCV extinction under the condition R0e<1. As a consequence, we derive the relationships among the stochastic persistence index R0s, the stochastic extinction index R0e and the threshold (the basic reproduction number R0) of the model without fluctuations. The condition R0>R0s>1 reveals that the existence of the white noises triggers the less stochastic persistence index. While, the condition R0<R0e<1 reveals that, when the intensities of the white noises are enhanced, the value R0e triggers the stochastic extinction.

ORCID iDs

Wang, Liangwei, Wei, Fengying, Jin, Zhen and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;

Persistent Identifier

https://doi.org/10.17868/strath.00091198
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