Study on a Respiratory Syncytial Virus SIRS Model with Age Structure

doi:10.3969/j.issn.1006-8074.2025.02.006

Mathematical Theory and Applications ›› 2025, Vol. 45 ›› Issue (2): 93-109.doi: 10.3969/j.issn.1006-8074.2025.02.006

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Study on a Respiratory Syncytial Virus SIRS Model with Age Structure

LIN Caihong¹,GAO Shukun¹, WANG Wencong¹, ZHANG Long^1,2,*

1. School of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China; 2. The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region,~Urumqi 830017, China

Online:2025-06-28 Published:2025-08-09
Supported by:
This work is supported by the Natural Science Foundation of Xinjiang Province~(No. 2022D01E41),~the National Natural Science Foundation of China~(No.~12261087),~the Open Project of Key Laboratory of Applied Mathematics of Xinjiang Autonomous Region~(No. 2021D04014)

Abstract

Abstract: In this paper, we study the epidemic model of respiratory syncytial virus SIRS with age structure. Firstly, the basic reproduction number $R_{0}$ of the model is calculated and the positivity and ultimate boundedness of the solution to the model under initial conditions are proven. Secondly, it is proven that when $R_{0}<1$, the disease-free equilibrium is locally and globally asymptotically stable;~and when $R_{0}>1$, the disease is uniformly persistent and there is at least a positive equilibrium. Finally, the effectiveness of the theoretical results is demonstrated by numerical simulation, and the impact of vaccination on disease transmission is predicted.

Key words: Respiratory syncytial virus (RSV), Age structure, Basic reproduction number, Uniform persistence, Stability

LIN Caihong, GAO Shukun, WANG Wencong, ZHANG Long. Study on a Respiratory Syncytial Virus SIRS Model with Age Structure[J]. Mathematical Theory and Applications, 2025, 45(2): 93-109.

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Study on a Respiratory Syncytial Virus SIRS Model with Age Structure

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