LONG-TIME BEHAVIOR OF AVIAN INFLUENZA MODEL WITH NONLOCAL DIFFUSION

Zhenyu Zhang; Kangkang Chang; Fuyu Wei; Guizhen Liang

doi:10.11948/20240061

2026 Volume 16 Issue 1

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Zhenyu Zhang, Kangkang Chang, Fuyu Wei, Guizhen Liang. LONG-TIME BEHAVIOR OF AVIAN INFLUENZA MODEL WITH NONLOCAL DIFFUSION[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 1-16. doi: 10.11948/20240061

Citation:

Zhenyu Zhang, Kangkang Chang, Fuyu Wei, Guizhen Liang. LONG-TIME BEHAVIOR OF AVIAN INFLUENZA MODEL WITH NONLOCAL DIFFUSION[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 1-16. doi: 10.11948/20240061

LONG-TIME BEHAVIOR OF AVIAN INFLUENZA MODEL WITH NONLOCAL DIFFUSION

1.
Academy of Fine Arts, Xinxiang University, Xinxiang 453003, China
2.
School of Mathematics and Statistics, Xinxiang University, Xinxiang 453003, China
3.
School of Materials Science and Engineering, Henan Institute of Technology, Xinxiang 453003, China

Author Bio: Email: zhangzhenyucc9664@gmail.com(Z. Zhang); Email: weifuyucc@163.com(F. Wei); Email: lgz3361@163.com(G. Liang)
Corresponding author: Email: changkangkang86@sina.com(K. Chang)
Fund Project: The research was supported in part by the Startup Foundation for Doctors of Xinxiang University (No. 1366020229) and the Key Research Projects of Higher Education Institutions in Henan Province (N0. 24B110015)

Abstract

Abstract

The aim of this study is to investigate the long-time behavior of a model of avian influenza incorporating nonlocal diffusion. We establish the existence, uniqueness, positivity and boundedness of the solution by constructing a Lyapunov function and utilizing the eigenvalue problem of the nonlocal diffusion term. The basic reproduction number is determined through the generation matrix method. By constructing Lyapunov function and using the comparison principle, we demonstrate the global stability and uniform persistence of the system. Numerical simulations are performed to validate our theoretical findings, indicating that diffusion has a pronounced impact on the disease. Our findings reveal that slight changes in the diffusion coefficient lead to significant changes in both susceptible and infected groups. Therefore, to control the development and spread of the disease, it is essential to cull avian populations and limit human movement during outbreaks.
- Avian influenza model /
- nonlocal diffusion /
- basic reproduction number /
- global stability /
- uniform persistence
MSC: 35E20, 37N35, 93E03

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References

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