Threshold dynamics of a nonlocal diffusion West Nile virus model with spatial heterogeneity

Kangkang Chang; Zhenyu Zhang; Guizhen Liang; Kangkang Chang; Zhenyu Zhang; Guizhen Liang

doi:10.3934/math.2023729

AIMS Mathematics

2023, Volume 8, Issue 6: 14253-14269. doi: 10.3934/math.2023729

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Research article

Threshold dynamics of a nonlocal diffusion West Nile virus model with spatial heterogeneity

1.
School of Mathematics and Statistics, Xinxiang University, Xinxiang 453003, China
2.
Academy of Fine Arts, Xinxiang University, Xinxiang 453003, China

Received: 11 February 2023 Revised: 03 April 2023 Accepted: 06 April 2023 Published: 17 April 2023
MSC : 35B40, 37N25, 92B05

In this study, we investigated the threshold dynamics of a spatially heterogeneous nonlocal diffusion West Nile virus model. By employing semigroup theory and continuous Fréchet-differentiable, we established the well-posedness of the solution. The expression for the basic reproduction number derived using the next-generation matrix method. The authors demonstrated the threshold dynamics of the system by constructing a Lyapunov function and applying the comparison principle. Finally, numerical simulations were used to validate the theorem results. It can be suggested that to control disease development rapidly, measures should be taken to reduce the spread of mosquitoes and birds.
- threshold dynamics,
- nonlocal diffusion,
- West Nile virus model,
- spatial heterogeneity
Citation: Kangkang Chang, Zhenyu Zhang, Guizhen Liang. Threshold dynamics of a nonlocal diffusion West Nile virus model with spatial heterogeneity[J]. AIMS Mathematics, 2023, 8(6): 14253-14269. doi: 10.3934/math.2023729

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Abstract

In this study, we investigated the threshold dynamics of a spatially heterogeneous nonlocal diffusion West Nile virus model. By employing semigroup theory and continuous Fréchet-differentiable, we established the well-posedness of the solution. The expression for the basic reproduction number derived using the next-generation matrix method. The authors demonstrated the threshold dynamics of the system by constructing a Lyapunov function and applying the comparison principle. Finally, numerical simulations were used to validate the theorem results. It can be suggested that to control disease development rapidly, measures should be taken to reduce the spread of mosquitoes and birds.

References

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