MODELING THE SPREAD OF WEST NILE VIRUS IN A SPATIALLY HETEROGENEOUS AND ADVECTIVE ENVIRONMENT

Jing Ge; Zhigui Lin; Huaiping Zhu

doi:10.11948/20200258

2021 Volume 11 Issue 4

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Jing Ge, Zhigui Lin, Huaiping Zhu. MODELING THE SPREAD OF WEST NILE VIRUS IN A SPATIALLY HETEROGENEOUS AND ADVECTIVE ENVIRONMENT[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1868-1897. doi: 10.11948/20200258

Citation:

Jing Ge, Zhigui Lin, Huaiping Zhu. MODELING THE SPREAD OF WEST NILE VIRUS IN A SPATIALLY HETEROGENEOUS AND ADVECTIVE ENVIRONMENT[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1868-1897. doi: 10.11948/20200258

MODELING THE SPREAD OF WEST NILE VIRUS IN A SPATIALLY HETEROGENEOUS AND ADVECTIVE ENVIRONMENT

1.
School of Mathematics and Statistics, Huaiyin Normal University, Huai'an 223300, China
2.
School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
3.
Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada

Corresponding author: Email: zglin68@hotmail.com(Z. Lin)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 11701206, 11911540464 and 11771381), Jiangsu Government Scholarship for Overseas Studies (No. JS-2018-038), NSERC and CIHR of Canada

Abstract

Abstract

In this paper, we put forward and explore a reaction-diffusion-advection system with free boundaries in spatially heterogeneous environment to model the spatial transmission of West Nile virus. The transmission dynamics are given for the model involving mosquitoes and birds, and the free boundaries are introduced to describe the moving fronts of the infected region. The spatial-temporal risk index $ R_0^F(t) $, which depends on time $ t $, spatial heterogeneity and advection intensity, is derived by variational method. Sufficient conditions for the virus to extinct or to persist are given. Our results show that, if $ R^F_0(\infty)\leq 1 $, the virus extinct eventually, and if $ R^F_0(t_0)\geq 1 $ for some $ t_0\geq 0 $, the virus will spread continuously, while if $ R^F_0(0)<1<R^F_0(\infty) $, the extinction or persistence of the virus depends on the initial scale of infected mosquitoes and birds, or the size of the infected region, the advection intensity and other factors. Finally, numerical simulations indicate that the advection intensity and the expanding capability affect the spreading fronts of the infected region.
- West Nile virus /
- heterogeneity /
- advection /
- free boundary /
- the risk index

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References

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