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Spreading and vanishing in a West Nile virus model with expanding fronts

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Abstract

We study a simplified version of a West Nile virus (WNv) model discussed by Lewis et al. (2006), which was considered as a first approximation for the spatial spread of WNv. The basic reproduction number R 0 for the non-spatial epidemic model is defined and a threshold parameter R 0 D for the corresponding problem with null Dirichlet boundary condition is introduced. We consider a free boundary problem with a coupled system, which describes the diffusion of birds by a PDE and the movement of mosquitoes by an ODE. The risk index R 0 F(t) associated with the disease in spatial setting is represented. Sufficient conditions for the WNv to eradicate or to spread are given. The asymptotic behavior of the solution to the system when the spreading occurs is considered. It is shown that the initial number of infected populations, the diffusion rate of birds and the length of initial habitat exhibit important impacts on the vanishing or spreading of the virus. Numerical simulations are presented to illustrate the analytical results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11371311) and Top-Notch Academic Programs Project of Jiangsu Higher Education Institutions (Grant No. PPZY2015B109).

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Authors and Affiliations

  1. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China

    Abdelrazig K. Tarboush, ZhiGui Lin & MengYun Zhang

  2. Department of Mathematics, Faculty of Education, University of Khartoum, Khartoum 321, Sudan

    Abdelrazig K. Tarboush

Authors
  1. Abdelrazig K. Tarboush
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  2. ZhiGui Lin
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  3. MengYun Zhang
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Correspondence to ZhiGui Lin.

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Tarboush, A.K., Lin, Z. & Zhang, M. Spreading and vanishing in a West Nile virus model with expanding fronts. Sci. China Math. 60, 841–860 (2017). https://doi.org/10.1007/s11425-016-0367-4

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  • DOI: https://doi.org/10.1007/s11425-016-0367-4

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