The Diffusive Model for West Nile Virus on a Periodically Evolving Domain

In this paper, we investigate the impact of a periodically evolving domain on the dynamics of the diffusive West Nile virus. A reaction-diffusion model on a periodically and isotropically evolving domain which describes the transmission of the West Nile virus is proposed. In addition to the classical basic reproduction number, the spatial-temporal basic reproduction number depending on the periodic evolution rate is introduced and its properties are discussed. Under some conditions, we explore the long-time behavior of the virus. The virus will go extinct if the spatial-temporal basic reproduction number is less than or equal to one. The persistence of the virus happens if the spatial-temporal basic reproduction number is greater than one. We consider special case when the periodic evolution rate is equivalent to one to better understand the impact of the periodic evolution rate on the persistence or extinction of the virus. Some numerical simulations are performed in order to illustrate our analytical results. Our theoretical analysis and numerical simulations show that the periodic change of the habitat range plays an important role in the West Nile virus transmission, in particular, the increase of periodic evolution rate has positive effect on the spread of the virus.