title: Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary.
abstract: In this paper, a reaction-diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Transmission dynamics are based on a simplified model involving mosquitoes and birds, and the free boundary is introduced to model and explore the expanding front of the infected region. The spatial-temporal risk index [Formula: see text], which involves regional characteristic and time, is defined for the simplified reaction-diffusion model with the free boundary to compare with other related threshold values, including the usual basic reproduction number [Formula: see text]. Sufficient conditions for the virus to vanish or to spread are given. Our results suggest that the virus will be in a scenario of vanishing if [Formula: see text], and will spread to the whole region if [Formula: see text] for some [Formula: see text], while if [Formula: see text], the spreading or vanishing of the virus depends on the initial number of infected individuals, the area of the infected region, the diffusion rate and other factors. Moreover, some remarks on the basic reproduction numbers and the spreading speeds are presented and compared.
authors.affiliation: School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China.
authors.forename: Zhigui
authors.initials: Z
authors.lastname: Lin
authors.affiliation: Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada. huaiping@mathstat.yorku.ca.
authors.forename: Huaiping
authors.identifier: 0000-0003-2718-595X
authors.initials: H
authors.lastname: Zhu
mesh_terms: D025041:Animal Migration; D000818:Animals; D050936:Basic Reproduction Number / Q000706:statistics & numerical data; D001717:Birds / Q000821:virology*; D003198:Computer Simulation; D003465:Culex / Q000821:virology; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D000072138:Mosquito Vectors / Q000821:virology*; D009656:North America / Q000453:epidemiology; D014901:West Nile Fever / Q000453:epidemiology / Q000635:transmission* / Q000821:virology; D014902:West Nile virus / Q000472:pathogenicity*
keywords: Free boundary; Host birds; Reaction–diffusion systems; Risk index; Spatial spreading; Spreading speeds; The basic reproduction number; Vector mosquitoes; West Nile virus