Open AccessCoexistence of a cross-diffusive West Nile virus model in a heterogenous environment
Author(s) -
Abdelrazig K. Tarboush,
Jun Ge,
Zhigui Lin
Publication year - 2018
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2018068
Subject(s) - basic reproduction number , diffusion , west nile virus , eigenvalues and eigenvectors , monotone polygon , mathematics , transmission (telecommunications) , reproduction , operator (biology) , statistical physics , computer science , physics , biology , virus , virology , ecology , demography , quantum mechanics , geometry , genetics , telecommunications , population , repressor , sociology , transcription factor , gene
This paper is concerned with a strongly-coupled elliptic system, which describes a West Nile virus (WNv) model with cross-diffusion in a heterogeneous environment. The basic reproduction number is introduced through the next generation infection operator and some related eigenvalue problems. The existence of coexistence states is presented by using a method of upper and lower solutions. The true positive solutions are obtained by monotone iterative schemes. Our results show that a cross-diffusive WNv model possesses at least one coexistence solution if the basic reproduction number is greater than one and the cross-diffusion rates are small enough, while if the basic reproduction number is less than or equal to one, the model has no positive solution. To illustrate the impact of cross-diffusion and environmental heterogeneity on the transmission of WNv, some numerical simulations are given.