Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment

Abstract

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.

On a partially degenerate West Nile virus model in closed advective environments

“…They demonstrated the existence of traveling wave solutions and calculated the rate of spatial spread of infection. For further related results on WNv epidemic models, see [1,[3][4][5]13,16,22,25,26,30,37,38,41,42,[47][48][49] and the references therein. It is worth noting that the virus primarily transmits between birds and mosquitoes, where birds act as primary reservoir hosts and mosquitoes as vectors.…”

West Nile virus IgG antibodies among blood donors in Sudan: a cross-sectional study

“…Arthropod-borne flavivirus (arboviruses) have a zoonotic cycle that includes both birds and mosquitoes as amplifiers and horses and humans as dead-end hosts [ [8] , [9] , [10] ], this cycle granted wide distribution of the virus, birds act as main of long-distance dispersal of the virus and mosquitoes diffuse the virus in a short distance) [ 5 , 8 ]. Currently, WNV is the widespread flavivirus exist in all continents except Antarctica [ 9 , 11 , 12 ]. Human to human transmissions of WNV do not occur in natural situations [ 6 ], it could occur through transplanted organs, blood transfusion, trans-placental infection, and mother-to-child transmission through breastfeeding [ 13 ].…”

“…In the absence of a vaccine and specific treatment, the only way to reduce infection is by raising awareness of the risk factors, reducing the risk of transmission through organ transplant and blood transfusion [ 10 , 12 ]. The present study aimed to determine WNV IgG antibodies among blood donors at Khartoum central blood bank, Sudan.…”

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

“…e dynamics of the spatial dependence model (1) has been studied. e existence and nonexistence of the coexistence states in a heterogeneous environment have been investigated in [18]. e impact of the environmental heterogeneity and seasonal periodicity on the transmission of WNv was considered in [19].…”