@article{Bao2022, 
author = {Xiaomei Bao and Canrong Tian},
title = {Stability in a Ross epidemic model with road diffusion},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {2},
pages = {2840-2857},
keywords = {epidemic model, basic reproduction number, asymptotic stability, road diffusion},
url = {https://www.sciopen.com/article/10.3934/math.2022157},
doi = {10.3934/math.2022157},
abstract = {Reaction-diffusion equations have been used to describe the dynamical behavior of epidemic models, where the spreading of infectious disease has the same speed in every direction. A natural question is how to describe the dynamical system when the spreading of infectious disease is directed diffusion. We introduce the road diffusion into a Ross epidemic model which describes the spread of infected Mosquitoes and humans. With the comparison principle the system is proved to have a unique global solution. By the approach of upper and lower solutions, we show that the disease-free equilibrium is asymptotically stable if the basic reproduction number is lower than 1 while the endemic equilibrium asymptotically stable if the basic reproduction number is greater than 1.}
}