Positive steady states of a SI epidemic model with cross diffusion

作者：

Highlights：

• A spatiotemporal SI epidemic model with nonlinear diffusion is proposed and sufficient conditions are derived for the coexistence of the susceptible and infected populations.

• The nonlinear diffusion terms are proposed for the first time in literature and through our analysis we have confirmed that coexistence of the participating species is possible under its influence.

• The system exhibits Turing instability and numerical simulations is carried out to observe the phenomenon of pattern formation.

• Our work provides a significant insight as how epidemic models are influenced by nonlinear diffusion.

摘要

•A spatiotemporal SI epidemic model with nonlinear diffusion is proposed and sufficient conditions are derived for the coexistence of the susceptible and infected populations.•The nonlinear diffusion terms are proposed for the first time in literature and through our analysis we have confirmed that coexistence of the participating species is possible under its influence.•The system exhibits Turing instability and numerical simulations is carried out to observe the phenomenon of pattern formation.•Our work provides a significant insight as how epidemic models are influenced by nonlinear diffusion.

论文关键词：Strongly coupled diffusion,Coupled upper and lower solutions,Coexistence,Turing instability,Pattern formation

论文评审过程：Received 2 February 2021, Revised 22 May 2021, Accepted 31 May 2021, Available online 30 June 2021, Version of Record 30 June 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126423