Global proprieties of an SIR epidemic model with nonlocal diffusion and immigration

Results in Physics

Mohammed Sh. Alhodaly¹  Tareq Saeed²  Anwar Zeb³  Salih Djilali⁴  Nadia Gul⁵ 

[1] Corresponding authors.;Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef, Algeria;Department of Mathematics, COMSATS University Islamabad, Abbottabad, 22060, Khyber Pakhtunkhwa, Pakistan;Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria;Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;

关键词: SIR model;    Immigration;    Global stability;    Nonlocal diffusion;    Lyapunov function;   

DOI  :  

来源: DOAJ

【 摘 要 】

Immigration is the responsible for transmitting disease from one country to another. In this research, we investigate the global proprieties of an SIR model with nonlocal dispersal and immigration. The main purpose is to show that immigration will eliminate the threshold dynamics known for SIR epidemic models, and leads to the persistence of the disease independently of the parameters. Based on Lipschitz continuity of parameters, it has been shown that the strictly positive equilibrium state exists and it is unique. Using the infected density equilibrium as the integral kernel of a Lyapunov function, we also proved the global attractiveness of the endemic equilibrium state, the mathematical findings are checked numerically.

【 授权许可】

Unknown