Global dynamics for an SIR patchy model with susceptibles dispersal

Advances in Difference Equations

Weiyun Cai¹  Luju Liu¹  Yusen Wu¹ 

[1] School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, P.R. China

关键词: H1N1 Influenza;    Epidemic Model;    Comparison Principle;    Endemic Equilibrium;    Basic Reproduction Number;   

DOI  :  10.1186/1687-1847-2012-131

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

AnSIRepidemiological model with suscptibles dispersal between two patches is addressed and discussed. The basic reproduction numbersR01andR02are defined as the threshold parameters. It shows that if bothR01andR02are below unity, the disease-free equilibrium is shown to be globally asymptotically stable by using the comparison principle of the cooperative systems. IfR01is above unity andR02is below unity, the disease persists in the first patch providedS21∗S22∗andS12∗>S11∗are satisfied, the unique endemic equilibrium is globally asymptotically stable by constructing the Lyapunov function. Furthermore, it follows that the susceptibles dispersal in the population does not alter the qualitative behavior of the epidemiological model.

【 授权许可】

CC BY