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AnS  I  Repidemiological model with suscptibles dispersal between two patches is addressed and discussed. The basic reproduction numbersR  01andR  02are defined as the threshold parameters. It shows that if bothR  01andR  02are below unity, the disease-free equilibrium is shown to be globally asymptotically stable by using the comparison principle of the cooperative systems. IfR  01is above unity andR  02is below unity, the disease persists in the first patch providedS  2   1  ∗    <   S  2   2  ∗. IfR  02is above unity,R  01is below unity, andS  1   2  ∗    <   S  1   1  ∗, the disease persists in the second patch. And ifR  01andR  02are above unity, and furtherS  2   1  ∗    >   S  2   2  ∗andS  1   2  ∗    >   S  1   1  ∗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.   Electronic supplementary material  The online version of this article (doi:10.1186/1687-1847-2012-131) contains supplementary material, which is available to authorized users.

Global dynamics for an SIR patchy model with susceptibles dispersal