An [Formula: see text] epidemiological model with suscptibles dispersal between two patches is addressed and discussed. The basic reproduction numbers [Formula: see text] and [Formula: see text] are defined as the threshold parameters. It shows that if both [Formula: see text] and [Formula: see text] are below unity, the disease-free equilibrium is shown to be globally asymptotically stable by using the comparison principle of the cooperative systems. If [Formula: see text] is above unity and [Formula: see text] is below unity, the disease persists in the first patch provided [Formula: see text]. If [Formula: see text] is above unity, [Formula: see text] is below unity, and [Formula: see text], the disease persists in the second patch. And if [Formula: see text] and [Formula: see text] are above unity, and further [Formula: see text] and [Formula: see text] 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