Competitive Exclusion In A Vector-host Epidemic Model With Discrete Delay

A multi-group model of a vector-borne disease with discrete delay in the vector and the host is investigated. It is showed that if the reproduction number of the mode Ro<1, the unique disease-free equilibrium is shown to be globally asymptotically stable. Without loss of generality strain one is assumed to have the largest reproduction number. In this case, the dominance equilibrium of strain one is shown to be locally stable. The basic reproduction number for a strain i(R(?)) is written as a product of the reproduction number of the vector (R(?)) and the reproduction number of the host (R(?)), i.e., R(?)=R(?)R(?). The competitive exclusion principle is derived under the somewhat stronger condition that if strain i suits strain i dominance equilibrium is globally asymptotically stable.