Competing species models with an infectious disease.

The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number R(1) determines the asymptotic behavior, so that the disease dies out if R(1) </= 1 and approaches a globally attractive endemic equilibrium if R(1) > 1. Because the disease-reduced reproduction and disease-related death rates are often different in two competing species, a shared disease can change the outcome of the competition. Models of SIR and SIRS type are also considered. A key result in all of these models with the frequency-dependent incidence is that the disease must either die out in both species or remain endemic in both species.