An analysis of the coexistence of two host species with a shared pathogen.

Population dynamics of two-host species under direct transmission of an infectious disease or a pathogen is studied based on the Holt-Pickering mathematical model, which accounts for the influence of the pathogen on the population of the two-host species. Through rigorous analysis and a numerical scheme of study, circumstances are specified under which the shared pathogen leads to the coexistence of the two-host species in either a persistent or periodic form. This study shows the importance of intrinsic growth rates or the differences between birth rates and death rates of the two host susceptible in controlling these circumstances. It is also demonstrated that the periodicity may arise when the positive intrinsic growth rates are very small, but the periodicity is very weak which may not be observed in an empirical investigation.