Extinction Effect of Parasites on Host Populations

Experimental studies have shown that parasites can reduce host density and even drive host population to extinction. Existing mathematical models for parasite-host interactions, while can address the host density reduction scenario, fail to explain such deterministic extinction phenomena. In order to understand the parasite induced host extinction, Ebert et al. (2000) formulated a plausible but ad hoc epidemiological microparasite model and its stochastic variation. The deterministic model, resembles a simple SI type model, predicts the existence of a globally attractive positive steady state. Their simulation of the stochastic model indicates that extinction of host is a likely outcome in some parameter regions. A careful examination of their ad hoc model reveals an often misinterpreted model assumption. Once this is corrected, we show that this model can indeed exhibit the observed parasite induced host extinction. This extinction dynamics resembles that of ratio-dependent predator-prey models. Mathematically, the extinction mechanism of this and ratio-dependent population models resulted from the degeneracy at the origin. We report here a complete global study of the revised parasite-host model. Biological implications and limitations of our findings are also presented. Short Title. Extinction effect of parasites on hosts