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 e#ect of parasites on hosts Key words: Microparasite model, Ratio-dependent predator-prey model, host extinction, global stability, biological control. AMS(MOS) Subject Classification(2000): 34C25, 34C35, 92D25. # Department of Mathematics, Kaohsiung Normal University, 802, Kaohsiung, Taiwan, R.O.C. Research supported by National Council of Science, Republic of China. + Department of Mathematics, Arizona state University, Tempe, AZ 85287-1804, U.S.A. Correspondence should be...

While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratiodependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics. Two trophic level Michaelis-Menten type ratio-dependent predator-prey system was globally and systematically analyzed in details recently. A distinct and realistic feature of ratio-dependence is its capability of producing the extinction of prey species, and hence the collapse of the system. Another distinctive feature of this model is that its dynamical outcomes may depend on initial populations levels. Theses features, if preserved in a three trophic food chain model, make it appealing for modelling certain biological control processes (where prey is a plant species, middle predator as a pest, and top predator as a biological control agent) where the simultaneous extinctions of pest and control agent is the hallmark of their successes and are usually dependent on the amount of control agent. Our results indicate that this extinction dynamics and sensitivity to initial population levels are not only preserved, but also enriched in the three trophic level food chain model. Specifically, we provide partial answers to questions such as: under what scenarios a potential biological control may be successful, and when it may fail. We also study the questions such as what conditions ensure the coexistence of all the three species in the forms of a stable steady state and limit cycle, respecti...