Journal of Mathematical Biology

, Volume 46, Issue 1, pp 17–30 | Cite as

Deterministic extinction effect of parasites on host populations

  • Tzy-Wei Hwang
  • Yang Kuang


 Experimental studies have shown that parasites can reduce host density and even drive host population to extinction. Conventional 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 suggests an alternative and plausible model assumption. With this modification, we show that the revised parasite-host model can exhibit the observed parasite induced host extinction. This finding strengthens and complements that of Ebert et al. (2000), since all continuous models are likely break down when all population densities are small. This extinction dynamics resembles that of ratio-dependent predator-prey models. We report here a complete global study of the revised parasite-host model. Biological implications and limitations of our findings are also presented.


Deterministic Model Host Population Parameter Region Extinction Effect Stochastic Variation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Tzy-Wei Hwang
    • 1
  • Yang Kuang
    • 2
  1. 1.Department of Mathematics, Kaohsiung Normal University, 802, Kaohsiung, Taiwan, R.O.C. Research supported by National Council of Science, Republic of China.TW
  2. 2.Department of Mathematics, Arizona state University, Tempe, AZ 85287-1804, U.S.A. e-mail: kuang@asu.eduUS

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