# American Institute of Mathematical Sciences

December  2011, 4(6): 1599-1610. doi: 10.3934/dcdss.2011.4.1599

## Novel dynamics of a simple Daphnia-microparasite model with dose-dependent infection

 1 Department of Mathematics, College of Medicine, Third Military Medical University, Chongqing, 400038 2 School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281

Received  March 2009 Revised  September 2009 Published  December 2010

Many experiments reveal that Daphnia and its microparasite populations vary strongly in density and typically go through pronounced cycles. To better understand such dynamics, we formulate a simple two dimensional autonomous ordinary differential equation model for Daphnia magna-microparasite infection with dose-dependent infection. This model has a basic parasite production number $R_0=0$, yet its dynamics is much richer than that of the classical mathematical models for host-parasite interactions. In particular, Hopf bifurcation, stable limit cycle, homoclinic and heteroclinic orbit can be produced with suitable parameter values. The model indicates that intermediate levels of parasite virulence or host growth rate generate more complex infection dynamics.
Citation: Kaifa Wang, Yang Kuang. Novel dynamics of a simple Daphnia-microparasite model with dose-dependent infection. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1599-1610. doi: 10.3934/dcdss.2011.4.1599
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