Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

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

Pages: 1599 - 1610, Volume 4, Issue 6, December 2011      doi:10.3934/dcdss.2011.4.1599

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Kaifa Wang - Department of Mathematics, College of Medicine, Third Military Medical University, Chongqing, 400038, China (email)
Yang Kuang - School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281, United States (email)

Abstract: 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.

Keywords:  Daphnia magna-microparasite model, dose-dependent infection, homoclinic orbit, heteroclinic orbit, limit cycle, Hopf bifurcation
Mathematics Subject Classification:  Primary: 92D25; Secondary: 34C60.

Received: March 2009;      Revised: September 2009;      Available Online: December 2010.