Novel dynamics of a simple Daphnia-microparasite
model with dose-dependent infection
Kaifa Wang - Department of Mathematics, College of Medicine, Third Military Medical University, Chongqing, 400038, China (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
Received: March 2009; Revised: September 2009; Published: December 2010.