Novel dynamics of a simple Daphnia-microparasite model with dose-dependent infection Kaifa Wang a* and Yang Kuang b a Department of Computers Science, Third Military Medical University, Chongqing, 400038, P. R. China. b Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, U.S.A. Abstract Many experiments reveal that Daphnia and its microparasite populations vary strongly in density and typically go through pronounced cycles. To better un- derstand such dynamics, we formulate a simple two dimensional autonomous ordinary differential equation model for Daphnia magna-microparasite infec- tion 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 math- ematical models for host-parasite interactions. In particular, Hopf bifurcation, stable limit cycle, homoclinic and heteroclinic orbit can be produced with suit- able parameter values. The model indicates that intermediate levels of parasite virulence or host growth rate generate more complex infection dynamics. Key words: Daphnia magna-microparasite model, dose-dependent infection, homoclinic orbit, heteroclinic orbit, limit cycle, Hopf bifurcation AMS subject classifications: 92D25, 34C60 1 Introduction Recently, theory on the effects of parasites on host population dynamics has received much attention and epidemiological models are often used to explain empirical results for host- parasite interaction system ([5, 8]). In these studies, authors are particularly interested in microparasites, that is, small, unicellular parasites that have direct reproduction within their * Corresponding author. E-mail addresses: kaifawang@yahoo.com.cn (K. Wang), kuang@asu.edu (Y. Kuang) 1