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Novel dynamics of a simple Daphnia microparasite model with dose-dependent infection. (English) Zbl 1214.92065
Summary: 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.
MSC:
92D30Epidemiology
65C20Models (numerical methods)
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
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