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

Kaifa Wang, Yang Kuang

Research output: Contribution to journalArticle

1 Scopus citations

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 magnamicroparasite 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.

Original languageEnglish (US)
Pages (from-to)1599-1610
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume4
Issue number6
DOIs
StatePublished - Dec 1 2011

Keywords

  • Daphnia magna-microparasite model
  • Dose-dependent infection
  • Heteroclinic orbit
  • Homoclinic orbit
  • Hopf bifurcation
  • Limit cycle

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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