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

Kaifa Wang, Yang Kuang

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 2011

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Infection
Dose
Dependent
Heteroclinic Orbit
Hopf bifurcation
Homoclinic Orbit
Ordinary differential equations
Limit Cycle
Hopf Bifurcation
Ordinary differential equation
Orbits
Vary
Model
Mathematical Model
Mathematical models
Cycle
Interaction
Experiment
Parasites
Experiments

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Novel dynamics of a simple Daphnia-microparasite model with dose-dependent infection. / Wang, Kaifa; Kuang, Yang.

In: Discrete and Continuous Dynamical Systems - Series S, Vol. 4, No. 6, 12.2011, p. 1599-1610.

Research output: Contribution to journalArticle

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