Stability of the endemic coexistence equilibrium for one host and two parasites

T. Dhirasakdanon, Horst Thieme

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically transmitted and cannot persists just by itself. We give several sufficient conditions for the equilibrium to be locally asymptotically stable. One of them is that the horizontal transmission is of density-dependent (mass-action) type. If the horizontal transmission is of frequency-dependent (standard) type, we show that, under certain conditions, the equilibrium can be unstable and undamped oscillations can occur. We support and extend our analytical results by numerical simulations and by two-dimensional plots of stability regions for various pairs of parameters.

Original languageEnglish (US)
Pages (from-to)109-138
Number of pages30
JournalMathematical Modelling of Natural Phenomena
Issue number6
StatePublished - Jan 2010


  • Routh-Hurwitz conditions
  • SI endemic model
  • coexistence of parasite strains
  • disease incidence
  • disease-related fertility reduction
  • horizontal transmission
  • undamped oscillations
  • vertical transmission

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


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