Math. Model. Nat. Phenom.
Volume 5, Number 6, 2010Ecology (Part 2)
|109 - 138
|08 April 2010
Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites
School of Mathematical and Statistical Sciences Arizona State
* Corresponding author. E-mail:
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.
Mathematics Subject Classification: 92D30 / 34C25 / 34D20
Key words: coexistence of parasite strains / disease incidence / SI endemic model / Routh-Hurwitz conditions / undamped oscillations / vertical transmission / horizontal transmission / disease-related fertility reduction
© EDP Sciences, 2010
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