# Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites

T. Dhirasakdanon; H. R. Thieme

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 6, page 109-138
- ISSN: 0973-5348

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topDhirasakdanon, T., and Thieme, H. R.. "Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites." Mathematical Modelling of Natural Phenomena 5.6 (2010): 109-138. <http://eudml.org/doc/197678>.

@article{Dhirasakdanon2010,

abstract = {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.},

author = {Dhirasakdanon, T., Thieme, H. R.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {coexistence of parasite strains; disease incidence; SI endemic model; Routh-Hurwitz conditions; undamped oscillations; vertical transmission; horizontal transmission; disease-related fertility reduction},

language = {eng},

month = {4},

number = {6},

pages = {109-138},

publisher = {EDP Sciences},

title = {Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites},

url = {http://eudml.org/doc/197678},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Dhirasakdanon, T.

AU - Thieme, H. R.

TI - Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/4//

PB - EDP Sciences

VL - 5

IS - 6

SP - 109

EP - 138

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/197678

ER -

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