Open AccessCompeting species models with an infectious disease
Author(s) -
Roberto A. Saenz,
Herbert W. Hethcote
Publication year - 2006
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2006.3.219
Subject(s) - infectious disease (medical specialty) , disease , epidemic model , biology , population , competition (biology) , basic reproduction number , disease transmission , ecology , competitive exclusion , mortality rate , demography , statistics , zoology , mathematics , virology , medicine , sociology
The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number R(1) determines the asymptotic behavior, so that the disease dies out if R(1) </= 1 and approaches a globally attractive endemic equilibrium if R(1) > 1. Because the disease-reduced reproduction and disease-related death rates are often different in two competing species, a shared disease can change the outcome of the competition. Models of SIR and SIRS type are also considered. A key result in all of these models with the frequency-dependent incidence is that the disease must either die out in both species or remain endemic in both species.