Order reprints

Competing species models with an infectious disease

Roberto A. Saenz Herbert W. Hethcote

*Corresponding author:  

MBE2006,1,219doi:10.3934/mbe.2006.3.219

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 $\mathbf{R}_1$ determines the asymptotic behavior, so that the disease dies out if $\mathbf{R}_1 \leq 1$ and approaches a globally attractive endemic equilibrium if $\mathbf{R}_1 > 1$. 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.

Please supply your name and a valid email address you yourself

Fields marked*are required

Article URL   http://www.aimspress.com/MBE/article/2902.html
Article ID   1551-0018_2006_1_219
Editorial Email  
Your Name *
Your Email *
Quantity *

Copyright © AIMS Press All Rights Reserved