Competitive exclusion in an infection-age structured model with environmental transmission

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Martcheva, Maia¹  Li, Xue-Zhi² 

[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA

[2] Xinyang Normal Univ, Dept Math, Xinyang 464000, Peoples R China

关键词: Mathematical models;    Age-since-infection;    Multi-strain;    Competitive exclusion;    Reproduction number;    Environmental transmission;    Avian influenza;   

DOI  :  10.1016/j.jmaa.2013.05.064

来源: Elsevier

【 摘 要 】

It has been shown in the past that for the most basic multi-strain ordinary differential equation (ODE) model of SIR-type a competitive exclusion principle holds. The competitive exclusion principle means that the strain with the largest reproduction number persists but eliminates all other strains with suboptimal reproduction numbers. In this paper, we extend the competitive exclusion principle to a multi-strain age-since-infection structured model of SIR/SI-type. We also include environmental transmission for each of the pathogens. The model describes well transmission of avian influenza or cholera. Using a Lyapunov functional, we are able to establish global stability of the disease-free equilibrium if all reproduction numbers are smaller or equal to one. If R-j, the reproduction number of strain j is larger than one, then a single-strain equilibrium, corresponding to strain j exists. This single strain equilibrium is locally stable whenever R-j > 1 and R-j is the unique maximal reproduction number. If R-1 > 1 is the maximal reproduction number, using a Lyapunov functional, we establish that the corresponding single-strain equilibrium E-1 is globally stable. That is, strain one eliminates all other strains, independently of their reproduction numbers as long as they are smaller than R-1. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free