Open AccessGlobal stability of a class of discrete age-structured SIS models with immigration
Author(s) -
Yicang Zhou,
Zhien Ma
Publication year - 2009
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.2009.6.409
Subject(s) - immigration , stability (learning theory) , basic reproduction number , population , mathematical economics , population growth , discrete time and continuous time , age structure , economics , mathematics , demography , computer science , sociology , geography , statistics , archaeology , machine learning
Immigration has an important influence on the growth of population and the transmission dynamics of infectious diseases. A discrete age-structured epidemic SIS model with immigration is formulated and its dynamical behavior is studied in this paper. It is found that population growth will be determined by the reproductive number and the immigration rate. In the simple case without infected immigration, the basic reproductive number is defined, and the global stability of equilibria is investigated. In the case with infected immigration, there is no disease-free equilibrium, and there always exists an endemic equilibrium, and the global stability conditions of the unique endemic equilibrium is obtained.