Global stability of a class of discrete
age-structured SIS models with immigration
-
Received:
01 December 2007
Accepted:
29 June 2018
Published:
01 March 2009
-
-
MSC :
Primary: 92D30; Secondary: 39A11.
-
-
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.
Citation: Yicang Zhou, Zhien Ma. Global stability of a class of discreteage-structured SIS models with immigration[J]. Mathematical Biosciences and Engineering, 2009, 6(2): 409-425. doi: 10.3934/mbe.2009.6.409
-
Abstract
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.
-
-
-
-