Open AccessA multi-group SIR epidemic model with age structure
Author(s) -
Toshikazu Kuniya,
Jinliang Wang,
Hisashi Inaba
Publication year - 2016
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2016109
Subject(s) - epidemic model , spectral radius , mathematics , basic reproduction number , lyapunov function , nonlinear system , exponential stability , constant (computer programming) , stability (learning theory) , graph , age structure , radius , group (periodic table) , pure mathematics , mathematical analysis , combinatorics , eigenvalues and eigenvectors , demography , physics , computer science , population , quantum mechanics , sociology , computer security , machine learning , programming language
This paper provides the first detailed analysis of a multi-group SIR epidemic model with age structure, which is given by a nonlinear system of 3n partial differential equations. The basic reproduction number R-0 is obtained as the spectral radius of the next generation operator, and it is shown that if R-0 1, then the disease-free equilibrium is globally asymptotically stable, while if R-0 > 1, then an endemic equilibrium exists. The global asymptotic stability of the endemic equilibrium is also shown under additional assumptions such that the transmission coefficient is independent from the age of infective individuals and the mortality and removal rates are constant. To our knowledge, this is the first paper which applies the method of Lyapunov functional and graph theory to a multi-dimensional PDE system