TY - JOUR
T1 - Global behavior of a multi-group SIS epidemic model with age structure
AU - Feng, Zhilan
AU - Huang, Wenzhang
AU - Castillo-Chavez, Carlos
N1 - Funding Information:
Keywords: Partial differential equations; Global stability; Quasi-irreducibility; Threshold conditions; Epidemic model ∗Corresponding author. E-mail address: huangw@email.uah.edu (W. Huang). 1Research was supported in part by NSF Grant DMS-0314575 and by James S. McDonnell Foundation Grant JSMF-220020052. 2Research was supported in part by NSF Grant DMS-0204676. 3Research was supported in part by the grant directed toward the Mathematical and Theoretical Biological Institute (MTBI) from the following institutions: National Science Foundation (NSF), National Security Agency (NSA) and Alfred P. Sloan Foundation.
PY - 2005/11/15
Y1 - 2005/11/15
N2 - We study global dynamics of a system of partial differential equations. The system is motivated by modelling the transmission dynamics of infectious diseases in a population with multiple groups and age-dependent transition rates. Existence and uniqueness of a positive (endemic) equilibrium are established under the quasi-irreducibility assumption, which is weaker than irreducibility, on the function representing the force of infection. We give a classification of initial values from which corresponding solutions converge to either the disease-free or the endemic equilibrium. The stability of each equilibrium is linked to the dominant eigenvalue s(A), where A is the infinitesimal generator of a "quasi-irreducible" semigroup generated by the model equations. In particular, we show that if s(A) < 0 then the disease-free equilibrium is globally stable; if s(A) > 0 then the unique endemic equilibrium is globally stable.
AB - We study global dynamics of a system of partial differential equations. The system is motivated by modelling the transmission dynamics of infectious diseases in a population with multiple groups and age-dependent transition rates. Existence and uniqueness of a positive (endemic) equilibrium are established under the quasi-irreducibility assumption, which is weaker than irreducibility, on the function representing the force of infection. We give a classification of initial values from which corresponding solutions converge to either the disease-free or the endemic equilibrium. The stability of each equilibrium is linked to the dominant eigenvalue s(A), where A is the infinitesimal generator of a "quasi-irreducible" semigroup generated by the model equations. In particular, we show that if s(A) < 0 then the disease-free equilibrium is globally stable; if s(A) > 0 then the unique endemic equilibrium is globally stable.
KW - Epidemic model
KW - Global stability
KW - Partial differential equations
KW - Quasi-irreducibility
KW - Threshold conditions
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U2 - 10.1016/j.jde.2004.10.009
DO - 10.1016/j.jde.2004.10.009
M3 - Article
AN - SCOPUS:27744440076
SN - 0022-0396
VL - 218
SP - 292
EP - 324
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -