Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501609 | Journal of Differential Equations | 2005 | 33 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Zhilan Feng, Wenzhang Huang, Carlos Castillo-Chavez,