Global behavior of a multi-group SIS epidemic model with age structure |
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Authors: | Zhilan Feng Wenzhang Huang Carlos Castillo-Chavez |
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Institution: | a Purdue University, West Lafayette, IN 47907, USA b University of Alabama in Huntsville, Huntsville, AL 35899, USA c Arizona State University, Tempe, AZ 85287, USA |
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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. |
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Keywords: | Partial differential equations Global stability Quasi-irreducibility Threshold conditions Epidemic model |
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