# American Institute of Mathematical Sciences

2016, 13(2): 381-400. doi: 10.3934/mbe.2015008

## Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds

 1 Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

Received  May 2015 Revised  September 2015 Published  December 2015

We study a model of disease transmission with continuous age-structure for latently infected individuals and for infectious individuals and with immigration of new individuals into the susceptible, latent and infectious classes. The model is very appropriate for tuberculosis. A Lyapunov functional is used to show that the unique endemic equilibrium is globally stable for all parameter values.
Citation: C. Connell McCluskey. Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 381-400. doi: 10.3934/mbe.2015008
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