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

C. Connell McCluskey

doi:10.3934/mbe.2015008

Article Contents

2016, Volume 13, Issue 2: 381-400. Doi: 10.3934/mbe.2015008

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

C. Connell McCluskey^1,

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

Received: April 30, 2015

Revised: August 31, 2015

Published: December 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 34K20, 92D30.

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