Open AccessGlobal stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds
Author(s) -
C. Connell McCluskey
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2015008
Subject(s) - age structure , immigration , epidemic model , infectious disease (medical specialty) , stability (learning theory) , lyapunov function , tuberculosis , disease , econometrics , demography , medicine , mathematics , computer science , geography , sociology , physics , population , archaeology , pathology , nonlinear system , quantum mechanics , machine learning
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.