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Global behaviour of an SIR epidemic model with time delay
Author(s) -
Tchuenche Jean M.,
Nwagwo Alexander,
Levins Richard
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.810
Subject(s) - mathematics , invariance principle , stability (learning theory) , epidemic model , basic reproduction number , variance (accounting) , lyapunov function , mathematical economics , epistemology , demography , computer science , nonlinear system , economics , population , philosophy , physics , accounting , quantum mechanics , machine learning , sociology
Abstract We study the stability of a delay susceptible–infective–recovered epidemic model with time delay. The model is formulated under the assumption that all individuals are susceptible, and we analyse the global stability via two methods—by Lyapunov functionals, and—in terms of the variance of the variables. The main theorem shows that the endemic equilibrium is stable. If the basic reproduction number ℛ 0 is less than unity, by LaSalle invariance principle, the disease‐free equilibrium E s is globally stable and the disease always dies out. By applying the integral averaging theory, we also investigate the stability in variance of the model. Copyright © 2006 John Wiley & Sons, Ltd.