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Local stability of an SIR epidemic model and effect of time delay
Author(s) -
Tchuenche Jean M.,
Nwagwo Alexander
Publication year - 2009
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.1136
Subject(s) - mathematics , epidemic model , linearization , stability (learning theory) , mathematical proof , basic reproduction number , discrete time and continuous time , lyapunov function , control theory (sociology) , nonlinear system , control (management) , statistics , computer science , geometry , population , demography , quantum mechanics , machine learning , artificial intelligence , sociology , physics
We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stability is given. The proofs are based on linearization and the application of Lyapunov functional approach. An upper bound of the critical time delay for which the model remains valid is derived. Numerical simulations are carried out to illustrate the effect of time delay which tends to reduce the epidemic threshold. Copyright © 2009 John Wiley & Sons, Ltd.