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Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence
Author(s) -
Teng Zhidong,
Wang Lei,
Nie Linfei
Publication year - 2015
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.3389
Subject(s) - mathematics , discretization , lyapunov function , basic reproduction number , epidemic model , class (philosophy) , nonlinear system , discrete time and continuous time , mathematical economics , section (typography) , zero (linguistics) , mathematical analysis , statistics , computer science , demography , population , artificial intelligence , linguistics , physics , philosophy , quantum mechanics , sociology , operating system
This paper deals with global dynamics of a class of delayed discrete susceptible‐infected‐recovered (SIR) compartmental epidemic models with general nonlinear incidence rate and disease‐induced mortality, which are proposed from the Mickens nonstandard discretization of the corresponding delayed continuous epidemic models. By constructing discrete Lyapunov functions, the sufficient conditions for the global attractivity of the disease‐free equilibrium and endemic equilibrium are established. Under some additional assumptions (see ( H 3 ) in Section 3 and ( H 4 ) in Section 4), it is shown that the disease‐free equilibrium is globally attractive when basic reproduction numberR 0 ≤ 1 , and whenR 0 > 1 , there is a unique endemic equilibrium, which is globally attractive. Furthermore, some special cases are discussed, and as corollaries, several idiographic results are established. Copyright © 2015 John Wiley & Sons, Ltd.