Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence. (29th January 2015)

• Record Type: Journal Article
• Authors: Teng, Zhidong; Wang, Lei; Nie, Linfei
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 18(2015:Dec. 15)
• Page Start: 4741
• Page End: 4759
• Publication Date: 2015-01-29
• Subjects: delayed discrete SIRS epidemic model -- global attractivity -- nonlinear incidence rate -- discrete Lyapunov function -- subclass39A30 Stability theory -- 92D30 Epidemiology; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3389
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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 ) inSection 3 and ( H 4 ) inSection 4 ), it is shown that the disease‐free equilibrium is globally attractive when basic reproduction number R 0 ≤ 1, and when R 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.