2017
DOI: 10.1002/mma.4391
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Global stability of a discrete multigroup SIR model with nonlinear incidence rate

Abstract: In this paper, by applying nonstandard finite difference scheme, we propose a discrete multigroup Susceptible‐Infective‐Removed (SIR) model with nonlinear incidence rate. Using Lyapunov functions, it is shown that the global dynamics of this model are completely determined by the basic reproduction number scriptR0. If scriptR0⩽1, then the disease‐free equilibrium is globally asymptotically stable; if scriptR0>1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Example… Show more

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Cited by 17 publications
(24 citation statements)
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“…However, as mentioned in [9], a general incidence rate may help us to gain the unification theory by the omission of unessential details. For more details about nonlinear incidence rates, we refer to see [10][11][12] and references cited in. Hence, inspired by the aforementioned literatures, we consider the following delayed model with general nonlinear incidence:…”
Section: Discrete Dynamics In Nature and Societymentioning
confidence: 99%
See 1 more Smart Citation
“…However, as mentioned in [9], a general incidence rate may help us to gain the unification theory by the omission of unessential details. For more details about nonlinear incidence rates, we refer to see [10][11][12] and references cited in. Hence, inspired by the aforementioned literatures, we consider the following delayed model with general nonlinear incidence:…”
Section: Discrete Dynamics In Nature and Societymentioning
confidence: 99%
“…However, how to select a proper discrete method so that the global properties of solutions of the corresponding continuous models can be efficiently preserved is still an open problem [14]. Recently, Mickens has made an attempt in this regard, by proposing a robust nonstandard finite difference (NSFD) scheme [15,16], which has been widely employed in the study of different kinds of epidemic models and one important advantage of Mickens' method is that it can be more efficient in preserving the global dynamics to the corresponding continuous epidemic models [10,[17][18][19][20][21][22][23]. However, there is no result about discrete viral infection model with time delays and immune response.…”
Section: Discrete Dynamics In Nature and Societymentioning
confidence: 99%
“…Giordano et al (2020) utilizam uma variação do modelo SIR (Suscetíveis, Infectados, Removidos) para modelar a epidemia na Itália, que intitularam SIDARTHE. São muitos parâmetros a serem estimados e eles concluem que uma infinidade de combinações com diferentes parâmetros consegue um mesmo resultado bom em termos de reproduzir o fenômeno real.…”
Section: Introductionunclassified
“…Our objective here is to present and analyse an SIR or SI like ODE model for non-smokers, tobacco smokers, and those who smoke e-cigarettes, incorporating peer pressure in the switch from tobacco to e-cigarette smoking. We note that differential equation models have been used extensively in modelling social problems and related issues, including the spread of infections; see, eg, Bissell,7,8 Bissell et al, 9 Buonomo et al, 10 Caiado, 11 Ciarcia et al, 12 Giacobbe and Mulone, 13 Giacobbe et al, 14 Gonzalez et al, 15 Guo et al, 16 Hethcote et al, 17 Huo and Song, 18 Huo and Wang, 19 Jung et al, 20 Mulone and Straughan, 21,22 Mulone et al, 23 Mushanyu et al, 24 Nyabadza et al, 25 Pomeroy, 26 Sharomi and Gumel, 27 Srivastava and Günerhan, 28 Straughan, 29 Takeuchi et al, 30 Usaini et al, 31 Walters, 32 Walters and Kendal, 33 Wang, 34 Wang et al, 35 Wang and Mulone, 36 Wang and Zhao, 37,38 Wang and Zou, 39 and Zhou et al 40 In particular, SIR models and ramifications thereof, such as those involving conformity bias (Walters, 32 Walters and Kendal, 33 and Bissell 8 ), incorporating external information (Buonomo et al 10 and Giacobbe et al 14 ), and allowing for multi-patch models (Wang and Mulone 36 ), have been employed in...…”
Section: Introductionmentioning
confidence: 99%