Stability of a delayed SIRS epidemic model with a nonlinear incidence rate

Xu, Rui; Ma, Zhien

doi:10.1016/j.chaos.2008.09.007

Cited by 120 publications

(67 citation statements)

References 17 publications

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“…The second one is the saturated incidence rate βSI 1+α1S+α2I , where α 1 and α 2 are the parameter that measure the inhibitory effect [1,4,10,11,18,20]. The third one is the standard incidence rate βSI S+I+R [6].…”

Section: The Mathematical Modelmentioning

confidence: 99%

Global Analysis for a Delay-Distributed SIR Epidemic Model

et al. 2013

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Abstract. One of the most tools for describing the incubation period in the epidemiological dynamic models is the distributed delays. In this paper, we propose a delay-distributed SIR epidemic model with a nonlinear incidence rate. Using the Lyapunov theory and LaSalle's principle, we show the global asymptotic stability of the disease-free and the endemic equilibria. This analysis extends and performs existing results.

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Section: The Mathematical Modelmentioning

confidence: 99%

Global Analysis for a Delay-Distributed SIR Epidemic Model

et al. 2013

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“…(4) The saturated incidence rate of the form /(1 + 2 ) ( [16][17][18][19][20][21]), where 2 is a positive constant. (5) The saturated incidence rate of the form /(1+ 1 + 2 ) ( [22][23][24][25]), where 1 , 2 is a positive constant.…”

Section: Introductionmentioning

confidence: 99%

An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate

Liu

2014

Abstract and Applied Analysis

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An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions ( , ) and ( ), respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number 0 .

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“…In recent years, more and more researchers are interested in the nonlinear incidence rate; especially the saturate incidence rate has been investigated by many authors in [12][13][14][15][16][17][18][19][20][21][22], in which the recruitment rate of the population is considered as a constant.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Delayed SIR Model with Exponential Birth and Saturated Incidence Rate

Wang¹,

Liu²,

Zhao³

2013

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In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stable without delay; and the endemic equilibrium is stable if the delay is under some condition. Moreover the dynamical behaviors from stability to instability will change with an appropriate critical value. At last, some numerical simulations of the model are given to illustrate the main theoretical results.

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Stability of a delayed SIRS epidemic model with a nonlinear incidence rate

Cited by 120 publications

References 17 publications

Global Analysis for a Delay-Distributed SIR Epidemic Model

Global Analysis for a Delay-Distributed SIR Epidemic Model

An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate

Analysis of a Delayed SIR Model with Exponential Birth and Saturated Incidence Rate

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