Global asymptotic stability of an SIR epidemic model with distributed time delay

Beretta, Edoardo; Hara, Tadayuki; Ma, Wanbiao; Takeuchi, Yasuhiro

doi:10.1016/s0362-546x(01)00528-4

Cited by 209 publications

(170 citation statements)

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“…More recently, Beretta and Takeuchi 23,24 analyzed the global stability properties of the disease-free equilibrium of generalized vector-borne disease models similar to (2.5). Takeuchi et al 25 and Beretta et al 26 extended this work by also considering stability of the endemic equilibrium. In Ref.…”

Section: Cookementioning

confidence: 92%

“…21 The focus of this paper is on a generalized epidemic model in which the disease is transmitted by vectors exhibiting a finite (extrinsic) incubation period before becoming infectious, along the lines of Refs. [22][23][24][25][26][27][28][29]. Two important complications to the aforementioned modeling efforts are considered: the first is the addition of seasonal effects to the model, motivated by the discussion above, which is incorporated by considering model parameters that experience abrupt changes in time.…”

Section: 13mentioning

confidence: 99%

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Switching Vaccination Schemes for Vector-Borne Diseases With Seasonal Fluctuations

Liu

Stechlinski

2017

J. Biol. Syst.

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Theory is developed for an epidemic model of a seasonally-spreading vector-borne disease using a hybrid system framework. Applicable to diseases spread by mosquitoes (e.g., chikungunya and Zika virus via Aedes albopictus), seasonal variations in transmission are modeled using switching parameters to represent term-time forcing. The vector agent is assumed to exhibit a period of incubation upon infection, modeled using a distribution. Three hybrid control strategies are analyzed in detail: switching cohort immunization, pulse vaccination at pre-specified times, and state-dependent pulse vaccination. Methods from switched systems theory are used to derive threshold disease eradication conditions involving the model parameters; convergence of solutions to a disease-free set or periodic solution is shown. A comprehensive analysis is performed to compare and contrast the different control schemes.

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Section: Cookementioning

confidence: 92%

Section: 13mentioning

confidence: 99%

Switching Vaccination Schemes for Vector-Borne Diseases With Seasonal Fluctuations

Liu

Stechlinski

2017

J. Biol. Syst.

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“…China. 3 College of Science, China University of Petroleum (East China), Qingdao, 266580, P.R. China.…”

Section: Competing Interestsmentioning

confidence: 99%

The extinction and persistence of a stochastic SIR model

Jiang

2017

Adv Differ Equ

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“…An SIR model with distributed delay was studied in [3,16,17]. The distributed delay allows infectivity to be function of the duration since infection, up to some maximum duration.…”

Section: Setting the Problemmentioning

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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Global asymptotic stability of an SIR epidemic model with distributed time delay

Cited by 209 publications

References 0 publications

Switching Vaccination Schemes for Vector-Borne Diseases With Seasonal Fluctuations

Switching Vaccination Schemes for Vector-Borne Diseases With Seasonal Fluctuations

The extinction and persistence of a stochastic SIR model

Global Analysis for a Delay-Distributed SIR Epidemic Model

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