Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination

Lahrouz, Aadil; Omari, Lahcen; Kiouach, Driss; Belmaâti, Aziza

doi:10.1016/j.amc.2011.12.024

Cited by 115 publications

(56 citation statements)

References 17 publications

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“…The vaccinated individuals lose their immunity at the rate of ν 4 . We assumed the same transmission rate in the form of βSI ψ(I) , where ψ represents a positive function such that ψ(0) = 1 and ψ ≥ 0, used by [16]. This generalizes the mass action incidence (i.e.…”

Section: Model Formulationmentioning

confidence: 99%

Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination

Khan

Badshah

et al. 2015

Int. J. Biomath.

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In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R 0 . If the basic reproduction number R 0 < 1, the diseasefree equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number R 0 > 1, the disease is uniformly persistent and the unique endemic equilibrium of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.

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Section: Model Formulationmentioning

confidence: 99%

Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination

Khan

Badshah

et al. 2015

Int. J. Biomath.

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“…During the past decade, many mathematical models, deterministic and stochastic, have been developed for the transmission dynamics of infectious diseases such as tuberculoses, measles, influenza, etc. (see for instance Casagrandi et al 2006;McCluskey and van den Driessche 2004;Hethcote 2000;Gray et al 2011;Dalal et al 2007;Lahrouz et al 2012 and references therein). The development of such models is aimed at both B Aadil Lahrouz lahrouzadil@gmail.com understanding observed epidemiological patterns and predicting the outcome of the introduction of public health interventions to control the spread of diseases.…”

Section: Introductionmentioning

confidence: 95%

“…Using the same method as by Lahrouz et al (2012), Lahrouz and Omari (2013), the existence and uniqueness of positive solution for system (10) holds with probability 1 if we start from any positive initial value (S(0), I (0)). Therefore, the above approach to introducing stochastic environmental noise into the deterministic model (1) is mathematically and biologically reasonable.…”

Section: Introductionmentioning

confidence: 96%

Effects of stochastic perturbation on the SIS epidemic system

2016

Self Cite

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In this paper we extend the classical SIS epidemic model from a deterministic framework to a stochastic one. We also study the long time behavior of the stochastic system. We mainly establish conditions for the extinction of disease from the population as well as the persistence of disease under different conditions. In the case of persistence, we show the existence of a stationary distribution. we found that the introduction of stochastic noise changes the basic reproduction number. The presented results are demonstrated by numerical simulations.

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“…It is wellknown that the rst SIRS epidemic model proposed by Kermack and McKendrick [1] in 1927, and many related models [2][3][4] were studied since then. The incidence rate with general form g(I)S play an important role in epidemic model.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a SIQS epidemic model with non-linear incidence rate and application in GMF information dissemination

Wang

2016

2016 35th Chinese Control Conference (CCC)

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A SIQS epidemic model with non-linear incidence rate is proposed.With or without considering the stochastic perturbations, we study two models. The existence and global stability of the equilibriums for deterministic model is obtained by theoretic analysis and the second Lyapunov functional method. For stochastic model, by using the Itôs formula and some famous results, we obtain the conditions for disease's extinction and stationary distribution. At last, the simulations verify the theoretic conclusions gotten and an example for the GMF information dissemination is given in the paper.

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Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination

Cited by 115 publications

References 17 publications

Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination

Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination

Effects of stochastic perturbation on the SIS epidemic system

Analysis of a SIQS epidemic model with non-linear incidence rate and application in GMF information dissemination

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