An SIR Model with Nonlinear Incidence Rate and Holling Type III Treatment Rate

Dubey, Preeti; Dubey, B.; Dubey, Uma S.

doi:10.1007/978-81-322-3640-5_4

Cited by 44 publications

(44 citation statements)

References 41 publications

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“…Especially, to establish the global stability of the endemic equilibrium, we use a geometrical approach [15] and a Lyapunov function. our results are consistent with those in [3,4], in the special case ( , ) = . The rest of this paper is organized as follows.…”

Section: Research In Applied Mathematicssupporting

confidence: 82%

“…In the present article, we extend the model from [3,4] to include general nonlinear incidence function ( , ), and we establish the complete global dynamics. Especially, to establish the global stability of the endemic equilibrium, we use a geometrical approach [15] and a Lyapunov function.…”

Section: Research In Applied Mathematicsmentioning

confidence: 99%

“…In (2015, [3]), Dubey et al considered the incidence function as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). They showed that the disease-free equilibrium is locally asymptotically stable when reproduction number is less than one and obtained the global stability of the endemic equilibrium using Lyapunov function.…”

Section: Research In Applied Mathematicsmentioning

confidence: 99%

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Stability Analysis of an SEIR Model with Treatment

Elkhaiar

Kaddar

2017

Research in Applied Mathematics

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Abstract. We study the dynamics of a SEIR epidemic model with nonlinear treatment function, that takes into account the limited availability of resources in community. Under some conditions we prove the existence of two possible equilibria: the disease-free equilibrium and the endemic equilibrium. Using Lyapunov's method and Li's geometrical approach, We also show that the reproduction number 0 is a threshold parameter: the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than unity and the unique endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than this critical value. In the end, we give some concluding remarks concerning the role of treatment on the epidemic propagation.

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Section: Research In Applied Mathematicssupporting

confidence: 82%

Section: Research In Applied Mathematicsmentioning

confidence: 99%

Section: Research In Applied Mathematicsmentioning

confidence: 99%

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Stability Analysis of an SEIR Model with Treatment

Elkhaiar

Kaddar

2017

Research in Applied Mathematics

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“…where a represents the maximal medical resources supplied per united time and is half-saturation constant, which measures the effect of being delayed for treatment. Other works have investigated the effects of the treatment on an epidemic (see [19][20][21][22][23][24][25]) and also its optimal control (see [26]). The motivation of this work comes from [10,11], where the authors studied an SIR epidemic model with nonlinear incidence function, and from [19][20][21], where the authors considered a special type of treatment function.…”

Section: Introductionmentioning

confidence: 99%

Global stability analysis for a generalized delayed SIR model with vaccination and treatment

et al. 2019

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In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, which are the two principal control measurements to reduce the disease burden. Using the Lyapunov functions, we show that the disease-free equilibrium state is globally asymptotically stable if R 0 ≤ 1, where R 0 is the basic reproduction number. On the other hand, the disease-endemic equilibrium is globally asymptotically stable when R 0 > 1. For a specific type of treatment and incidence functions, our analysis shows the success of the vaccination strategy, as well as the treatment depends on the initial size of the susceptible population. Moreover, we discuss, numerically, the behavior of the basic reproduction number with respect to vaccination and treatment parameters. MSC: 34D03; 92D30

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“…the bi-linear incidence rate, saturated incidence rate, etc. [15,[21][22][23][24]. Similarly some authors [25][26][27][28][29] used the rate of incidence in the form aSI 1 + bI .…”

Section: Introductionmentioning

confidence: 99%

Global Stability Analysis of Logistically Grown SIR Model with Loss of Immunity, Inhibitory Effect, Crowding Effect and its Protection Measure

Ghosh¹,

Susmita²

2018

CMST

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In this paper we have considered an SIR model with logistically grown susceptible in which the rate of incidence is directly affected by the inhibitory factors of both susceptible and infected populations and the protection measure for the infected class. Permanence of the solutions, global stability and bifurcation analysis in the neighborhood of equilibrium points has been investigated here. The Center manifold theory is used to find the direction of bifurcations. Finally numerical simulation is carried out to justify the theoretical findings.

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An SIR Model with Nonlinear Incidence Rate and Holling Type III Treatment Rate

Cited by 44 publications

References 41 publications

Stability Analysis of an SEIR Model with Treatment

Stability Analysis of an SEIR Model with Treatment

Global stability analysis for a generalized delayed SIR model with vaccination and treatment

Global Stability Analysis of Logistically Grown SIR Model with Loss of Immunity, Inhibitory Effect, Crowding Effect and its Protection Measure

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