Dynamics of an SIR epidemic model with limited medical resources revisited

Zhou, Linhua; Fan, Meng

doi:10.1016/j.nonrwa.2011.07.036

Cited by 205 publications

(133 citation statements)

References 19 publications

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“…Then substituting (15) in (16) and comparing the coefficients of similar power of u 2 , uσ and σ 2 on both sides of the equation we get…”

Section: Bifurcation Analysis Of Disease Free Equilibrium (0mentioning

confidence: 99%

“…The mathematics of such dynamics are known from references [7][8][9][10][11]. In most of the articles researchers considered the constant birth rates of the susceptible populations [12][13][14][15][16][17], which is not realistic in some populations. So the authors in [18][19][20] considered exponential/logistic growth rate of the susceptible populations.…”

Section: Introductionmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

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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“…Then substituting (15) in (16) and comparing the coefficients of similar power of u 2 , uσ and σ 2 on both sides of the equation we get…”

Section: Bifurcation Analysis Of Disease Free Equilibrium (0mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Ghosh¹,

Susmita²

2018

CMST

View full text Add to dashboard Cite

show abstract

“…Capasso and Serio [8] used the case when l = h = 1, i.e., g(I) = investigating the cholera epidemic in Bari in 1973. Due to the nonlinearity and saturation property of these incidence rates, SIR epidemic models usually possess multiple endemic equilibria and rich nonlinear dynamics [5][6][7][8][9][10][11][12]. Furthermore, a compartmental model with nonlinear incidence rate is usually used to explore the impact of intervention strategies on the transmission dynamics of infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamics of an SIR Epidemic Model with Nonlinear Saturate Incidence and Recovery Rate

Cui

Qiu

Liu

et al. 2017

Entropy

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Susceptible-infectious-removed (SIR) epidemic models are proposed to consider the impact of available resources of the public health care system in terms of the number of hospital beds. Both the incidence rate and the recovery rate are considered as nonlinear functions of the number of infectious individuals, and the recovery rate incorporates the influence of the number of hospital beds. It is shown that backward bifurcation and saddle-node bifurcation may occur when the number of hospital beds is insufficient. In such cases, it is critical to prepare an appropriate amount of hospital beds because only reducing the basic reproduction number less than unity is not enough to eradicate the disease. When the basic reproduction number is larger than unity, the model may undergo forward bifurcation and Hopf bifurcation. The increasing hospital beds can decrease the infectious individuals. However, it is useless to eliminate the disease. Therefore, maintaining enough hospital beds is important for the prevention and control of the infectious disease. Numerical simulations are presented to illustrate and complement the theoretical analysis.

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“…In literature, a huge variety of continuous-time models have been developed in order to understand disease transmission dynamics and to study epidemiological processes [1][2][3]. Y.Enatsu [4] apply a variation of Euler backward discretization in order to study a discrete SIR epidemic model with a class of nonlinear incidence rate and a distributed latent period.…”

Section: Introductionmentioning

confidence: 99%

On the Analysis of Discrete Epidemic Models with Specific Nonlinear Incidence Rate

2016

International Journal of Scientific and Innovative Mathematical

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Dynamics of an SIR epidemic model with limited medical resources revisited

Cited by 205 publications

References 19 publications

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

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

Complex Dynamics of an SIR Epidemic Model with Nonlinear Saturate Incidence and Recovery Rate

On the Analysis of Discrete Epidemic Models with Specific Nonlinear Incidence Rate

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