Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds

Shan, Chunhua; Zhu, Huaiping

doi:10.1016/j.jde.2014.05.030

Cited by 121 publications

(100 citation statements)

References 14 publications

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“…Unfortunately, there are some technical obstacles that cannot be overcome at present stage. On the other hand, one may propose some more realistic but complex models, such as considering the impact of the number of hospital beds [62] on system (1.4) . We leave these investigations for future research.…”

Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

Lan

Lin

Wei

et al. 2019

Journal of the Franklin Institute

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In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number R s 0 is established: the disease can be eradicated almost surely if R s 0 < 1 and under mild extra conditions, whereas if R s 0 > 1 , the densities of the distributions of the solution can converge in L 1 to an invariant density by using the Markov semigroups theory. Finally, based on realistic parameters obtained from previous literatures, numerical simulations have been performed to verify our analytical results.

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Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

Lan

Lin

Wei

et al. 2019

Journal of the Franklin Institute

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“…Under this consideration, Shan and Zhu [24] defined the recovery rate as a function of b , the number of hospital beds, and I , the number of infectives.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates

Liu

Zhang

2017

PLoS ONE

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The transmission of infectious diseases has been studied by mathematical methods since 1760s, among which SIR model shows its advantage in its epidemiological description of spread mechanisms. Here we established a modified SIR model with nonlinear incidence and recovery rates, to understand the influence by any government intervention and hospitalization condition variation in the spread of diseases. By analyzing the existence and stability of the equilibria, we found that the basic reproduction number is not a threshold parameter, and our model undergoes backward bifurcation when there is limited number of hospital beds. When the saturated coefficient a is set to zero, it is discovered that the model undergoes the Saddle-Node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation of codimension 2. The bifurcation diagram can further be drawn near the cusp type of the Bogdanov-Takens bifurcation of codimension 3 by numerical simulation. We also found a critical value of the hospital beds bc at and sufficiently small a, which suggests that the disease can be eliminated at the hospitals where the number of beds is larger than bc. The same dynamic behaviors exist even when a ≠ 0. Therefore, it can be concluded that a sufficient number of the beds is critical to control the epidemic.

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“…Particularly, the capacity of the hospital settings and effectiveness and efficiency of the treatment may influence the recovery rate [13]. In classical epidemic models, the recovery rate is usually assumed to be proportional to the number of infected, which means that the resources of the health system are quite sufficient for the infectious disease [1].…”

Section: Introductionmentioning

confidence: 99%

“…Based on the World Health Organization (WHO) Statistical Information System, hospital bed-population ratio (HBPR), the number of available hospital beds per 10,000 population, is used by health planners as a method of estimating resource availability to the public [13,15]. To study the impact of HBPR, Shan and Zhu [13] proposed the following nonlinear recovery rate function of the number of hospital beds per 10,000 population b and the number of infective individuals I…”

Section: Introductionmentioning

confidence: 99%

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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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Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds

Cited by 121 publications

References 14 publications

A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates

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

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