Modeling the spread and control of dengue with limited public health resources

Abdelrazec, Ahmed; Bélair, Jacques; Shan, Chunhua; Zhu, Huaiping

doi:10.1016/j.mbs.2015.11.004

Cited by 94 publications

(53 citation statements)

References 34 publications

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“…I ( t ) represents the number of infected individuals,

γ ((), b false(t false), I false(t false))

is assumed to be an increasing function of b ( t ) and a decreasing function of the number of infected individuals I ( t ). We set μ 1 and μ 0 to be the maximum and minimum per capita hospitalisation rate respectively because of sufficient and insufficient resources; see, for instance, Abdelrazec et al It is important to note that a similar function was suggested in Shan and Zhu . Unlike in Shan and Zhu, where b is constant, in this paper, b is dynamic.…”

Section: Introductionmentioning

confidence: 94%

“…Recovery of EVD patients remains an international concern, since there is still no treatment against the disease. So recovery from EVD largely depends on other factors like behavioural change or the availability of physicians, nurses, Ebola treatment centres, and hospital beds . The effects of limited hospital beds on the evolution of a disease have been studied, with an application to the control of dengue fever; see previous studies.…”

Section: Introductionmentioning

confidence: 99%

“…The effects of limited hospital beds on the evolution of a disease have been studied, with an application to the control of dengue fever; see previous studies. () In the case of EVD, Kucharski and Camacho used a stochastic mathematical model to measure the impact of control measures in Sierra Leone at community level, with the introduction of isolation beds. However, thousands of beds were necessary at the national level to hospitalise the very large number of EVD patients .…”

Section: Introductionmentioning

confidence: 99%

“…So, unlike in Kucharski et al, we use a deterministic model to study the dynamics of EVD with limited hospital admission capacity with the number of newly available beds being time dependent. To estimate resource availability to the public, health planners use hospital bed–population ratio, ie, the number of hospital beds available for 10 000 population . From 2005 to 2012, the number of beds available per every 10 000 people in Guinea was 3, before the emergence of EVD in the country .…”

Section: Introductionmentioning

confidence: 99%

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Modelling the potential impact of limited hospital beds on Ebola virus disease dynamics

Njankou

Nyabadza

2018

Math Methods in App Sciences

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MSC Classification: 92B05; 93C15; 92D30; 97M10 During the 2013-2015 Ebola virus disease outbreak, admission into a health facility depended on the availability of hospital beds and health personnel. The limited number of such important logistics contributed to the escalation of the epidemic. We use a compartmental model to study the dynamics of Ebola virus disease when there is a limited number of beds for patients. We use a non-linear hospitalisation rate and formulate the rate at which the time-dependent number of available beds evolves. The model shows a backward bifurcation. Simulation results show that bed supply in Ebola treatment units contribute to the reduction of the number of individuals infected by Ebola virus. The model fitting results suggest that a timely supply of sufficient beds to Ebola treatment units limits the spread of the disease. Despite the fact that bed supplies to Ebola treatment units are not in themselves a control measure, they contribute to the reduction of the disease spread, by keeping the infectious in one place, during their infectious period.These results have important implications to the management and control of the disease.

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“…I ( t ) represents the number of infected individuals,

γ ((), b false(t false), I false(t false))

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling the potential impact of limited hospital beds on Ebola virus disease dynamics

Njankou

Nyabadza

2018

Math Methods in App Sciences

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“…Their study showed that the SIR model with standard saturate incidence and recovery rate (2) has rich and interesting dynamics such as backward bifurcation, saddle-node bifurcation, Hopf bifurcation and cusp type of Bogdanov-Takens bifurcation of codimension 3. Recently, Abdelrazec et al [16] applied the recovery rate (2) to investigate the impact of available resources of the health system on the spread and control of dengue fever, which could be helpful for public health authorities in their planning of a proper resource allocation for the control of dengue transmission. Motivated by these points, our model thus incorporates both nonlinear incidence rate and recovery rate to well control the emerging infectious.…”

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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A dengue fever model with free boundary incorporating the time‐periodicity and spatial‐heterogeneity

Zhu

Zhang

et al. 2021

Math Methods in App Sciences

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Propagation of dengue fever is characterized by periodicity and seasonality and further influenced by geographic heterogeneity. To account for these characteristics, we formulate a dengue model in a spatial-heterogeneous and time-periodic environment. Moreover, the free boundary is additionally incorporated into our model to reflect the boundary change of region where dengue virus spreads. Employing the properties of the contagion risk threshold, that is the spatial-temporal basic reproduction ratio, we derive some sufficient conditions regarding the vanishing and spreading of virus. Importantly, the long-time asymptotic behavior of solution is studied in depth when spreading happens. Our findings manifest that as time goes on, dengue virus will behave periodically when spreading. Finally, these phenomena are numerically simulated and epidemiologically explained.

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Modeling the spread and control of dengue with limited public health resources

Cited by 94 publications

References 34 publications

Modelling the potential impact of limited hospital beds on Ebola virus disease dynamics

Modelling the potential impact of limited hospital beds on Ebola virus disease dynamics

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

A dengue fever model with free boundary incorporating the time‐periodicity and spatial‐heterogeneity

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