Abstract
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.
Highlights
Classical susceptible-infectious-removed (SIR) epidemic models with bilinear incidence rate typically have at most one endemic equilibrium; the disease will die out when the basic reproduction number is less than unity and will persist otherwise [1,2,3,4]
Is the per capital natural death rate of the population; e ≥ 0 is the per capita disease-induced death rate; μ(b, I ) is the per capita recovery rate of infectious individuals incorporating the impact of the capacity and limited resources of the health care system, and b > 0 is the number of available hospital beds per 10,000 population
Due to the important biological significance of hospital beds, in this paper, we have investigated an SIR epidemic model to simulate the impact of a limited health care system in terms of the number of hospital beds
Summary
Classical susceptible-infectious-removed (SIR) epidemic models with bilinear incidence rate typically have at most one endemic equilibrium; the disease will die out when the basic reproduction number is less than unity and will persist otherwise [1,2,3,4]. 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 incorporates both nonlinear incidence rate and recovery rate to well control the emerging infectious. Is the per capital natural death rate of the population; e ≥ 0 is the per capita disease-induced death rate; μ(b, I ) is the per capita recovery rate of infectious individuals incorporating the impact of the capacity and limited resources of the health care system, and b > 0 is the number of available hospital beds per 10,000 population. A brief discussion is presented and conclusions are presented in the final section
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