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Entropy 2017, 19(7), 305; doi:10.3390/e19070305

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

1
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
2
Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
3
State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China
4
Department of Geography, Hong Kong Baptist University, Kowloon, Hong Kong, China
*
Author to whom correspondence should be addressed.
Received: 10 May 2017 / Revised: 18 June 2017 / Accepted: 21 June 2017 / Published: 27 June 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
View Full-Text   |   Download PDF [968 KB, uploaded 28 June 2017]   |  

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. View Full-Text
Keywords: nonlinear saturate incidence rare; nonlinear recovery rate; number of hospital beds; backward bifurcation; saddle-node bifurcation; Hopf bifurcation nonlinear saturate incidence rare; nonlinear recovery rate; number of hospital beds; backward bifurcation; saddle-node bifurcation; Hopf bifurcation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Cui, Q.; Qiu, Z.; Liu, W.; Hu, Z. Complex Dynamics of an SIR Epidemic Model with Nonlinear Saturate Incidence and Recovery Rate. Entropy 2017, 19, 305.

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