Abstract
A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction numberℝ0is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.
Highlights
In recent years, efforts have been made to develop realistic mathematical models for the transmission dynamics of known and emerging infectious diseases [1,2,3,4,5,6,7,8]
In order to model the impact of limited medical resource on infectious disease transmission precisely and provide a method to estimate a suitable treatment capacity for a disease, we propose an epidemic model with saturation recovery
We proposed a SIR epidemic model with saturation recovery to understand the impact of limited medical resource on infectious disease transmission
Summary
Efforts have been made to develop realistic mathematical models for the transmission dynamics of known and emerging infectious diseases [1,2,3,4,5,6,7,8]. We will focus on the impact of limited medical resource or treatment capacity on infectious disease transmission. It is important to understand the impact of limited medical resource on disease transmission and to determine a suitable treatment capacity for a disease. In order to model the impact of limited medical resource on infectious disease transmission precisely and provide a method to estimate a suitable treatment capacity for a disease, we propose an epidemic model with saturation recovery.
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