منابع مشابه
Rich dynamics of an SIR epidemic model
Over the past one hundred years, mathematics has been used to understand and predict the spread of diseases, relating important public-health questions to basic transmission parameters. From prehistory to the present day, diseases have been a source of fear and superstition. A comprehensive picture of disease dynamics requires a variety of mathematical tools, from model creation to solving diff...
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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 m...
متن کاملThreshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures.
In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number R0, is less than or equal to unity, then the disease-free equilibrium of the...
متن کاملComplex Dynamics of an SIR Epidemic Model with Nonlinear Saturate Incidence and Recovery Rate
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...
متن کاملImpact of discontinuous treatments on disease dynamics in an SIR epidemic model.
We consider an SIR epidemic model with discontinuous treatment strategies. Under some reasonable assumptions on the discontinuous treatment function, we are able to determine the basic reproduction number R₀, confirm the well-posedness of the model, describe the structure of possible equilibria as well as establish the stability/instability of the equilibria. Most interestingly, we find that in...
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Modelling and Control
سال: 2010
ISSN: 2335-8963,1392-5113
DOI: 10.15388/na.2010.15.1.14365