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| The Thresholds of Some Epidemic Models |
| CUI Yumei, CHEN Shanshan, FU Xinchu
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| College of Sciences, Shanghai University, Shanghai 200444, China |
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Abstract This paper introduces the derivation of basic reproduction numbers for several epidemic models. The basic reproduction number plays an important role in describing the dynamic behavior of infectious disease models,which is an important indicator to determine the prevalence of diseases. Therefore, the basic reproductive number is a significant reference for the prevention and control of diseases and the immunization strategy. The basic reproduction numbers can be derived by means of the definition, the monotonicity of the infected individuals at the initial moment, the existence of the positive equilibrium and the local stability of the disease-free equilibrium, the numerical simulation,respectively. This paper introduces many epidemic models especially network model and calculates their basic reproduction numbers. Finally, we analyze the changes in the basic reproduction numbers during different periods.
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Received: 08 May 2017
Published: 16 January 2019
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