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Global stability of infectious disease models with contact rate as a function of prevalence index

1. Maestría en Ciencias de la Salud, Escuela Superior de Medicina, Instituto Politécnico Nacional, Plan de San Luis y Díaz Mirón s/n, Col. Casco de Santo Tomas, Del. Miguel Hidalgo, 11340, Ciudad de México, Mexico
2. Maestría en Ciencias de la Complejidad, Universidad Autónoma de la Ciudad de México, San Lorenzo 290, Col. Del Valle Sur Del.Benito Juárez, 03100, Ciudad de México, Mexico
3. International Prevention Research Institute, 96 Cours Lafayette, 69006 Lyon, France

In this paper, we consider a SEIR epidemiological model with information-related changes in contact patterns. One of the main features of the model is that it includes an information variable, a negative feedback on the behavior of susceptible subjects, and a function that describes the role played by the infectious size in the information dynamics. Here we focus in the case of delayed information. By using suitable assumptions, we analyze the global stability of the endemic equilibrium point and disease-free equilibrium point. Our approach is applicable to global stability of the endemic equilibrium of the previously defined SIR and SIS models with feedback on behavior of susceptible subjects.

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Keywords Behavioral epidemiology; information variable; negative feedback; Lyapunov function; global stability

Citation: Cruz Vargas-De-León, Alberto dOnofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences and Engineering, 2017, 14(4): 1019-1033. doi: 10.3934/mbe.2017053

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