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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 1084769, 12 pages
Research Article

Qualitative Stability Analysis of an Obesity Epidemic Model with Social Contagion

1Maestría en Ciencias de la Complejidad, Universidad Autónoma de la Ciudad de México, 03100 Ciudad de México, Mexico
2Maestría en Ciencias de la Salud, Escuela Superior de Medicina, Instituto Politécnico Nacional, Plan de San Luis S/N, Miguel Hidalgo, Casco de Santo Tomas, 11350 Ciudad de México, Mexico
3Maestría en Matemáticas Aplicadas, Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas CU, 39087 Chilpancingo, GRO, Mexico

Correspondence should be addressed to Cruz Vargas-De-León

Received 1 October 2016; Accepted 13 December 2016; Published 24 January 2017

Academic Editor: Tetsuji Tokihiro

Copyright © 2017 Enrique Lozano-Ochoa et al. 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.


We study an epidemiological mathematical model formulated in terms of an ODE system taking into account both social and nonsocial contagion risks of obesity. Analyzing first the case in which the model presents only the effect due to social contagion and using qualitative methods of the stability analysis, we prove that such system has at the most three equilibrium points, one disease-free equilibrium and two endemic equilibria, and also that it has no periodic orbits. Particularly, we found that when considering (the basic reproductive number) as a parameter, the system exhibits a backward bifurcation: the disease-free equilibrium is stable when and unstable when , whereas the two endemic equilibria appear from (a specific positive value reached by and less than unity), one being asymptotically stable and the other unstable, but for values, only the former remains inside the feasible region. On the other hand, considering social and nonsocial contagion and following the same methodology, we found that the dynamic of the model is simpler than that described above: it has a unique endemic equilibrium point that is globally asymptotically stable.