Qualitative Stability Analysis of an Obesity Epidemic Model with Social Contagion

Abstract

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 diseasefree equilibrium and two endemic equilibria, and also that it has no periodic orbits. Particularly, we found that when considering 0 (the basic reproductive number) as a parameter, the system exhibits a backward bifurcation: the disease-free equilibrium is stable when 0 < 1 and unstable when 0 > 1, whereas the two endemic equilibria appear from * 0 (a specific positive value reached by 0 and less than unity), one being asymptotically stable and the other unstable, but for 0 > 1 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.

The Impact of Media Coverage on Obesity

“…In [18] the authors experimented a system of SIS difference equation model and drew a similar conclusion. In [19] a new model is introduced for taking into account both social and nonsocial contagion risks of obesity. A way to complete the actions is to consider the role of the media that could be important.…”

Mathematical Analysis of an Obesity Model with Eating Behaviors

“…Second, it is estimated that genetic factors account for 40-90% of the population variation in body mass index (BMI) [9]. There have been some mathematical researches in the aim to reveal mechanisms of propagation of obesity [1,6,8,11,17,18,21,22]. Basically, these models divide the population into the compartments of normal population, overweight population and obesity individuals and consider the contagious transmission between normal individuals and overweight individuals.…”

A mathematical-epidemiological model of obesity control

“…La divulgación de esta alternativa de análisis de la obesidad como epidemia permitirá obtener una alternativa más de investigación para una toma de decisiones de precisión. En la literatura universal sobre modelamiento matemático de la obesidad, existen dos aspectos de su estudio, uno desde el punto de vista epidemiológico ya que debido a malos hábitos en la alimentación o actividad física, estos han sido factores de propagación en las poblaciones diversas de esta enfermedad crónica, la obesidad (modelo basado en la población) como en [1], [2], [3] y el otro punto de vista es fisiológico en cuanto al tipo de alimento que se consume (modelo basado en el individuo) [3]. Aquí proponemos modelos que nosotros planteamos a partir de otros modelos que perturbamos según algún nuevo aspecto que consideraremos y la sugerencia es el control de la obesidad traducido en dietas u otras razones de reducción de la población con sobrepeso u obeso.…”