Mathematical Modeling for the Obesity Dynamics with Psychological and Social Factors

Abstract

We develop a mathematical model for the obesity dynam- ics to investigate the long term obesity trend with the consideration of psychological and social factors due to the increasing prevalence of obe- sity around the world. Many mathematical models for obesity dynamics adopted the modeling idea of infectious disease and treated overweight and obese people infectious and spreading obesity to normal weight. However, this modeling idea is not proper in obesity modeling because obesity is not an infectious disease. In fact, weight gain and loss are related to social interactions among different weight groups not only in the direction from overweight/obese to normal weight but also the other way around. Thus, we consider these aspects in our model and implement personal weight gain feature, a psychological factor such as body image dissatis- faction, and social interactions such as positive support on weight loss and negative criticism on weight status from various weight groups. We show that the equilibrium point with no normal weight population will be unstable and that an equilibrium point with positive normal weight pop- ulation should have all other components positive. We conduct computer simulations on Korean demography data with our model and demonstrate the long term obesity trend of Korean male as an example of the use of our model.