Abstract
Variations in individual body mass and composition have long been a key focus in the health sciences, particularly now that overweight and obesity are considered as public health problems. We study a mathematical model that describes body mass variations which are determined by the energy balance between caloric intake and total energy expenditure. To calculate the change in caloric intake and energy expenditure over time, we proposed a relationship for each of these quantities, and we used measured values that are reported in the literature for the initial conditions. To account for small variations in the daily energy balance of an individual, we include social interactions as the multiplication of two terms: social proximity and social influence. We observe that social interactions have a considerable effect when the body mass of an individual is quite constant and social interactions take random values. However, when an individual's mass value changes (either increases or decreases), social interactions do not have a notable effect. In our simulation, we tested two different models that describe the body mass composition, and it resulted that one fits better the data.
Highlights
Overweight and obesity have become worldwide health problems because they cause several diseases [1,2,3,4]
The model proposed by Chow and Hall [18] mainly focuses on the differences between caloric intake and total energy expenditure; this model is capable of incorporating new terms such as the term we introduce to describe social interactions
Where F is the individual’s fat mass; L is lean mass; I is the caloric intake; E is the total energy expenditure; rF is the energy density associated with body fat; rL is the energy density associated with lean mass; and p is calculated as follows: p~ 1 1za ð4Þ
Summary
Overweight and obesity have become worldwide health problems because they cause several diseases [1,2,3,4]. Case, as indicated by his negative personal energetic difference (figure 3), interacting with individuals whose routine leads to an increase in body mass (we use a positive sign in equations (15) and (16)) undermines his attempt to lose weight. Case iii: We use a random value for the social energy influence DE that is selected from a uniform distribution of points in the range of [0,300] kcal/day, a random sign for the social interaction in equations (15) and (16), and we vary b uniformly from (0,1), in the first example (figure 3) These parameters produce small variations over time that are more irregular than those in figure 3 (figure 9). Future work can be performed to explain the effect of social networks on variations in mass
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