The Impact of Media Coverage on Obesity

Abstract

In this paper, we develop a deterministic compartmental model for the obesity dynamics. Contrary to other contributions on this subject we explore the impact of the media on the spreading of this phenomenon in a constant population. Stability analysis shows that the disease-free equilibrium point is globally asymptotically stable when the number of reproduction is less than unity. We also show that the endemic equilibrium point when it exists is globally asymptotically stable under some conditions.

A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes

“…The data used for the computational simulations are extracted from the literature or assumed. The parameter values for the computational simulations are (α * ) α = 2 (assumed), (β * ) α = 0.2 (assumed), M α S = 667.685 [28], M α D = 4.1 (assumed), β α 1 = 0.25 (assumed), ε = 0.007 [10], η α = 0.1 [10], γ α = 0.0015 [10], δ α = 0.002 [10], µ α = 1 70.5 [26], d α = 0.07 (assumed), t H = 1.02 (assumed), t D = 1.03 (assumed), µ α d = 0.013 (assumed), α α 1 = 0.1 (assumed), α α 2 = 0.35 [45,46], α α 3 = 0.4 [45,46], and α = 0.3, 0.5, 0.7, 0.9, 1. The initial conditions are S = 874.1400, O w = 1.2000, O b = 1.5000 and D = 100.0000 on the scale of 10000 individuals.…”

“…We will study the joint variations of the parameters associated with transitions through the compartments associated with body weight and diabetes as a consequence of weight. The intervals of the parameters are η ∈ [0.00028, 0.1], γ ∈ [0.00028, 0.0015], δ ∈ [0.00035, 0.002] (extracted from [10]), α 2 ∈ [0.35, 0.49] and α 3 ∈ [0.3, 0.53] (extracted from [45,46]). The joint variation of the selected parameters provides us with information on how they will influence the ℜ 0 , for different fractional orders.…”

“…In recent years, the use of mathematical models to study the dynamics of obesity and overweight has increased [6]- [10]. Ejima et al [6] presented a mathematical model that studies the genetic and non-genetic effects that lead to obesity and among the results they obtained was that homozygous individuals are more susceptible to both the risk of social contagion and the risk of spontaneous weight gain.…”

“…Al-Tuwairqi and Matbouli [9] proposed two mathematical models to study the impact of fast food on the increase in obesity and the role of physical activity. Pietrus et al [10] developed a mathematical model to study the impact of media on the dynamics of obesity in a population.…”

Mathematical Model for the Study of Obesity in a Population and Its Impact on the Growth of Diabetes

“…Al-Tuwairqi and Matbouli [2] proposed two mathematical models to study the impact of fast food on obesity and the role that exercise plays in weight gain separately and showed that physical activity has a significant role in reducing weight. These works contributed to the construction of others models in particular, Bernard et al [6] developed a deterministic compartmental model for the dynamic of obesity and explored the impact of the media on the propagation of this phenomenon in a constant population. In the modeling of diabetes, we find works such as the one of Dubey and Goswami [12] who presented a model of diabetes and its complications involving the fractional operator with exponential kernel.…”