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A Mathematical Model to Study the Joint Effects of Genetics and Diet on Obesity

Obesity has become one of the most pervasive epidemics facing North America today. According to the Centers for Disease Control and Prevention (CDC), more than one-third (34.9%) of adults in the United States are obese, and approximately 17% of children and adolescents aged 2 - 19 years are obese. Obesity is correlated with other serious health threats such as diabetes and cardiovascular diseases that increase an individual’s mortality risk. Previous studies show that a particular SNP (rs9939609 ) in the fat mass and obesity associated FTO gene is associated with the expression of obesity. A poor choice of diet and nutrition may lead to obesity. In this study, we build a system of non-linear ordinary differential equations that considers both genetic and environmental effects on populations with three distinct genotypes (AA, Aa and aa). The autosomal dominant allele is A, therefore individuals who have the genotypes AA and Aa express the FTO gene. Equilibria analysis and simulation results show that over a long period of time, when the birth frequency of each genotype is dependent on current allele frequencies, the proportion of populations with the dominant allele goes to 0, or the dominant allele A is outbred by the recessive gene allele. Simulation results further show that having the allele A has a stronger impact on obesity than the diet environment. Thus the effect of environmental factors on the dynamics of obesity are negligible at best. Fitness and genetic selection trumps any environmental bias. This study provides a significantly new insight into the synergic impact that genetics and diet play on obesity, which is rarely studied by traditional biological tools, such as GWAS. Note that with genetic inheritance, environment makes no significant impact on the prevalence of obesity in the long term.

Article Number: MTBI-12-01

Year:  2015

Fangyuan Hong - Mount Holyoke College
Victoria Kelley - James Madison University
Kevin Molina-Serranom - University of Puerto Rico Mayaguez
DemetriusRhodes–University of South Carolina Beaufort
Daniel Burkow - Arizona State University
Marlio Paredes - Arizona State University 
Karen Rios-Soto - University of Puerto Rico Mayaguez, Arizona State University