# American Institute of Mathematical Sciences

2009, 6(4): 873-887. doi: 10.3934/mbe.2009.6.873

## A mathematical model of weight change with adaptation

 1 Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043, United States 2 Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07043, United States, United States 3 Department of Medicine, Endocrine Research Unit, Mayo Clinic and Mayo Foundation, Rochester, MN 55905, United States 4 Pennington Biomedical Research Center, Ingestive Behavior Laboratory, Baton Rouge, LA 70808, United States

Received  November 2008 Revised  March 2009 Published  September 2009

As obesity and its related health problems grow around the world, efforts to control and manage weight is increasing in importance. It is well known that altering and maintaining weight is problematic and this has led to specific studies trying to determine the cause of the difficulty. Recent research has identified that the body reacts to forced weight change by adapting individual total energy expenditure. Key factors are an adaptation of resting metabolic rate, non-exercise activity thermogenesis and dietary induced thermogenesis. We develop a differential equation model based on the first law of thermodynamics that incorporates all three adjustments along with natural age related reduction of the resting metabolic rate. Forward time simulations of the model compare well with mean data in both overfeeding and calorie restriction studies.
Citation: Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin. A mathematical model of weight change with adaptation. Mathematical Biosciences & Engineering, 2009, 6 (4) : 873-887. doi: 10.3934/mbe.2009.6.873
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