A setpoint based dieting model

A mathematic model of weight loss during under eating is proposed in the form of a simple energy balance ODE. The model accounts for the bodyʹs changing energy requirement per pound as weight is lost around an individual weight setpoint of stable equilibrium and is compared to a constant energy per pound model. The energy requirement per pound of body mass is formed from a linear fit from the equilibrium value to a constructed minimum (starvation) level. The resulting ODE is nonlinear in weight but has an analytical solution. Analysis is conducted in normalized (dimensionless) parameters for universal comparison. The model predicts weight loss as a function of time, the new caloric requirements for maintenance at the reduced weight and that these parameters are dependent on the Fat Free Mass Ratio (FFMR) existing at the setpoint weight.