Modeling weight loss with differential equations

This comes from a talk I’m giving at Penguicon 2012. The talk in general is about weight loss and getting healthy but part of it involves doing some predictive modeling of future weights based on calorie counting.

Consider the question “if I eat X number of calories a day, will I gain or lose weight?”. It’s a supremely practical question but without doing some research it isn’t immediately apparent how to answer this. The best place to start is one of the formulas for calculating basal metabolic rate. The obligatory Wikipedia link provides some more background but in short it gives us a formula for the “baseline” number of calories our body needs. Mifflin-St. Jeor is considered by many [citation needed] to be the most accurate. It is of the form:

In this formula, m is mass in kilograms, h is height in centimeters, a is age in years, and s is a gender offset which is either +5 for men or -161 for women. This gives us P, our basal metabolic rate in calories. An interesting thing about BMR is that it’s a measure of your caloric needs at more or less complete rest. A normal person’s caloric needs to maintain weight will usually be strictly greater than their BMR. Because of this, P is usually scaled by an “activity factor” which factors in daily life. This can range from ~1.2 for someone with a desk job who gets no exercise to ~1.9 for someone who engages in some serious workouts. Now that we know our caloric needs, how can use this to model where our weight will be in the future? Continue reading “Modeling weight loss with differential equations”