The energy economy of zombies was modeled in two different ways. The simplest model indicted total extinction of the zombie population in 230 days. The slightly more sophisticated model indicated a 90% die-off every 350 days. Both of these analysis are for "warm" climates where significant calorie burn is not required to maintain body temperature.
In the event of a total, zombie apocalypse there will be a total collapse of industry and agriculture. Consequently, zombie energy needs must be met by zombie effort fueled by food. The only readily available source of food is other zombie bodies.
The simplest model
The simplest model is to assume the basal energy state and to calculate the body weight glide path given certain starting state assumptions.
If one assumes the base population consists entirely of 50th percentile, Caucasian men and 50th percentile Caucasian women then one starts with:
- 180 pound males carrying 54 pounds of body fat with a basal energy consumption rate (basically sleeping) of 1365 Calories per day.
- 143 pound females carrying 57 pounds of body fat with a basal energy consumption rate of 936 Calories per day. (Source)
Assuming that the lean body mass can be diminished by 50% before fatality occurs then the final, projected longevity for our population is 154 days for the males and 229 days for the females.
The slightly more complex model
The slightly more complex model assumes that zombies will eat other zombies. It assumes zombies will engage in two hours of "foraging" at a rate of 3.0 METs and assumes perfect allocative efficiency. The additional activity drives the maintenance Calories to approximately 1600 Calories per day for males and 1100 Calories for females.
The average zombie's body is comprised of enough calories to sustain 153 other zombies for one day. That results in a decay rate of 0.654% per day.
So a population of one million at the start of the apocalypse will be reduced to approximately 100,000 at the end of the first year, 10,000 at the end of the second year, 1000 at the end of the third year and so on. At some point the amount of time spent "foraging" increases due to the increasing scarcity of sleeping zombies to butcher and the decay rate will increase. That is, the decay rate will increase as the net energy return on investment fall due to depletion factors.