Although it is widely held that infections and eating difficulties are hallmarks of advanced dementia,25 there are few prospective data on the incidence of these complications. Over the course of 18 months, more than half of the residents in our study had infectious episodes, and 86% had eating problems.
So 10 billion people is the uppermost population limit where food is concerned. Because it's extremely unlikely that everyone will agree to stop eating meat, Wilson thinks the maximum carrying capacity of the Earth based on food resources will most likely fall short of 10 billion.
One way to develop a model that incorporates a carrying capacity is to make the reproduction be proportional not only to the population size but also to the fraction of unused carrying capacity. The resulting model is the logistic model for population growth. Let $P_t$ denote the population size in time period $t$. Let $M$ be the carrying capacity, which is the population size that the environment can support. Then, $\ 1 displaystyle \frac{P_t}{M}$ is the fraction of the carrying capacity that is used, and. $\ 2 displaystyle 1 - \frac{P_t}{M}$ is the unused fraction of the carrying capacity.