Mathematical Analysis of an Age-Structured Population Model Applicable to Early Humans
Min Gao, Vanderbilt University
Location: Stevenson 1307
The age structure of human populations is exceptional among animal species. Unlike most species, human juvenility is extremely extended and death is not coincident with the end of the reproductive period. Recently, a mathematical model was developed to examine the age structure of early humans, which reveals an extraordinary balance of human fertility and mortality. This model has two types of nonlinear mortalities, one term corresponding to the effects of crowding and the other term corresponding to the senescent burden on the juvenile population. We study this semilinear partial differential equation with a nonlinear boundary condition. We analyze the existence, uniqueness and regularity of solutions to the model equations. An intrinsic growth constant is obtained and linked to the existence and the stability of the trivial or the positive equilibrium. The model supports the hypothesis that the age structure of early humans was robust in its balance of juvenile, reproductive, and senescent classes.