The logistic, two-sex, age-structured population model with births outside marriages
Abstract
In this dissertation, the logistic effect is introduced into the two-sex population model introduced by Hoppensteadt to remedy the trouble that the population grows indefinitely. Birth from single mothers is also introduced into the model considering its significant portion in all births in U.S. and some other western countries. The first problem gets addressed is the existence and uniqueness of continuous and classical solutions. We give some sufficient conditions for a unique continuous solution to exist locally and have the solution extended to a global one. Then under some mild assumptions on the vital rates the existence and uniqueness of the classical solution is established. After the well-posedness of the model gets assured, the behavior of the model is studied and the condition for the existence of non-trivial equilibria is explored. An upper bound for the total population is given to estimate the carrying capacity from parameters. Finally, numerical method is applied to investigate the effect of marriage functions and evaluate different influences from different choice of marriage functions on the goodness of fit of simulations during the ten-year period between consecutive U.S. censuses.
Degree
Ph.D.
Advisors
Milner, Purdue University.
Subject Area
Biostatistics|Mathematics
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