An age-structured two-sex population model
Abstract
The one-sex stable population theory is a fundamental theoretical tool in mathematical demography. However, it cannot answer questions related to the existence and interplay of the sexes. In this work we consider an age structured two-sex population model proposed in the seventies almost simultaneously by Fredrickson and Hoppensteadt. Chapter 1 of this work contains an overview of the one-sex stable population theory and a discussion of its importance in mathematical demography. Chapter 2 concentrates on the most problematic component of the Fredrickson-Hoppensteadt model, namely the marriage function. The marriage function is an unknown nonlinear operator which assigns the density of single males and single females to the density of marriages. We also consider a simulation based approach to comparing the marriage functions and discuss its advantages and disadvantages. In Chapter 3 we analyze the Fredrickson-Hoppensteadt model and we prove existence and uniqueness of continuous and classical solutions while keeping the assumptions on the parameters to a minimum and as close to physical reality as possible. In Chapter 4 we show that the Fredrickson-Hoppensteadt model supports persistent solutions (that is, separable solutions in which the time dependent function is an exponential) with a common growth rate for males and females and with a general form of the marriage operator. This result extends a known result for a specific form of the marriage operator. The construction presented here, although more complex, shares properties with the one-sex stable population theory. We believe it provides a good starting point for the development of a two-sex population theory.
Degree
Ph.D.
Advisors
Milner, Purdue University.
Subject Area
Biostatistics|Demographics
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