A Mathematical Analysis of an Age-Sex-Space-Structured Population Dynamics Model with Random Mating and Females' Pregnancy

Article type: Research Article

Authors: Skakauskas, Vladas

Affiliations: Faculty of Mathematics, Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. E-mail: [email protected]

Abstract: We discuss an age-sex-structured population dynamics deterministic model taking into account random mating of sexes, females' pregnancy and its dispersal in whole space. This model can be derived from the previous one (Skakauskas, 1995) describing migration mechanism by the general linear elliptic operator of second order and includes the male, single (nonfertilized) female and fertilized female subclasses. Using the method of the fundamental solution for the uniformly parabolic second-order differential operator with bounded Hölder continuous coefficients we prove the existence and uniqueness theorem for the classic solution of the Cauchy problem for this model. In the case where dispersal moduli of fertilized females are not depending on age of the mated male we analyze population growth and decay.

Keywords: population dynamics, random mating, gestation of males, pregnancy, migration

DOI: 10.3233/INF-1998-9307

Journal: Informatica, vol. 9, no. 3, pp. 365-386, 1998