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A Mathematical Analysis of an Age-sex-space-structured Population Dynamics Model with Random Mating and Females' Pregnancy

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 Holder 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. In the paper (Skakauskas, 1994) we have developed a general deterministic model for an age-sex-structured population dynamics taking into account random mating of sexes without formation of permanent male-female couples, female's pregnancy, possible de- struction of the fetus (abortion), and female's sterility periods after abortion and delivery. The population is divided into five components: one male and four female, the latter four being the single (nonfertilized) female, fertilized female, female from sterility pe- riod after abortion, and female from sterility one following delivery. Each sex has three age-grades: pre-reproductive, reproductive, and post-reproductive. It is assumed that for each sex the commencement of each grade as well as the duration of the gestation and female's sterility periods are independent of individuals or time. Latter, in (Skakauskas, 1995), we generalized this model for the spatially dispersing population in whole space. Spatial dispersal mechanism in this model is described by an integral operator. In the present paper we simplify the model in (Skakauskas, 1995) by neglecting abor- tion and female's sterility periods, replace the integral describing operator migration by