Product solutions and asymptotic behaviour of sex-age-dependent populations with random mating and females'' pregnancy

This paper deals with some models for an age-sex (or age-sex-space)-structured population consisting of male, single and fertilized female subclasses taking into account random coupling of sexes (for a period of mating only) and females' pregnancy. The principal specialization of the age structure is that the death moduli can be decomposed into the sum of two terms. The first term depends on age only and represents death by natural causes, while the second one is a function of the population spatial density and represents environmental effects or equals zero for unlimited populations. For all models separable solutions are presented and, for certain forms of the vital rates, the asymptotic behaviour of separable and general solutions for non-dispersing population is demonstrated. For the stationary non-dispersing population the possible oscillation in the female age distribution is analyzed. For the dispersing population two different types of separable and a type of non-separable solution are presented.