Informatica

A model for an age-sex-structured nonlimited population dynamics with the harmonic mean type mating law and females' pregnancy is presented. The existence and uniqueness theorem for the general case of vital rates is proved, the extinction and growth of the population are considered, and a class of the product (separable) solutions is obtained.

A general model for pair formation in age, sex, and sociologically structured interacting human communities is presented. More precisely, the religion factor is taken into account. The model describes dynamics of interacting religions which tolerate both uniconfessional pairs and those with different religions. Two particular models are analyzed. One of them describes the uniconfessional pairs dynamics and allows the religion change only for the sake of marriage. The other one demonstrates the evolution of communities forbidding any confession change. In the case of constant vital rates solutions of these two models are constructed and the longtime behavior of the total numbers of single adults and pairs of each community is demonstrated.

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.

The unique solvability and asymptotic behavior for large time of two cases of symmetric bisexual population model are presented. One of them includes the harmonic mean mating law, while in the other one pair formation occurs only within the same age class.