Informatica

Two models for an age-structured nonlimited population dynamics with maternal care of offspring are presented. One of them deals with a bisexual population and includes a harmonic mean type mating of sexes and females' pregnancy. The other one describes dynamics of an asexual population. Migration is not taken into account. 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 for these two models. The long-time behavior of the asexual population is obtained in the stationary case of vital rates.

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.