A One-Sex Population Dynamics Model with Discrete Set of Offsprings and Child Care

We present a one-sex age-structured population dynamics deterministic model with a discrete set of offsprings, child care, environmental pressure, and spatial migration. All individuals have pre-reproductive, reproductive, and post-reproductive age intervals. Individuals of reproductive age are divided into fertile single and taking child care groups. All individuals of pre-reproductive age are divided into young (under maternal care) and juvenile (offspring who can live without maternal care) classes. It is assumed that all young offsprings move together with their mother and that after the death of mother all her young offsprings are killed. The model consists of integro-partial differential equations subject to the conditions of the integral type. Number of these equations depends on a biologically possible maximal newborns number of the same generation produced by an individual. The existence and uniqueness theorem is proved, separable solutions are studied, and the long time behavior is examined for the solution with general type of initial distributions in the case of non-dispersing population. Separable and more general (nonseparable) solutions, their large time behavior, and steady-state solutions are studied for the population with spatial dispersal, too

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability

Modelling of a One-Sex Age-Structured Population Dynamics with Child Care

The Sharpe-Lotka-Mckendrick-von Foerster one-sex population model and Fredrickson-Hoppensteadt-Staroverov two-sex population one are well known in mathematical biology. But they do not describe dynamics of populations with child care. In recent years some models were proposed to describe dynamics of the wild population with child care. Some of them are based on the notion of the density of offsprings under maternal (or parental) care. However, such models do not ensure the fact that offsprings under maternal (or parental) care move together with their mothers (or both parents). In recent years to solve this problem, some models of a sex-age-structured population, based on the discrete set of newborns, were proposed and examined analytically. Numerical schemes for solving of a one-sex age-structured population model with and without spatial dispersal taking into account a discrete set of offsprings and child care are proposed and results are discussed in this paper. The model consists of partial integrodifferential equations subject to conditions of the integral type. Numerical experiments exhibit the stability of the separable solutions to these models

Numerical solving of coupled systems of parabolic and ordinary differential equations

Two coupled systems of parabolic and nonlinear ordinary differential equations arising in kinetics of heterogeneous reactions are studied numerically by using computer calculations. Some numerical results are discussed

On a Fluid Outflow from a Bottle Turned Upside-Down

An incompressible viscous as well as nonviscous fluid outflow from an axially symmetric bottle turned upside-down is considered. This problem relates the gravity acceleration and air bubbles inflow into the bottle and in the mathematical sense presents a very complicated task. The simplified setting of problem based on a one-dimensional approximation of the fluid flow is proposed and results of numerical experiments are discussed

The Structure Modeling of Material Composed of the Orthotropic Crystals

In this paper the model of a elastic composite medium which consists of a matrix containing a set of orthotropic crystals with the random orientation of the anisotropy axes is presented. The axes orientation is described by the Gauss distribution. The numerical investigation is proposed for rectangular plate, when the normal strains are given in the one side. Other sides are free of strain. The finite - difference technique is used for model discretization

The evolution of the panmiction” population taking into account destruction of the foetus

„The evolution of the panmiction” population taking into account destruction of the foetus" Mathematical Modelling Analysis, 1(1), p. 67-75 First Published Online: 14 Oct 201

Solvability and Asymptotic Behavior of a Population Problem Taking into Account Random Mating and Females' Pregnancy

Two deterministic age-sex-structured population dynamics models are discussed taking into account random mating of sexes (without formation of permanent male-female couples), possible destruction of the fetus (abortion), and female's pregnancy. One of them deals with both random and directed diffusion in the whole space while in the other the population is assumed to be nondispersing. The population consists of three components: one maleand two female, the latter two being the single (nonfertilized) female and the fertilized one. The case of a separable solution of the limited nondispersing population (in which death moduli can be decomposed into the sum of two terms where one of them depends on time and age and theother is a function of time and the population size) is analyzed. The existence of a unique solution of the Cauchy problem for the nondispersing population model is proved and its longtime behavior is demonstrated. An analogous situation for the dispersing population is analyzed, too