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.

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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.

A model of a population dynamics is solved numerically taking into account a discrete set of offsprings and the nonlinear (directed) diffusion. The model consists of a system of integro-partial differential equations subject to conditions of integral type. A spread of initially lokalized population is studied. Some numerical results are discussed.

A model for description of an age-structured population dynamics taking into account a discrete set of offspring, their care, and spatial diffusion in two-dimensional space is studied numerically. The model consists of a coupled system of integro-partial differential equations. Some results are illustrated by figures.