Modelling of a One-Sex Age-Structured Population Dynamics with Child Care - Repšys, Š.; Skakauskas, V. (Nonlinear Analysis: Modelling and Control, 2007)
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.