Abstract
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.
Highlights
Many species of wild animals care for their offsprings
In [6], a model for two sex population with strong maternal and weak paternal care is given. The care of this type means that all young offsprings die if their mother dies, but they are protected from the inevitable death in the case of death of their father
Numerical schemes are based on the method of the characteristic lines
Summary
Many species of wild animals care for their offsprings This phenomenon is natural for many species of mammals and birds and forms the main difference between the behavior of the population taking child care and that without maternal (or parental) duties [1, 8]. In [6], a model for two sex population with strong maternal and weak paternal care is given The care of this type means that all young offsprings die if their mother dies, but they are protected from the inevitable death in the case of death of their father. Such models do not ensure the fact that offsprings under maternal (or parental) care move together with their mothers (or both parents) To solve this problem, some models of a sex-age-structured population, based on the discrete set of newborns, were proposed.
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