A pair-formation model with a discrete set of offsprings and child care

Abstract

We present a discrete newborns set-based deterministic model for a two-sex population structured by age and marital status. The model includes the spatial migration, a weighted harmonic mean-type pair formation function, and strong parental care and neglects the separation of pairs. Each sex has pre-reproductive and reproductive age intervals. All adult (of reproductive age) individuals are divided into single males, single females, and permanent pairs. All pairs are of two types: pairs without offsprings under parental care at the given time and pairs taking care of their young offsprings. All individuals of pre-reproductive age are divided into young (under parental care) and juvenile (offsprings who can live without parental care but cannot produce offsprings) groups. It is assumed that births can only occur from couples and after the death of any of the pair partner all young offsprings of this pair die. The model consists of integro-partial differential equations subject to the conditions of integral type. The number of these equations depends on the biologically possible maximal newborns number of the same generation produced by a pair. A class of separable solutions is studied for this model.