A two-sex population dynamics model with strong parental care

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

“…In this section by using computer modelling, we study both nondispersing population model (1)- (5) and model (20)-(23) of the population with the spatial diffusion. We assume that integer n in both models is equal to 3.…”

“…The existence and uniqueness theorem for problems (7)-(9), (5), and (10), (11) is proved and, in the case of stationary vital rates, the large time behavior of solution (6) is given in [1,8].…”

“…In [2][3][4][5], four age-structured population dynamics models with child care are proposed, two for one-sex and the other two for two-sex population. The main requirement in these papers is that all offsprings under maternal (or parental) care die if their mother (or any of their parents) dies.…”

Separable Solutions to an Interacting Human Communities Model

“…(2.1)-(2.7) correspond to solutions (w 1 ,w 2 , λ) of problem (3.12)-(3.15) and (3.7). To treat the existence or nonexistence of separable solutions we follow the papers [10,9] in which we used the Prüss and Schappacher [4] method applied for the investigation of separable solutions to the Staroverov [11] model with the Keyfitz-Hadeler pair formation function [5]. According to this method, we have to reformulate system (3.12)-(3.15) and then apply Schauder's fixed-point principle [6].…”

“…references in Hadeler [2], Prüss and Schappacher [4]). Both random mating (without formation of permanent male-female couples) and monogamous marriage models (see Frederickson [1], Hoppensteadt [3], Staroverov [11], Hadeler [2], Skakauskas [9] and references therein) are usually used. The most general sex-age-structured population deterministic model taking into account marriages has been proposed by Hoppensteadt [3] and Staroverov [11], and consists of a system of three integro-differential equations for the densities of single (unmarried) females, single males, and pairs.…”