An Age Structure Model With Age-Migration Flow (A Mathematical Population Model)

Abstract

This study deals with an age structured model with migration effect to study the dynamics of human population. The proposed model is a modified form of Mckendrick Von-Foerster equation (M-F Model) which has a partial differential equation of first order with initial condition and boundary condition. The initial condition is defined by the number of people of zero age and boundary condition given by the population at initial time, by using the partial differential equation defined as the dynamical flow that affect the dynamics of population density per ages, that means migration between ages, deaths per ages and total migration in the system. Our model is a deterministic model, in which we ignored the fertility rate and births are determined by birth rate. The variables in this model are continuous variables with range R⁺ {0} except for age migration whose range is R . A continuous time model is taken into account for the solution of the age structured model with some condition. The modified model allows forecasting the age dependent population density in the social system and beneficial in resources allocation and government policies.