Incorporating Migration Into an Age-Structured Population Model With Variable Mortality Rate

Abstract

We modify the McKendrick-von Foerster population model, an age-structured population model, by including a net migration term to model population dynamics when net migration is a significant contributor to population size. Net migration is treated as a continuous function of age and time. We consider the model's mortality rate as both a constant and as a function of age. By allowing the mortality rate to be a function of age, the model better captures more realistic death rates. We then apply this model to the United States population. When the mortality rate is considered as a constant, the model has 3.95% relative error. When the mortality rate is considered as a function of age, it yields a better approximation with a 2.33% relative error. This more accurate model of population dynamics can provide a framework for studying the effect of policy changes and major events on populations and sub-populations.