Optimum population distribution described by dynamic models and controlled by immigration and job creation

Abstract

In this thesis, dynamic mathematical models are constructed to describe the population distribution in Canada based on the model in previous work by Ahmed and Rahim [1]. Numerical results demonstrate that the model population is in close agreement with the actual population. This indicates that the presented model can be used as a valuable tool for describing the dynamics of population distribution. We also demonstrate that by using modern Systems and Optimal Control theory [2], it is possible to formulate optimum immigration and job creation strategies while maintaining population level close to certain pre-specified targets. An optimization algorithm [2] is then developed based on dynamic programming and gradient algorithm approach. Unknown parameters such as birth rate, death rates and transition rates are estimated and identified. The system model obtained by using the identified parameters is then augmented by adding a fourth equation describing the dynamics of unemployment rate. This model is then used to formulate a control problem with immigration and job creation rates being the decision (control) variables. Using optimal control theory, optimum immigration and job creation policies are determined. Results are illustrated by numerical simulation and they are found to be very encouraging.