Optimal control theoretic approach to health care investment

Abstract

Health care is ever more important with aging population. Assuming the number of doctors per patient is a good proxy for patient satisfaction, optimal investment in number of doctors may be in the form of investment in local doctors which requires heavy investment in universities and laboratories,and transferring foreign doctors into the country who require considerably higher salaries than local doctors. No additional investment is required for foreign doctors. An optimal control methodology is employed to determine the optimal investment plans for the two alternative sources of doctors to maximize the net(of costs) patient satisfaction over a time horizon.Two models are considered. In one,the population is assumed to remain constant and in the other population is assumed to be increase at an exponential rate. It found that a nation with insufficient number of doctors at the beginning of the time horizon should increase the investment in local doctors gradually while employing foreign doctors as to equate their salaries to the marginal satisfaction of the patients.An equilibrium exists and it is stable.