An application of optimal control in medical systems: optimal investment strategy in doctors

Health care is ever more important with the aging population and with the increased awareness of the importance of the medical systems due to the corona crisis that showed the capacity of the health care infrastructure, especially in terms of numbers of health care personnel such as doctors, was not sufficient. Assuming that the number of doctors per patient is one of the determinants of patient satisfaction, optimal investments in new doctors, specialist doctors and foreign doctors are analyzed. Optimal Control Theory is employed to determine the optimal investment strategy for new doctors (new graduates), specialists and foreign doctors to maximize the net (of costs) patient satisfaction over a fixed time horizon. It is found that a nation with an insufficient number of total doctors and specialist doctors at the beginning of the planning horizon should increase the investment in new doctors as a quadratic function of time, increase the local specialist doctors linearly, while employing foreign doctors as to equate their cost to the marginal satisfaction of patients.