OPTIMAL CONTROL THEORETIC APPROACH TO INVESTMENT IN DOCTORS
Keywordsinvestment in doctors, optimal control theory, patient satisfaction
AbstractHealth care is ever more important with aging population. Assuming the number of doctors per patient is one of the determinants of patient satisfaction, optimal investment in practitioner doctors, specialist doctors and foreign doctors are analyzed given the total number of doctors (domestic) are exogenously determined. The high cost of investment in specialist doctors are weighted against the high salaries of imported foreign doctors.
An optimal control theory is employed to determine the optimal investment plans for the two alternative sources of specialist doctors to maximize the net (of costs) patient satisfaction over a fixed time horizon.
It is found that a nation with insufficient number of specialist doctors at the beginning of the time horizon should increase the investment in local specialist doctors gradually while employing foreign doctors as to equate their salaries to the marginal satisfaction of the patients. An equilibrium point exists, and it is stable.
Babcock, J.M., Babcock, B.D., & Schwartz, M.Z. (2013). Maintaining sufficient and quality physician’s workforce: the role of for-profit medical schools. Health Services Insight, 6, 87-98. http://dx.doi.org/10.413/HSI.S10462.
Batbata, E., Dorjdagva, J., Livsannyam, A., Savino, M.M., & Amneta, P. (2017). Determinants of patient satisfaction. A systematic review. Perspectives on Public Health, 137(2), 89-101. http://dx.doi.org/10.1177/1757913916634136.
Boquiran, V.M., Hack, T., Beaver, K. , & Williamson, S. (2015). What do measures of patient satisfaction with the doctor tell us? Patient Educating and Counseling, 98(12), 1465-1473. http://dx.doi.org/10.1016/j.pec.2015.05.020.
Chojnicki, X., & Moullan, Y. (2018). Is there a “pig cycle” in the labor supply of doctors? How training and immigration policies respond to physician shortages. Social Science Medicine, 200, 227-237. http://dx.doi.org/10.1016/j.socscimed.2018.01.038.
Cooper, R.A. (2009). States with more physicians have better health care. Health Affairs, 28(1), 91-102. http://dx.doi.org/10.1377/hlthaff.28.1.w91.
Crimson (2017). Top 7 medical Schools Producing the Best Doctors in Australia and New Zealand, https://www.crimsoneduaction.org/za/blog/topmedical-schoolaustralia/ Newzealand.Published (accessed: 24.07.2019).
Eurostat (2018). Statistics explained, Health care personnel-Physicians.pp.1, https://ec.europa.eu/eurostat/statistics-explained/pdfscache/37382.pdf (accessed: 31.07.2019).
Faezipor, M., & Ferreira, S. (2013). A systems dynamic point of view of patient satisfaction in health care. Procedia Computer Science, 16(1), 148-156. http://dx.doi.org/10.1016/j.procs.2013.01.016.
Farahani, M., Subramanian, S.V., & Canning, D. (2009). The effects of changes in health resources on infant mortality in short- and long-run: A longitudinal econometric analysis. Social Science & Medicine, 68(11), 1918-1925. http://dx.doi.org/10.1016/j. socscimed.2009.03.023.
Grover, A. (2006). Critical care workforce: a policy perspective. Critical Care Medicine, 34(3), 7-11.
Hansen, E. (2011). Applications of optimal control to infectious disease modelling. Ph.D. Thesis. Kingston, Ontario, Canada: Queens University.
Hockey, P.M., & Marshall, M.N. (2009). Doctors and quality improvement. Journal of the Royal Society of Medicine, 102(5), 173-176. http://dx.doi.org/10.1258/ jrsm.2009.090065.
Kamien, M.I, & Schwartz, N.L. (1991). Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management 2nd Edition. Amsterdam: Elsevier.
Kerr, E. (2019). 10 Most Expensive Private Medical Schools. US News and World Report, https://www.usnews.com/education/best-graduate-schools/the-short-list-gradschool/articles/most-expensive private-medical-schools (accessed: 13.01.2019).
Lin, F., Muthuraman, K., & Lawley, M. (2010). An optimal control theory approach to non-pharmaceutical interventions. BMC Infectious Diseases, 10(32), 1-13. http:// dx.doi.org/10.1186/1471-2334-10-32.
Merkley, A., & Bickmore, A.M. (2017). The Top Five Recommendations for Improving the Patient Experience. Health Catalyst, 1-7.
Momoh, A.A., & Fügenschuh, A. (2018). Optimal control of intervention strategies and cost effectiveness analysis for a Zika virus model. Operations Research for Health Care, 18, 99-111. http://dx.doi.org/10.1016/j.orhc.2017.08.004.
Nylenna, M., Bjertnaes, Ø.A., Saunes, I.S., & Lindahl, A.K. (2015). What is Good Quality of Health Care? Professions and Professionalism: Special Issue: Professional Satisfaction and the Quality of Medical Care, 5 (1), 1-15. http://dx.doi.org/10.7577/pp.909.
OECD (2017). Health at a Glance 2017: OECD Indicators. Paris: OECD Publishing. http://dx.doi.org/10.1787/19991312.
OECD Data (2017). Doctors, https:/data.oecd.org/healthres/doctors.htm (accessed: 31.07.2019).
OECD (2019a). Health Statistics Nov.2019 – Frequently Requested Data, https://www.oecd.org/health/OECD-Health-Statistics-2019-Frequently-Requested-Data.xls (accessed: 13.01.2019).
OECD (2019b). GDP, volume – annual growth rates in percentage, https://stats.oecd.org/index.aspx?queryid=60703 (accessed: 13.01.2019).
OECD (2019c). Better Policies for Better Health. Health Work Force policies in OECD countries, https://www.oecd.org/health/health-systems/Health-workforce-policies- in-oecd-countries-Policy-brief.pdf. (accessed: 31.07.2019).
OECD (2019d). Life expectancy, https://stats.oecd.org/index.aspx?queryid=30114. (accessed: 13.01.2019).
OLCDB (2018). Overview of the cost of training health professional. Canadian Ministry of Health.
Pando, C. (2016). The influence of number of physicians on infant mortality across nations. Lehigh Review, 24, 61-71.
Pontryagin, L.S., Bolyantski, V.G., Gamkrelidze, R.V., & Mischenko, E.F. (1963). The Mathematical Theory of Optimal Processes. New York: Wiley Science. http://dx.doi.org/10.1002/zamm.19630431023.
Rowthorn, R., & Toxvaerd, F. (2012). The optimal control of infectious diseases via prevention and treatment. CEPR Discussion Paper, DP8925.
Sargen, M., Hooker, R.S., & Cooper, R.A. (2011). Gaps in supply of advance practice nurses and physicians’ assistants. Journal of American College of Surgeons, 212(6), 991- 999. http://dx.doi.org/10.1016/j.jamcollsurg.2011.03.005.
Scheffler, R.M., & Arnold, D.R. (2019). Shortages and surpluses of doctors and nurses in the OECD: What looms ahead? Health Economics, Policy and Law, 14(29), 274-290. http://dx.doi.org/10.1017/S174413311700055X.
Scheffler, R.M., Liu, J.X., Kinfu, Y., & Poz, M.R.D. (2008). Forecasting the global shortage of physicians: An economic-and needs based approach. Bulleting of World Health Organization, 86(7), 516-523.
Senić, V., & Marinković, V. (2012). Patient care, satisfaction and service quality in health care. International Journal of Consumer Studies, 37(3), 312-319. http://dx.doi.org/10.1111/j.1470-6431.2012.01132.x.
Sharomi, O., & Malik, T. (2017). Optimal control in Epidemiology. Annals of Operations Research, 251(1-2), 55-71. http://dx.doi.org/10.1007/s10479-015-1834-4.
Shetty, A., & Shetty, S. (2014). The correlation between physicians to population (1000) ratio and life expectancy. Journal of Medicine and Clinical Research, 2(4), 699-706.
Tehrani, A.B., Feldman, S.R., Camacho, F., Rajesh, F.T., & Balakrishnan, R. (2011). Patient Satisfaction with Outpatient Medical Care in the United States. Health Outcomes Research in Medicine, 2(4), 197-202. http://dx.doi.org/10.1016/j.ehrm.2011.09.001.
Vernon, J.A., & Hughen, W.K. (2006). A primer on dynamic optimization and optimal control in pharma economics. Value in Health, 9(2), 106-113. http://dx.doi.org/10.1111/ j.1524-4733.2006.00088.x.
Vuković, M., Gvozdenović, B.S., Gajić, T., Gajić, B.S., Jakovljević, M., & McCormick, B.P. (2012). Validation of a patient satisfaction questionnaire in primary health care. Public Health, 126(8), 710-718. http://dx.doi.org/10.1016/j.puhe.2012.03.008.
World Bank (2017). World Bank Data, https://data.worldbank.org/indicator/SP.DYN. IMRT.IN (accessed: 01.08.2019).
World Health Organization (2019). Density of physicians (total number per 1000 population, latest available year), https://www.who.int/gho/health_workforce/physicians_ density/en (accessed: 01.08.2019).
World Health Organization (2018). Progress towards the SDGs: A selection of data from World Health Statistics, https://www.who.int/gho/publications/world_health_statistics/ 2018/EN_WHS2018_SDGhighlights.pdf?ua=:2018 (accessed: 13.01.2019).
World Health Organization (2018). World health statistics 2018: monitoring health for the SDGs, sustainable development goals. CC BY-NC-SA 3.0 IGO.5., https://apps.who.int/iris/handle/10665/272596 (accessed: 31.07.2019).
World Health Organization, World Bank, & OECD (2018). Delivering Quality Health Services: A Global Imperative for Universal Health Coverage. Genève: World Health Organization.
Xesfingi, S., & Vozikis, A. (2016). Patient satisfaction with the healthcare system: Assessing the impact of socio-economic and healthcare provision factors. BMC Health Services Research, 16, 94. http://dxd.doi.org/10.1186/s12913-016-1327-4.
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