Hastane kapasitesini aşmayacak şekilde Covid-19 yayılımının geri adımlamalı kontrolü

Year 2021, , 554 - 565, 15.04.2021

Haci Mehmet Guzey

https://doi.org/10.17714/gumusfenbil.753297

Abstract

COVID-19 salgınının, İtalya örneğine dayanan sosyal uzaklaştırma önlemleri ile geri adımlamalı kontrol metodu kullanılarak hastanede yatması gereken hasta sayısının, mevcut yatak kapasitesini geçmeyecek şekilde kontrolü ele alınmıştır. Sosyal mesafe önlemleri, sokağa çıkma yasağı gibi önlemler ile devletler ve yerel idareler salgının yayılmasını önlemek istemektedir. Salgının tamamen yayılmasını önlemek ancak mutlak bir tecrit ile olabilecekken, bu çözüm sosyal hayatın ve ekonominin aşırı derecede olumsuz etkilenmesine sebep verecektir. Bu nedenle, her bir ülke/şehir, en azından kendi yatak kapasitesini aşmayacak şekilde salgını kontrol altına almak isteyecektir. Bu makaledeki bulgular, şehir yöneticilerine veyahut genel idarecilere, salgını yönetmek için referans teşkil edecektir. İnsanların salgınla olan alakasına göre, bu makalede toplum sekiz bölüme ayrılmıştır. Bunlarda bir gurup ise tedavisi zaruri olmuş guruptur. Geri adımlamalı denetleyici vasıtasıyla, hastaneye yatması gereken hasta sayısının, mevcut yatak kapasitesinden az değerde tutulduğu ispatlanmıştır. Benzetim sonuçları da iddia edilen kontrolcünün sorunsuz çalıştığını göstermektedir.

Keywords

Covid-19, Geri adımlamalı kontrol, Yayılım kontrolü

Back-stepping control of Covid-19 spread not to exceed hospital capacity

Abstract

In this paper, controlling the number of patients who are required to stay in hospitals due to covid-19 through back-stepping controller is considered by using data from Italy.. States and local administrations want to prevent the spread of the outbreak, with measures such as social distance measures, curfews. Even though the absolute control of the pandemic can be reached through absolute isolation, this solution will cause excessive negative effects on social life and economy. Therefore, each country/city would like to control the outbreak, at least not exceeding its bed capacity. The results of this article has potential of serving as a reference for city administrators or general administrators to manage the outbreak. Based on the current health condition of the people due to the epidemic, society is divided into eight sections in this article. One of these eight population groups is the ones whose hospital treatment is mandatory. With the back-stepping controller, it is proven that the number of patients who need to be hospitalized can be kept below the current bed capacity. Simulation results also show that the proposed controller is effectively controls the patients those need to be hospitalized.

Keywords

Covid-19, Back-stepping control, Spread control

References

• Barbarossa, M. V., Fuhrmann, J., Heidecke, J., Varma, H. V., Castelletti, N., Meinke, J. H., Krieg, S. and Lippert, T. (2020). A first study on the impact of current and future control measures on the spread of COVID-19 in Germany. medRxiv preprint. https://doi.org/10.1101/2020.04.08.20056630.
• Bin, M., Cheung, P., Crisostomi, E., Ferraro, P., Myant, C., Parisini, T. and Shorten R. (2020). On fast multi-shot epidemic interventions for post lockdown mitigation: Implications for simple COVID-19 models. arXiv:2003.09930.
• Casella F. (2020). Can the COVID-19 epidemic be managed on the basis of daily data? IEEE Control Systems Letters, 5(3), 1079-1084. https://doi.org/10.1109/LCSYS.2020.3009912
• Casella F. (2021). Can the COVID-19 Epidemic be controlled on the basis of daily test reports?. IEEE Control Systems Letters. 5(3),1079-1084. https://doi.org/10.1109/LCSYS.2020.3009912.
• Dehning, J., Zierenberg, J., Spitzner, F. P., Wibral, M., Neto, J. P., Wilczek, M. and Priesemann, V. (2020). Inferring COVID-19 spreading rates and potential change points for case number forecasts. Science 369(6500). https://doi.org/10.1126/science.abb9789
• German, R., Djanatliev, A., Maile, L., Bazan, P. and Hackstein, H. (2020). Modeling exit strategies from COVID-19 lockdown with a focus on antibody tests. medRxiv preprint. https://doi.org/10.1101/2020.04.14.20063750.
• Giordano, G., Blanchini, F., Bruno, R., Colaneri, P., Filippo, A. D., Matteo, A. D. and Colaneri, M. (2020). Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nature Medicine.26, 855–860. https://doi.org/10.1038/s41591-020-0883-7
• Guzey, H. M., Xu, H. and Sarangapani, J. (2016). Neural network‐based finite horizon optimal adaptive consensus control of mobile robot formations. Optimal Control Applications and Methods 37(5), 1014‐1034. https://doi.org/10.1002/oca.2222
• Guzey, H. M., Vignesh, N., Jagannathan, S., Dierks, T. and Acar, L. (2017). Distributed consensus-based event-triggered approximate control of nonholonomic mobile robot formations, American Control Conference (ACC), Seattle, WA, 3194-3199. https://doi.org/10.23919/ACC.2017.7963439
• Guzey, H. M., Dierks, T. and Jagannathan, S. (2019). Modified consensus-based output feedback control of quadrotor UAV formations using neural networks. Journal of Intelligent & Robotic Systems 94, 283–300. https://doi.org/10.1007/s10846-018-0961-y
• Kissler, S., Tedijanto, C., Lipsitch, M. and Grad, Y. H. (2020). Social distancing strategies for curbing the COVID-19 epidemic, medRxiv preprint. https://doi.org/10.1101/2020.03.22.20041079.
• Lauro, F. D., Kiss, I. Z., Rus, D. and Santina, C. D. (2021). Covid-19 and flattening the curve: A feedback control perspective. IEEE Control Systems Letters 5(4), 1435-1440. https://doi.org/10.1109/LCSYS.2020.3039322.
• Maharaj, S. and Kleczkowski, A. (2012). Controlling epidemic spread by social distancing: Do it well or not at all. BMC Public Health 12 (679), 1–16. https://doi.org/10.1186/1471-2458-12-679
• Maier, B. F. and Brockmann, D. (2020). Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China. Science 368(6492) 742-746. https://doi.org/10.1126/science.abb4557.
• Tsay, C., Lejarza, F., Stadtherr, M. A. and Baldea, M. (2020). Modeling, state estimation, and optimal control for the US COVID-19 outbreak. Scientific Reports 10, 10711. https://doi.org/10.1038/s41598-020