نوع مقاله : مقاله کامل پژوهشی
نویسندگان
1 دانشجو‌ی کارشناسی ارشد، گروه مهندسی برق، دانشگاه صنعتی همدان، همدان، ایران
2 دانشیار، گروه مهندسی برق، دانشگاه صنعتی همدان، همدان، ایران
چکیده
بیماری کرونا ویروس یا کووید 19 یک بیماری واگیردار بوده که توسط ویروس کرونا ایجاد شده و یک تهدید و نگرانی برای سلامت و اقتصاد کشورها است. اگرچه تولید و توزیع واکسن این بیماری هم اکنون در حال انجام است اما مداخلات غیردارویی هم‌چنان به عنوان یک استراتژی مهم و اساسی برای کنترل شیوع این ویروس در کشور‌های جهان در حال اجرا می‌باشد. هم اکنون با توجه به شرایط موجود، داشتن یک مدل دینامیکی مناسب از این بیماری، اطلاعاتی را در مورد نحوه‌ی رفتار، شیوع، سرعت انتقال و سایر پارامتر‌ها در اختیار قرار خواهد داد. روش‌های مختلف مدل‌سازی ریاضی برای تجزیه و تحلیل الگوهای انتقال این بیماری جدید پیشنهاد شده است. در این مقاله با استفاده از حسابان کسری، دینامیک کووید 19 مورد بررسی قرار گرفته است. یکی از مزیت‌های مهم حسابان کسری که می‌تواند در مدل‌سازی و کنترل بیماری‌های همه‌گیر بسیار کارآمد باشد، داشتن حافظه‌ی بلندمدت است. با داشتن مدل دینامیکی انتقال و شیوع ویروس، تمرکز بر یک استراتژی کنترلی بر اساس مداخلات غیردارویی می‌تواند حائز اهمیت باشد. در این مقاله یک روش کنترل مد لغزشی مرتبه‌ی کسری تطبیقی جدید جهت اتخاذ تصمیمات غیردارویی پیشنهاد شده است. روش پیشنهادی در این مقاله جهت کنترل مداخلات غیردارویی، یک کنترل کننده‌ی مد لغزشی فعال مرتبه‌ی کسری تطبیقی جدید است که به دلیل مقاوم بودن در برابر نامعینی‌های پارامتری و اغتشاشات سیستم می‌تواند عمل‌کرد مناسبی داشته باشد.
کلیدواژه‌ها
موضوعات
عنوان مقاله [English]
Analysis of Fractional Order SEIR Model for Covid 19 and Investigation of its Spread Management with a Novel Adaptive Fractional Order Nonlinear Controller
نویسندگان [English]
- Amir Veisi 1
- Hadi Delavari 2
1 M.Sc. Student, Department of Electrical Engineering, Hamedan University of Technology, Hamedan, Iran
2 Associate Professor, Department of Electrical Engineering, Hamedan University of Technology, Hamedan, Iran
چکیده [English]
Coronavirus, or Covid 19, is a contagious disease caused by the coronavirus and is a threat to the health and economy of countries. Although vaccine production and distribution are currently underway, but non-pharmacological interventions are still being implemented as an important and fundamental strategy to control the spread of the virus in countries around the world. Now, according to the existing conditions, having a suitable dynamic model of this disease will provide information to the relevant authorities about the behavior, prevalence, speed of transmission, and other parameters. Various mathematical modeling methods have been proposed to analyze the transmission patterns of this new disease. In this paper, using fractional calculus, the dynamics of Covid 19 will be investigated. One of the major advantages of fractional calculus, which can be very effective in modeling and controlling epidemics, is its long-term memory property. With a dynamic model of virus transmission and prevalence, focusing on a control strategy based on non-pharmacological interventions can be important. In this paper, a new adaptive fractional order sliding mode controller is proposed for non-pharmacological decisions. The proposed method in this paper for controlling non-pharmacological interventions is an adaptive fractional order active sliding mode control, which can have a good performance due to its robustness against parameter uncertainty and system disturbances.
کلیدواژه‌ها [English]
- Covid 19
- Fractional Order SEIR Model
- Fractional Calculus
- Sliding Mode Control
- Fractional Adaptation Law
- Coronavirus (covid-19). https://covid19.who.int
- Banholzer, et al., Estimating the impact of non-pharmaceutical interventions on documented infections with COVID-19: A cross-country analysis. medRxiv, 2020
- for Disease Control, P. (CDC), https://www.cdc.gov/coronavirus/2019-ncov/i ndex.html.
- Carletti, D. Fanelli, and F. Piazza, COVID-19: the unreasonable effectiveness of simple models. arXiv preprint arXiv:2005.11085, 2020.
- Tagliazucchi, et al., Lessons from being challenged by COVID-19. Chaos, Solitons & Fractals, 2020. 137: p. 109923.
- Ivorra, et al., Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. Comm. in Non. Sci. and Num. Sim., 2020. 88: p. 105303.
- uñez, et al., Potentials of constrained sliding mode control as an intervention guide to manage COVID19 spread. medRxiv, 2020.
- Zamir, et al., Non Pharmaceutical Interventions for Optimal Control of COVID19. Computer Methods and Programs in Biomedicine, 2020. 196: p. 105642.
- Ullah, et al., Optimal control analysis of vector-host model with saturated treatment. The European Physical Journal Plus, 2020. 135(10): p. 1-25.
- H Morris, et al., Optimal, near-optimal, and robust epidemic control. arXiv preprint arXiv:2004.02209, 2020.
- A Pazos, and F. Felicioni, A control approach to the Covid-19 disease using a SEIHRD dynamical model. medRxiv, 2020.
- A Gondim, and L. Machado, Optimal quarantine strategies for the COVID-19 pandemic in a population with a discrete age structure. arXiv preprint arXiv:2005.09786, 2020.
- M Morato, et al., An Optimal Predictive Control Strategy for COVID-19 (SARS-CoV-2) Social Distancing Policies in Brazil. arXiv preprint arXiv:2005.10797, 2020.
- Tsay, et al., Modeling, state estimation, and optimal control for the US COVID-19 outbreak. arXiv preprint arXiv:2004.06291, 2020.
- Berger, Feedback control of the COVID-19 pandemic with guaranteed non-exceeding ICU capacity. arXiv preprint arXiv:2008.09426, 2020.
- Ibeas Hernández, M. De la Sen Parte, and S. Alonso Quesada, Robust Sliding Control of SEIR Epidemic Models. 2014.
- Xiao, Y., X. Xu, and S. Tang, Sliding mode control of outbreaks of emerging infectious diseases. Bulletin of mathematical biology, 2012. 74(10): p. 2403-2422.
- Khalili Amirabadi, A. Heydari, and M. Zarrabi, Analysis and control of SEIR epedemic model via sliding mode control. Advanced Modeling and Optimization, 2016. 18(1): p. 153-162.
- T Angulo, et al., A simple criterion to design optimal nonpharmaceutical interventions for epidemic outbreaks. medRxiv, 2020.
- Rohith, and K. Devika, Dynamics and control of COVID-19 pandemic with nonlinear incidence rates. Nonlinear Dynamics, 2020. 101(3): p. 2013-2026.
- Brauer, C. Castillo-Chavez, and C. Castillo-Chavez, Mathematical models in population biology and epidemiology. Vol. 2. 2012: Springer.
- M Anderson, and R.M. May, Infectious diseases of humans: dynamics and control. 1992: Oxford university press.
- B Hamzah, et al., CoronaTracker: worldwide COVID-19 outbreak data analysis and prediction. Bull World Health Organ, 2020. 1.(32)
- J Clifford, et al., Interventions targeting air travellers early in the pandemic may delay local outbreaks of SARS-CoV-2. medRxiv, 2020.
- Tang, et al., An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov). Infectious disease modelling, 2020. 5: p. 248-255.
- Tang, et al., Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions. Journal of clinical medicine, 2020. 9(2): p. 462.
- Xiong, and H. Yan, Simulating the infected population and spread trend of 2019- nCov under different policy by EIR model. Available at SSRN 3537083, 2020.
- Rajagopal, et al., A fractional-order model for the novel coronavirus (COVID-19) outbreak. Nonlinear Dynamics, 2020. 101(1): p. 711-718.
- Awais, et al., Modeling and simulation of the novel coronavirus in Caputo derivative. Results in physics, 2020. 19: p. 103588.
- A Baba, and B.A. Nasidi, Fractional Order Model for the Role of Mild Cases in the Transmission of COVID-19. Chaos, Solitons & Fractals, 2020: p. 110374.
- Higazy, MA. Alyami, New Caputo-Fabrizio fractional order SEIASqEqHR model for COVID-19 epidemic transmission with genetic algorithm based control strategy. Alexandria Engineering Journal, 2020: Elsevier.
- Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. 1998: Elsevier.
- Dai, and W. Chen, New power law inequalities for fractional derivative and stability analysis of fractional order systems. Nonlinear Dynamics, 2017. 87(3): p. 1531-1542.
- Li, Y., Y. Chen, and I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Computers & Mathematics with Applications, 2010. 59(5): p. 1810-1821.
- W Hethcote, The mathematics of infectious diseases. SIAM review, 2000. 42(4): p. 599-653.
- D Ames, et al., Safety-critical control of active interventions for COVID-19 mitigation. Ieee Access, 2020. 8: p. 188454-188474.
)