Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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OPTIMAL CONTROL STRATEGY TO COMBAT THE SPREAD OF COVID-19 IN ABSENCE OF EFFECTIVE VACCINE

  • BISWAS, M.H.A. (Mathematics Discipline, Khulna University) ;
  • KHATUN, M.S. (Mathematics Discipline, Khulna University) ;
  • ISLAM, M.A. (Mathematics Discipline, Khulna University) ;
  • MANDAL, S. (Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University) ;
  • PAUL, A.K. (Mathematics Discipline, Khulna University) ;
  • ALI, A. (Department of Mechanical, Robotics and Industrial Engineering, Lawrence Technological University)
  • Received : 2021.04.29
  • Accepted : 2022.01.28
  • Published : 2022.05.30
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Abstract

Many regions of the world are now facing the second wave of boomed cases of COVID-19. This time, the second wave of this highly infectious disease (COVID-19) is becoming more devastating. To control the existing situation, more mass testing, and tracing of COVID-19 positive individuals are required. Furthermore, practicing to wear a face mask and maintenance of physical distancing are strongly recommended for everyone. Taking all these into consideration, an optimal control problem has been reformulated in terms of nonlinear ordinary differential equations in this paper. The aim of this study is to explore the control strategy of coronavirus-2 disease (COVID-19) and thus, minimize the number of symptomatic, asymptomatic and infected individuals as well as cost of the controls measures. The optimal control model has been analyzed analytically with the help of the necessary conditions of very well-known Pontryagin's maximum principle. Numerical simulations of the optimal control problem are also performed to illustrate the results.

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References

  1. R. Acuna-Soto, D.W. Stahle, M.K. Cleaveland, M.D. Therrell, Megadrought and Megadeath in 16th Century Mexico, Emerging Infectious Diseases 8 (2002), 360-362. https://doi.org/10.3201/eid0804.010175
  2. A.S. Austin, A pest in the land: new world epidemics in a global perspective, University of New Mexico Press, 2003.
  3. B. Batista, D. Dickenson, K. Gurski, M. Kebe, N. Rankin, Minimizing disease spread on a quarantined cruise ship: A model of COVID-19 with asymptomatic infections, Math. Biosci. 329 (2020), 108442. https://doi.org/10.1016/j.mbs.2020.108442
  4. M.H.A. Biswas, L.T. Paiva, M.D.R. de Pinho, A SEIR Model for Control of Infectious Diseases with Constraints, Mathematical Biosciences and Engineering 11 (2014), 761-784. https://doi.org/10.3934/mbe.2014.11.761
  5. M.H.A. Biswas, On the Evaluation of AIDS/HIV Treatment: An optimal Control Approach, Current HIV Research 12 (2014), 1-12. https://doi.org/10.2174/1570162X1201140716094638
  6. M.H.A. Biswas,. Necessary Conditions for Optimal Control Problems with State Constraints: Theory and Applications, PhD Thesis, Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Portugal, 2013.
  7. M.H.A. Biswas, AIDS epidemic worldwide and the millennium development strategies: A light for lives, HIV and AIDS Review 11 (2012), 87-94. https://doi.org/10.1016/j.hivar.2012.08.004
  8. M.H.A. Biswas, Optimal Control of Nipah Virus (NiV) Infections: A Bangladesh Scenario, Journal of Pure and Applied Mathematics: Advances and Applications 12 (2014), 77-104.
  9. M.H.A. Biswas, On the Immunotherapy of HIV Infections via Optimal Control with Constraint, Proceedings of the 18th International Mathematics Conference, Dhaka, 20-22 March 2014, 51-54.
  10. M.H.A. Biswas, Optimal Chemotherapeutic Strategy for HIV Infections-State Constrained Case, Proceedings of the 1st PhD Students Conference in Electrical and Computer Engineering, Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Portugal, 2012.
  11. M.H.A. Biswas, Model and Control Strategy of the Deadly Nipah Virus (NiV) Infections in Bangladesh, Research & Reviews in Biosciences 6 (2012), 370-377.
  12. M.H.A. Biswas, M.M. Haque, U.K. Mallick, Optimal Control Strategy for the Immunotherapeutic Treatment of HIV Infection with State Constraint, Optimal Control. Applications and Methods 40 (2019), 1-12. https://doi.org/10.1002/oca.2459
  13. M.H.A. Biswas, M.A. Islam, S. Akter, S. Mandal, M.S. Khatun, S.A. Samad, A.K. Paul, M.R. Khatun, Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak, Computer Modeling in Engineering & Sciences 125 (2020), 1033-1060. https://doi.org/10.32604/cmes.2020.012792
  14. D.S. Ceron et al., Self-reported loss of smell without nasal obstruction to identify COVID-19. The multicenter Coranosmia cohort study, Jourmal of Infection 81 (2020), 614-620.
  15. T.M. Chen, J. Rui, Q. Wang, Z. Zhao, J. Cui, and L. Yin, A Mathematical Model for Simulating the Phase-Based Transmissibility of A Novel Coronavirus, Infectious Diseases of Poverty 9 (2020).
  16. Coronavirus Pandemic Report, Retrieved from https://www.worldometers.info/coronavirus/. Accessed on 10 October 2020.
  17. F. Di, et al., Science of the Total Environment Minimization of spreading of SARS-CoV-2 via household waste produced by subjects affected by COVID-19 or in quarantine, Sci. Total Environ. 743 (2020), 140803. https://doi.org/10.1016/j.scitotenv.2020.140803
  18. P. Eckardt, et al., Hospital affiliated long term care facility COVID-19 containment strategy by using prevalence testing and infection control best practices, Am. J. Infect. Control 000 (2020), 7-10.
  19. A.J. Ekonomou, Byzantine Rome and the Greek Popes, Lexington Books, 2007.
  20. W.H. Fleming, and R.W. Rishel, Deterministic and Stochastic Optimal Control, Springer Verlag, New York, 1975.
  21. C. Garcia-vidal, et al., Incidence of co-infections and super-infections in hospitalized patients with COVID-19: a retrospective cohort study, Clinical Microbiology and Infection 27 (2021), 83-88. https://doi.org/10.1016/j.cmi.2020.07.041
  22. E. Gignoux, R. Idowu, L. Bawo, L. Hurum, A. Sprecher, M. Bastard, K. Porten, Use of Capture-Recapture to Estimate Underreporting of Ebola Virus Diseases, Montserrado Country, Liberia, Emerging Infectious Diseases 21 (2015), 2265-2267. https://doi.org/10.3201/eid2112.150756
  23. J.N. Hays, Epidemics and pandemics their impacts on human history, Santa Barbara, CA: ABC-CLIO, 2005.
  24. M.H. Kabir, M.O. Gani, S. Mandal, M.H.A. Biswas, Modeling the dispersal effect to reduce the infection of COVID-19 in Bangladesh, Sensors International 1 (2020), 100043. https://doi.org/10.1016/j.sintl.2020.100043
  25. M.S. Khatun, M.H.A. Biswas, Optimal control strategies for preventing hepatitis B infection and reducing chronic liver cirrhosis incidence, Infectious Disease Modelling 5 (2020), 91-110. https://doi.org/10.1016/j.idm.2019.12.006
  26. M.S. Khatun, M.H.A. Biswas, Mathematical analysis and optimal control applied to the treatment of leukemia, Journal of Applied Mathematics and Computing 64 (2020), 331-353. https://doi.org/10.1007/s12190-020-01357-0
  27. M.S. Khatun, M.H.A. Biswas, Modeling the effect of adoptive T cell therapy for the treatment of leukemia, Computational and Mathematical Methods 2 (2019), 15-45.
  28. J. Koenemann, G. Licitra, M. Alp, M. Diehl, Open OCL-Open Optimal Control Library Robotics Science and Systems, Workshop submission, Extended abstract, 2019.
  29. G.C. Kohn, Encyclopedia of Plague and Pestilence: From Ancient Times to the Present, Checkmark Books, Princeton, New Jersey, 2002
  30. A.J. Kucharski, T.W. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, M.E. Eggo, Early Dynamics of Transmission and Control of COVID-19: A Mathematical Modelling Study, The Lancet Infectious Diseases 20 (2020), 30144-4.
  31. J. Lin, et al., Science of the Total Environment Containing the spread of coronavirus disease 2019 (COVID-19): Meteorological factors and control strategies, Sci. Total Environ. 744 (2020), 140935. https://doi.org/10.1016/j.scitotenv.2020.140935
  32. Q. Lin, S. Zhao, D. Gao, Y. Lou, S. Wang, S.S. Musa, M.H. Wang, Y. Cai, W. Wang, L. Yang, H. Daihai, A Conceptual Model for the Coronavirus Disease 2019 (COVID-19) Outbreak in Wuhan, China with Individual Reaction and Governmental Action, International Journal of Infectious Diseases 93 (2020), 211-216. https://doi.org/10.1016/j.ijid.2020.02.058
  33. T. Maugh, An Empire's Epidemic, Retrieved from https://www.ph.ucla.edu. Accessed on 20 March 2020.
  34. Mayo Clinic, Coronavirus disease 2019 (COVID-19) - Symptoms and causes Retrieved from https://www.mayoclinic.org/diseases-conditions/coronavirus/symptoms-causes/syc-20479963 on 14 April 2020. Accessed on 18 October 2020.
  35. NCBI, COVID-19 and Vascular disease, Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7438984/. Accessed on 18 October 2020.
  36. K.D. Patterson, Typhus and its control in Russia, Med Hist. 37 (1993), 361-381. https://doi.org/10.1017/S0025727300058725
  37. W.E. Paul, Fundamental immunology, Lippincott Williams & Wilkins, 2008, ISBN: 978-0-7817-6519-0.
  38. A. Prichard, J. Fothergill, Influenza in 1775, The Lancet, 143 (1894), 175-176. https://doi.org/10.1016/S0140-6736(01)66026-4
  39. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mishchenko, The mathematical theory of optimal processes, John Wiley and Sons, USA, 1962.
  40. W. Rosen, Justinian's Flea: Plague, Empire, and the Birth of Europe, New York, 2007.
  41. T.A. Rowe, M. Patel, R.O. Conor, S. Mcmackin, V. Hoak, L.A. Lindquist, COVID-19 exposures and infection control among home care agencies, Arch. Gerontol. Geriatr. 91 (2020), 104214. https://doi.org/10.1016/j.archger.2020.104214
  42. S. Scasciamacchia, L. Serrecchia, L. Giangrossi, G. Garofolo, A. Balestrucci, G. Sammartino, A. Fasanella, Plague Epidemic in the Kingdom of Naples, 1656-1658, Emerging Infectious Diseases 18 (2012), 186-188. https://doi.org/10.3201/eid1801.110597
  43. D.G. Smith, Coronavirus May Be a Blood Vessel Disease, Which Explains Everything, Retrieved from https://elemental.medium.com/coronavirus-may-be-a-blood-vessel-disease-which-explains-everything-2c4032481ab2. Accessed on 18 October 2020.
  44. A. Suzuki, Smallpox and the epidemiological heritage of modern Japan: Towards a total history, Medical History 55 (2011), 313-318. https://doi.org/10.1017/S0025727300005329
  45. UNAIDS report on the global AIDS epidemic 2010, Global report, Retrieved from https://www.unaids.org/globalreport/documents/20101123GlobalReportfullen.pdf. Accessed on 5 September 2020.
  46. World Health Organization (WHO), Retrieved from https://www.who.int/emergencies/diseases/novel-coronavirus-2019/covid-19-vaccines. Accessed on 5 September 2020.
  47. J. Wu, K. Leung, G.M. Leung, Nowcasting and Forecasting the Potential Domestic and International Spread of the 2019-Ncov Outbreak Originating in Wuhan, China: A Modelling Study, Lancet 395 (2020), 689-697. https://doi.org/10.1016/s0140-6736(20)30260-9
  48. X. Xu, P. Chen, J. Wang, J. Feng, H. Zhou, X. Li, W. Zhong, P. Hao, Evolution of the Novel Coronavirus from the Ongoing Wuhan Outbreak and Modeling of Its Spike Protein for Risk of Human Transmission, Science China Life Sciences 63 (2020), 457-460. https://doi.org/10.1007/s11427-020-1637-5
  49. S. Zhang, M. Diao, Y. Wenbo, L. Pei, Z. Lin, D. Chen, Estimation of the Reproductive Number of Novel Coronavirus (COVID-19) and the Probable Outbreak Size on the Diamond Princess Cruise Ship: A Data-driven Analysis, International Journal of Infectious Diseases 93 (2020), 201-214. https://doi.org/10.1016/j.ijid.2020.02.033
  50. S. Zhao, S. Salihu, L. Qianying, Jinjun, G. Yang, W. Wang, Y. Lou, L. Yang, D. Gao, H. Daihai, H.W. Maggie, Estimating the Unreported Number of Novel Coronavirus (2019-nCoV) Cases in China in the First Half of January 2020: A Data-Driven Modelling Analysis of the Early Outbreak, Journal of Clinical Medicine 9 (2020).
  51. S. Zhao, Q. Lin, J. Ran, S.S. Musa, G. Yang, W. Wang, Y. Lou, D. Gao, L. Yang, D. He, M.H. Wang, Preliminary Estimation of the Basic Reproduction Number of Novel Coronavirus (2019-nCoV) in China, from 2019 to 2020: A Data-Driven Analysis in the Early Phase of the Outbreak, International Journal of Infectious Diseases 92 (2020), 214-217. https://doi.org/10.1016/j.ijid.2020.01.050