Journal of applied mathematics & informatics

  • 제42권4호
  • /
  • Pages.945-968
  • /
  • 2024
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

IMPLEMENTATION OF LAPLACE ADOMIAN DECOMPOSITION AND DIFFERENTIAL TRANSFORM METHODS FOR SARS-COV-2 MODEL

  • N. JEEVA (PG and Research Department of Mathematics, The Madura College (affiliated to Madurai Kamaraj University)) ;
  • K.M. DHARMALINGAM (PG and Research Department of Mathematics, The Madura College (affiliated to Madurai Kamaraj University)) ;
  • S.E. FADUGBA (Department of Mathematics, Ekiti State University) ;
  • M.C. KEKANA (Department of Mathematics and Statistics, Tshwane University of Technology) ;
  • A.A. ADENIJI (Department of Mathematics and Statistics, Tshwane University of Technology)
  • 투고 : 2024.01.24
  • 심사 : 2024.04.22
  • 발행 : 2024.07.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This study focuses on SIR model for SARS-CoV-2. The SIR model classifies a population into three compartments: susceptible S(t), infected I(t), and recovered R(t) individuals. The SARS-CoV-2 model considers various factors, such as immigration, birth rate, death rate, contact rate, recovery rate, and interactions between infected and healthy individuals to explore their impact on population dynamics during the pandemic. To analyze this model, we employed two powerful semi-analytical methods: the Laplace Adomian decomposition method (LADM) and the differential transform method (DTM). Both techniques demonstrated their efficacy by providing highly accurate approximate solutions with minimal iterations. Furthermore, to gain a comprehensive understanding of the system behavior, we conducted a comparison with the numerical simulations. This comparative analysis enabled us to validate the results and to gain valuable understanding of the responses of SARS-CoV-2 model across different scenarios.

키워드

과제정보

The authors wish to thank Tshwane University of Technology for their financial support and the Madura college for their continuous support and encouragement.

참고문헌

  1. WHO, Coronavirus disease (COVID-19). https://www.who.int/emergencies/diseases/novel-coronavirus-2019. 
  2. B. Hu, P. Ning, J. Qiu, V. Tao, A.T. Devlin, H. Chen, J. Wang, & H. Lin, Modeling the complete spatiotemporal spread of the COVID-19 epidemic in mainland China, International Journal of Infectious Diseases 110 (2021), 247-257. 
  3. M. Hasoksuz, S. Kilic, & F. Sarac, Coronaviruses and SARS-COV-2, Turkish Journal of Medical sciences 50 (2020), 549-556. 
  4. M.A. Johansson, T.M. Quandelacy, S. Kada, P.V. Prasad, M. Steele, J.T. Brooks, R.B. Slayton, M. Biggerstaff, & J.C. Butler, SARS-CoV-2 Transmission From People Without COVID-19 Symptoms, JAMA Network Open 4 (2021), e2035057. 
  5. 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. 
  6. N.G. Davies, S. Abbott, R.C. Barnard, C.I. Jarvis, A.J. Kucharski, J.D. Munday, C.A.B. Pearson, T.W. Russell, D.C. Tully, A.D. Washburne, T. Wenseleers, A. Gimma, W. Waites, K.L.M. Wong, K. Van Zandvoort, J.D. Silverman, K. Diaz-Ordaz, R. Keogh, R.M. Eggo, W.J. Edmunds, Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England, Science 372 (2021), 6538. 
  7. Y. Liu, A.A. Gayle, A. Wilder-Smith, & J. Rocklov, The reproductive number of COVID-19 is higher compared to SARS coronavirus, Journal of Travel Medicine 27 (2020), 2. 
  8. M. Veera Krishna, Mathematical modelling on diffusion and control of COVID-19, Infectious Disease Modelling 5 (2020), 588-597. 
  9. D. Mart'inez-Rodr'iguez, G. Gonzalez-Parra, & R. Villanueva, Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach, Epidemiologia 2 (2021), 140-161. 
  10. G. Gonzalez-Parra, D. Mart'inez-Rodr'iguez, & R. Villanueva-Mic'o, Impact of a New SARS-CoV-2 Variant on the Population: A Mathematical Modeling Approach, Mathematical and Computational Applications 26 (2021), 25. 
  11. M. Makhoul, H.H. Ayoub, H. Chemaitelly, S. Seedat, G.R. Mumtaz, S. Al-Omari, & L.J. Abu-Raddad, Epidemiological Impact of SARS-CoV-2 Vaccination: Mathematical Modeling Analyses, Vaccines 8 (2020), 668. 
  12. A. Salimipour, T. Mehraban, H.S. Ghafour, N.I. Arshad, & M. Ebadi, RETRACTED: SIR model for the spread of COVID-19: A case study, Operations Research Perspectives 10 (2023), 100265. 
  13. I. Cooper, A. Mondal, & C.G. Antonopoulos, A SIR model assumption for the spread of COVID-19 in different communities, Chaos, Solitons & Fractals 139 (2020), 110057. 
  14. M. D'Arienzo, & A. Coniglio, Assessment of the SARS-CoV-2 basic reproduction number, R0, based on the early phase of COVID-19 outbreak in Italy, Biosafety and Health 2 (2020), 57-59. 
  15. M. Ahumada, A. Ledesma-Araujo, L. Gordillo, & J. Mar'in, Mutation and SARS-CoV-2 strain competition under vaccination in a modified SIR model, Chaos, Solitons & Fractals 166 (2023), 112964. 
  16. A. McMahon, & N.C. Robb, Reinfection with SARS-CoV-2: Discrete SIR (Susceptible, Infected, Recovered) Modeling Using Empirical Infection Data, JMIR Public Health and Surveillance 6 (2020), e21168 
  17. M. Venkatasen, S.K. Mathivanan, P. Jayagopal, P. Mani, S. Rajendran, U. Subramaniam, A.C. Ramalingam, V.A. Rajasekaran, A. Indirajithu, & M. Sorakaya Somanathan, Forecasting of the SARS-CoV-2 epidemic in India using SIR model, flatten curve and herd immunity, Journal of Ambient Intelligence and Humanized Computing (2020), 1-9. 
  18. C. Roberto Telles, H. Lopes, & D. Franco, SARS-COV-2: SIR Model Limitations and Predictive Constraints, Symmetry 13 (2021), 676. 
  19. Z.W. Tong, Y.P. Lv, R.U. Din, I. Mahariq, & G. Rahmat, Global transmission dynamic of SIR model in the time of SARS-CoV-2, Results in Physics 25 (2021), 104253. 
  20. I. Sahu, & S.R. Jena, SDIQR mathematical modelling for COVID-19 of Odisha associated with influx of migrants based on Laplace Adomian decomposition technique, Modeling Earth Systems and Environment 9 (2023), 4031-4040. 
  21. A. Raza, M. Farman, A. Akgul, M.S. Iqbal, A. Ahmad, Simulation and numerical solution of fractional order Ebola virus model with novel technique[J], AIMS Bioengineering 7 (2020), 194-207. 
  22. P. Pue-on, Laplace Adomian decomposition method for solving Newell-Whitehead-Segel equation, Applied Mathematical Sciences 7 (2013), 6593-6600. 
  23. Liberty Ebiwareme, Fun-Akpo Pere Kormane, & Edmond Obiem Odok, Simulation of unsteady MHD flow of incompressible fluid between two parallel plates using Laplace-Adomian decomposition method, World Journal of Advanced Research and Reviews 14 (2022), 136-145. 
  24. F. Haq, K. Shah, G.U. Rahman, Y. Li, & M. Shahzad, Computational Analysis of Complex Population Dynamical Model with Arbitrary Order, Complexity (2018), 1-8. 
  25. J. Xu, H. Khan, R. Shah, A. Alderremy, S. Aly, & D. Baleanu, The analytical analysis of nonlinear fractional-order dynamical models, AIMS Mathematics 6 (2021), 6201-6219. 
  26. N. Jeeva, K.M. Dharmalingam, Mathematical analysis of new SEIQR model via Laplace Adomian decomposition method, Indian Journal of Natural Science 15, (2024) 72148-72157. 
  27. M. Thongmoon, & S. Pusjuso, The numerical solutions of differential transform method and the Laplace transform method for a system of differential equations, Nonlinear Analysis: Hybrid Systems 4 (2010), 425-431. 
  28. A. Harir, S. Melliani, H. El Harfi, & L.S. Chadli, Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model, International Journal of Differential Equations (2020), 1-7. 
  29. A.M. Batiha, B. Batiha, A new method for solving epidemic model, Aust. J. Basic Appl. Sci. 5 (2011), 3122-3126. 
  30. B. Batiha, The solution of the prey and predator problem by differential transformation method, Int. J. Basic Appl. Sci. 4 (2015), 36. 
  31. A. Adeniji, O. Mogbojuri, M. Kekana, & S. Fadugba, Numerical solution of rotavirus model using Runge-Kutta-Fehlberg method, differential transform method and Laplace Adomian decomposition method, Alexandria Engineering Journal 82 (2023), 323-329.