DOI QR코드

DOI QR Code

EPIDEMIC SEIQRV MATHEMATICAL MODEL AND STABILITY ANALYSIS OF COVID-19 TRANSMISSION DYNAMICS OF CORONAVIRUS

  • S.A.R. BAVITHRA (Department of Mathematics, Periyar University) ;
  • S. PADMASEKARAN (Department of Mathematics, Periyar University)
  • 투고 : 2023.04.26
  • 심사 : 2023.07.12
  • 발행 : 2023.11.30

초록

In this study, we propose a dynamic SEIQRV mathematical model and examine it to comprehend the dynamics of COVID-19 pandemic transmission in the Coimbatore district of Tamil Nadu. Positiveness and boundedness, which are the fundamental principles of this model, have been examined and found to be reliable. The reproduction number was calculated in order to predict whether the disease would spread further. Existing arrangements of infection-free, steady states are asymptotically stable both locally and globally when R0 < 1. The consistent state arrangements that are present in diseases are also locally steady when R0 < 1 and globally steady when R0 > 1. Finally, the numerical data confirms our theoretical study.

키워드

과제정보

The second author is supported by the fund for improvement of Science and Technology Infrastructure (FIST) of DST (SR/FST/MSI-115/2016).

참고문헌

  1. Anwar Zeb, et. al., Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class, BioMed Research International 2020 2020, Article ID 3452402. https://doi.org/10.1155/2020/3452402
  2. Ashwin Muniyappan, et. al., Stability and Numerical Solutions of Second Wave Mathematical Modeling on COVID-19 and Omicron Outbreak Strategy of Pandemic: Analytical and Error Analysis of Approximate Series Solutions by Using HPM, Mathematics 343 (2022). DOI: https://doi.org/10.3390/math10030343
  3. E. Beretta and V. Cappasso, On the general structure of epidemic system: Global stability, Comput. Math. Appl. 12 (1986), 677-694. DOI: 10.1016/0898-1221(86)90054-4
  4. Bin-Guo Wang, et. al., A mathematical model reveals the in the influence of NPIs and vaccination on SARS-CoV-2 Omicron Variant, Nonlinear Dynamics 111 (2023), 3937-3952. DOI: https://doi.org/10.21203/rs.3.rs-1324280/v1.
  5. B. Buonomo and S. Rionero, On the stability for SIRS epidemic models with general nonlinear incidence rate, Appl. Mat. Comput. 217 (2010), 4010-4016. DOI: 10.1016/j.amc.2010.10.007
  6. Byul Nim Kim, et. al., Mathematical model of COVID-19 Transmission Dynamics in South Korea: The impacts of travel, social distancing and early detection, Processes 8 (2020). DOI: 10.3390/pr8101304.
  7. G.E. Chatzarakis, et. al., A dynamic SIqIRV Mathematical model with non-linear force of isolation, infection and cure, Nonauton. Dyn. Syst. 9 (2022), 56-67. https://doi.org/10.1515/msds-2022-0145
  8. S. Dickson, et. al., SQIRV Model for Omicron Variant with time delay, Aust. J. Math. Anal. Appl. 19 (2022), Art. 16.
  9. S. Dickson, et. al., Stability Analysis Of B.1.1.529 SARS-Cov-2 Omicron Variant Mathematical Model: The Impacts Of Quarantine And Vaccination, Nonauton. Dyn. Syst. 9 (2022), 290-306. https://doi.org/10.1515/msds-2022-0158
  10. S. Dickson, et. al., Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination, Int. J. Dynam. Control 11 (2023), 2215-2231. https://doi.org/10.1007/s40435-023-01146-0.
  11. S. Dickson, et. al., A Caputo-type fractional-order SQIRV mathematical model for Omicron variant, Contemporary Mathematics(Singapore), 4 (2023), 620-636.
  12. Daniel Deborah O∗, Mathematical Model for the Transmission of Covid-19 with Nonlinear Forces of Infection and the need for Prevention Measure in Nigeria, J. Inf. Dis. and Epidemiology 6 (2020), 1-12. DOI: 10.23937/2474-3658/1510158
  13. W. Derrick and S.I. Grossman, Elementary Differential Equations with Applications: Short Course, Addison-Wesley Publishing Company, Philippines, 1976.
  14. O. Diekmann, et. al., On the definition and computation of the basic reproduction number R0 in models for infectious disease, J. Math. Biol. 28 (1990), 365-382. DOI: 10.1007/BF00178324
  15. L. Esteva-Peralta and J.X. Velasco-Hernandez, M-Matrices and local stability in epidemic model, Math. Comp. Model. 36 (2002), 491-501. DOI: 10.1016/S0895-7177(02)00178-4
  16. Fatma Ozkose, et. al., Fractional order modelling of Omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom, Chaos, Solitons and Fractals 157 (2022), 111954. DOI: https://doi.org/10.1016/j.chaos.2022.111954
  17. P. Haukkanen and T. Tossavainen, A generalization of descartes rule of signs and fundamental theorem of algebra, Appl. Math. Comput. 218 (2011), 1203-1207. DOI: 10.1016/j.amc.2011.05.107
  18. Kiran, et. al., Effect of population migration and punctuated lockdown on the spread of infectious diseases, Nonautonomous Dynamical Systems 8 (2021), 251-266. https://doi.org/10.1515/msds-2020-0137
  19. P. Kumar, Suat Erturk, A case study of COVID-19 epidemic in India via new generalised Caputo type fractional derivatives, Math. Methods. Appl, Sci. (2021), 1-14. DOI: 10.1002/mma.7284
  20. E.S. Kurkina and E.M. Kotsova, Mathematical Modeling of the propagation of Covid-19 pandemic waves in the world, Comp. math. and modeling 32 (2021), 147-170. DOI: 10.23937/2474-3658/1510158
  21. J.P. La-Salle and S. Lefschetz, Stability by Liapunovs Direct Method, Academic press, New York, 1961.
  22. G.H. Li and Y.X. Zhang, Dynamic behavior of a modified SIR model in epidemic diseases using non linear incidence rate and treatment, PlosOne 12 (2017), e0175789. DOI: 10.1371/journal.pone.0175789
  23. Z. Ma and J. Li, Dynamical Modeling and Analysis of Epidemics, World Scientific Publishing Co. Pte. Ltd., 2009, pages 512. DOI: 10.1142/6799.
  24. Maski Tomochi, Mitsuo Kono, A mathematical model for COVID-19pandemic-SIIR model: Effects of asymptomatic individuals, J. Gen. and Fam. Med. 22 (2021), 5-14. DOI: 10.1002/jgf2.382
  25. M.O. Oke, et. al., Mathematical Modeling and Stability Analysis of a SIRV Epidemic Model with Non-linear Force of Infection and Treatment, Comm. App. Math. 10 (2019), 717-731. https://doi.org/10.26713/cma.v10i4.1172
  26. Pakwan Riyapan, et. al., A mathematical model of COVID-19 pandemic: A case study of Bangkok, Thailand, Computational and Mathematical models in Medicine 2021 (2021), 6664483, 1-11.
  27. J.P.R.S. Rao and M.N. Kumar, A dynamic model for infectious diseases: The role of vaccination and treatment, Chaos Solitons and Fractals 75 (2015), 34-49. DOI: 10.1016/j.chaos.2015.02.004
  28. Sudhanshu Kumar Biswas, et. al., Covid-19 pandemic in India: A mathematcal model study, Nonlinear Dyn., Springer Nature B.V., 2020. DOI: 10.1007/s11071-020-05958-z
  29. S. Dickson, et. al., Stability of Delayed Fractional order SEIQIcRVW mathematical model for Omicron variant, Int. J. Dynam. Control (2023). https://doi.org/10.1007/s40435-023-01287-2.
  30. Tyagi, et. al, Analysis of infectious disease transmission and prediction through SEIQR epidemic model, Nonautonomous Dynamical Systems 8 (2021), 75-86. https://doi.org/10.1515/msds-2020-0126
  31. P. Van den Driessche and J. Watmough, Reproduction Number and sub threshold epidemic equilibrium for compartmental models for disease transmission, Math. Biosci. 180 (2002), 29-48. DOI: 10.1016/S0025-5564(02)00108-6
  32. W. Yang, et. al., Global analysis for a general epidemiological model with vaccination and varying population, J. Math. Anal. Appl. 372 (2010), 208-223. DOI: 10.1016/j.jmaa.2010.07.017