Analysis of the Logistic Growth Model With Taylor Matrix and Collocation Method

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DOI: https://doi.org/10.28924/2291-8639-21-2023-58
Published: Jun 23, 2023
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Elçin Çelik, Deniz Uçar, Analysis of the Logistic Growth Model With Taylor Matrix and Collocation Method, Int. J. Anal. Appl., 21 (2023), 58.

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Elçin Çelik, Deniz Uçar

Abstract

Early analysis of infectious diseases is very important in the spread of the disease. The main aim of this study is to make important predictions and inferences for Covid 19, which is the current epidemic disease, with mathematical modeling and numerical solution methods. So we deal with the logistic growth model. We obtain carrying capacity and growth rate with Turkey epidemic data. The obtained growth rate and carrying capacity is used in the Taylor collocation method. With this method, we estimate and making predictions close to reality with Maple. We also show the estimates made with the help of graphics and tables.

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References

  1. C.H. Edwards, D.E. Penny, D.T. Calvis, Differential Equations and Boundary Value Problems Computing and Modeling, 5th Edition, Pearson, London, 2015.
  2. E. Gökmen and E. Çelik, A Numerical Method for Solving Continuous Population Models for Single and Interacting Species, Sakarya Univ. J. Sci. 23 (2019), 403-412. https://doi.org/10.16984/saufenbilder.410641.
  3. E. Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, New York, 2006.
  4. E. Pelinovsky, A. Kurkin, O. Kurkina, et al. Logistic Equation and COVID-19, Chaos Solitons Fractals. 140 (2020), 110241. https://doi.org/10.1016/j.chaos.2020.110241.
  5. J.M. Last, A Dictionary of Epidemiology, 2nd Edition, Oxford University Press, Oxford, 1988.
  6. K. Roosa, Y. Lee, R. Luo, et al. Real-Time Forecasts of the COVID-19 Epidemic in China from February 5th to February 24th, 2020, Infect. Dis. Model. 5 (2020), 256-263. https://doi.org/10.1016/j.idm.2020.02.002.
  7. K. Wu, D. Darcet, Q. Wang, et al. Generalized Logistic Growth Modeling of the COVID-19 Outbreak: Comparing the Dynamics in the 29 Provinces in China and in the Rest of the World, Nonlinear Dyn. 101 (2020), 1561-1581. https://doi.org/10.1007/s11071-020-05862-6.
  8. L.J. Allen, F. Brauer, P. Van den Driessche, et al. Mathematical Epidemiology, Vol. 1945, Springer, Berlin, 2008.
  9. M. Batista, Estimation of The Final Size of The Coronavirus Epidemic by The Logistic Model, Preprint, 2020. https://doi.org/10.1101/2020.02.16.20023606.
  10. M. Jain, P.K. Bhati, P. Kataria, et al. Modelling Logistic Growth Model for COVID-19 Pandemic in India, in: 2020 5th International Conference on Communication and Electronics Systems (ICCES), IEEE, COIMBATORE, India, 2020: pp. 784–789. https://doi.org/10.1109/ICCES48766.2020.9138049.
  11. M. Sezer, A Method for the Approximate Solution of the Second-order Linear Differential Equations in Terms of Taylor Polynomials, Int. J. Math. Educ. Sci. Technol. 27 (1996), 821-834. https://doi.org/10.1080/0020739960270606.
  12. M. Sezer, A. Karamete, M. Gülsu, Taylor Polynomial Solutions of Systems of Linear Differential Equations With Variable Coefficients, Int. J. Computer Math. 82 (2005), 755-764. https://doi.org/10.1080/00207160512331323336.
  13. N.M. Ferguson, Mathematical Prediction in Infection, Medicine. 37 (2009), 507-509. https://doi.org/10.1016/j.mpmed.2009.07.004.