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Year 2023, Volume: 11 Issue: 2, 131 - 140, 31.10.2023

Zafer Öztürk Halis Bilgil Sezer Sorgun

Abstract

References

  • [1] Kermack W.O., McKendrick, A.G. A contribution to the mathematical theory of epidemics, in: Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character, 115 (772), (1927), 700–721.
  • [2] Valleron A. J. Roles of Mathematical Modeling in Epidemiology, Comptes Rendus de I’Academie des Sciences - Series III- Sciences de la Vie, 323 (5), (2000), 429–433.
  • [3] Allen L. J. S. An Introduction to Mathematical Biology, Department of Mathematics and Statistics, Texas Tech University, Pearson Education., (2007), 348.
  • [4] Hethcote, H. W. The mathematics of infectious diseases, SIAM review, 42(4) , (2000), 599–653.
  • [5] O¨ ztu¨rk, Z., Bilgil, H., & Sorgun, S. Application of Fractional SIQRV Model for SARS-CoV-2 and Stability Analysis, Symmetry, 15(5), (2023), 1048.
  • [6] Linda, J.S.A. An Introduction to Mathematical Biology, Pearson Education Ltd., USA, (2007), pp. 123–127.
  • [7] Bailey N. T. J. , The Mathematical Theory of Infectious Diseases and its Application (Hafner Press), New York (1975).
  • [8] Hethcote H.,Zhien M., Shengbing L. Effects of quarantine in six endemic models for infectious diseases, Mathematical Biosciences , 180 , (2002), 141160.
  • [9] O¨ ztu¨rk, Z., Bilgil, H., & Sorgun, S. Application of Fractional SPR Psychological Disease Model in Turkey and Stability Analysis, Journal of Mathematical Sciences and Modelling, 6(2), (2023), 49-55.
  • [10] O¨ ztu¨rk, Z., Bilgil, H., Sorgun, S. Stability Analysis of Fractional PSQp Smoking Model and Application in Turkey, New Trends in Mathematical Sciences, 10(4), (2022), 54-62.
  • [11] Liu, X.; Takeuchi, Y.; Iwami, S., Liu, X.; Takeuchi, Y.; Iwami, S. SVIR epidemic models with vaccination strategies, J. Theor. Biol. , 253 , (2008), 1–11.
  • [12] Trawicki, M.B. Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity, Mathematics, 5(1), (2017), 7.
  • [13] O¨ ztu¨rk, Z., Sorgun, S., Bilgil H. SIQRV Modeli ve Nu¨merik Uygulaması, Avrupa Bilim ve Teknoloji Dergisi, (28), (2021), 573-578.
  • [14] Eckalbar, J.C.; Eckalbar, W.L. Dynamics of an SIR model with vaccination dependent on past prevalence with high-order distributed delay. Biosystems , 129, (2015), 50–65.
  • [15] O¨ ztu¨rk, Z., Sorgun, S., Bilgil, H., Erdinc¸, U¨ . New exact solutions of conformable time-fractional bad and good modified Boussinesq equations. Journal of New Theory, (37), (2021), 8-25.
  • [16] I. Podlubny, Fractional Differential Equations, Academy Press, San Diego CA, (1999).
  • [17] Bilgil, H., Yousef, A., Erciyes, A., Erdinc¸, U¨ ., O¨ ztu¨rk, Z. A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event. Journal of Computational and Applied Mathematics, 425, (2023), 115015.
  • [18] Yaro, D., Omari S., S. K., Harvim, P., Saviour, A. W., Obeng, B. A. Generalized Euler method for modeling measles with fractional differ ential equations. Int. J. Innovative Research and Development, (2015), 4.
  • [19] Tartof, S. Y., Slezak, J. M., Fischer, H., Hong, V., Ackerson, B. K., Ranasinghe, O. N., & McLaughlin, J. M., Effectiveness of mRNA BNT162b2 COVID-19 vaccine up to 6 months in a large integrated health system in the USA: a retrospective cohort study. The Lancet, 398(10309), (2021), 1407-1416.
  • [20] O¨ zko¨se, F., Yavuz, M., Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey. Computers in biology and medicine, 141, (2022), 105044.
  • [21] Joshi, H., Jha, B. K., Yavuz, M. Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data. Mathematical Biosciences and Engineering, 20(1), (2023), 213-240.
  • [22] O¨ zko¨se, F., Yavuz, M., S¸ enel, M. T., Habbireeh, R. Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom. Chaos, Solitons & Fractals, 157, (2022), 111954.
  • [23] Yavuz, M., Cos¸ar, F. O¨ ., Gu¨nay, F., O¨ zdemir, F. N. A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign. Open Journal of Modelling and Simulation, 9(3), (2021), 299-321.
  • [24] Ahmad, S., Qiu, D., ur Rahman, M. Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator. Mathematical Modelling and Numerical Simulation with Applications, 2(4), (2022), 228-243.
  • [25] Demir, I., Kirisci, M. Forecasting COVID-19 disease cases using the SARIMA-NNAR hybrid model. Universal Journal of Mathematics and Applications, 5(1), (2022), 15-23.
  • [26] Joshi, H., Yavuz, M., Townley, S., Kumar Jha, B. Stability Analysis of a Non-singular Fractional-order COVID-19 Model with Nonlinear Incidence and Treatment Rate., (2023), Physica Scripta.
  • [27] C¸ akan, U¨ . Stability Analysis of a Mathematical Model SI u I a QR for COVID-19 with the Effect of Contamination Control (Filiation) Strategy. Fundamental Journal of Mathematics and Applications, 4(2), (2021), 110-123.
  • [28] Yavuz, M., Cos¸ar, F. O¨ ., Usta, F. A novel modeling and analysis of fractional-order COVID-19 pandemic having a vaccination strategy. In AIP Conference Proceedings (Vol. 2483, No. 1, p. 070005). AIP Publishing LLC.,(2022, November).
  • [29] P´erez, A. G., Oluyori, D. A. A model for COVID-19 and bacterial pneumonia coinfection with community-and hospital-acquired infections., (2022), arXiv preprint arXiv:2207.13265.
  • [30] Haq, I. U., Ali, N., Nisar, K. S. An optimal control strategy and Gr¨unwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model. Mathematical Modelling and Numerical Simulation with Applications, 2(2), (2022), 108-116.
  • [31] Yavuz, M., Haydar, W. Y. A. A new mathematical modelling and parameter estimation of COVID-19: a case study in Iraq. AIMS Bioengineering, 9(4), (2022), 420-446.

Fractional SIQRV Model for COVID-19 and Numerical Solutions

Year 2023, Volume: 11 Issue: 2, 131 - 140, 31.10.2023

Zafer Öztürk Halis Bilgil Sezer Sorgun

Abstract

There is a pandemic situation caused by the COVID-19 epidemic almost all over the world. Despite the measures taken to prevent this epidemic and the vaccine studies developed, the course of the epidemic changes period as the virus mutates and changes its structure. The common opinion of the experts is that the most important weapon in the ght against the epidemic is the vaccine.In this paper, a new fractional SIQRV model was obtained by adding a class of vaccinated individuals to the SIQR (Susceptible-Infected-Quarantine-Recovered) epidemic disease model. Fractional derivatives are used in the sense of Caputo. In the newly created fractional SIQRV model, the total population is divided into ve parts. Mathematical analyses were performed on susceptible individuals (S), infective individuals (I), quarantined individuals (Q), recovered individuals (R) and vaccinated individuals (V). Numerical results were got with the help of Generalized Euler Method and graphs were drawn.

Keywords

Fractional SIQRV Model Pandemic Generalized Euler Method Quarantine Vaccination Caputo Fractional Derivative

References

  • [1] Kermack W.O., McKendrick, A.G. A contribution to the mathematical theory of epidemics, in: Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character, 115 (772), (1927), 700–721.
  • [2] Valleron A. J. Roles of Mathematical Modeling in Epidemiology, Comptes Rendus de I’Academie des Sciences - Series III- Sciences de la Vie, 323 (5), (2000), 429–433.
  • [3] Allen L. J. S. An Introduction to Mathematical Biology, Department of Mathematics and Statistics, Texas Tech University, Pearson Education., (2007), 348.
  • [4] Hethcote, H. W. The mathematics of infectious diseases, SIAM review, 42(4) , (2000), 599–653.
  • [5] O¨ ztu¨rk, Z., Bilgil, H., & Sorgun, S. Application of Fractional SIQRV Model for SARS-CoV-2 and Stability Analysis, Symmetry, 15(5), (2023), 1048.
  • [6] Linda, J.S.A. An Introduction to Mathematical Biology, Pearson Education Ltd., USA, (2007), pp. 123–127.
  • [7] Bailey N. T. J. , The Mathematical Theory of Infectious Diseases and its Application (Hafner Press), New York (1975).
  • [8] Hethcote H.,Zhien M., Shengbing L. Effects of quarantine in six endemic models for infectious diseases, Mathematical Biosciences , 180 , (2002), 141160.
  • [9] O¨ ztu¨rk, Z., Bilgil, H., & Sorgun, S. Application of Fractional SPR Psychological Disease Model in Turkey and Stability Analysis, Journal of Mathematical Sciences and Modelling, 6(2), (2023), 49-55.
  • [10] O¨ ztu¨rk, Z., Bilgil, H., Sorgun, S. Stability Analysis of Fractional PSQp Smoking Model and Application in Turkey, New Trends in Mathematical Sciences, 10(4), (2022), 54-62.
  • [11] Liu, X.; Takeuchi, Y.; Iwami, S., Liu, X.; Takeuchi, Y.; Iwami, S. SVIR epidemic models with vaccination strategies, J. Theor. Biol. , 253 , (2008), 1–11.
  • [12] Trawicki, M.B. Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity, Mathematics, 5(1), (2017), 7.
  • [13] O¨ ztu¨rk, Z., Sorgun, S., Bilgil H. SIQRV Modeli ve Nu¨merik Uygulaması, Avrupa Bilim ve Teknoloji Dergisi, (28), (2021), 573-578.
  • [14] Eckalbar, J.C.; Eckalbar, W.L. Dynamics of an SIR model with vaccination dependent on past prevalence with high-order distributed delay. Biosystems , 129, (2015), 50–65.
  • [15] O¨ ztu¨rk, Z., Sorgun, S., Bilgil, H., Erdinc¸, U¨ . New exact solutions of conformable time-fractional bad and good modified Boussinesq equations. Journal of New Theory, (37), (2021), 8-25.
  • [16] I. Podlubny, Fractional Differential Equations, Academy Press, San Diego CA, (1999).
  • [17] Bilgil, H., Yousef, A., Erciyes, A., Erdinc¸, U¨ ., O¨ ztu¨rk, Z. A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event. Journal of Computational and Applied Mathematics, 425, (2023), 115015.
  • [18] Yaro, D., Omari S., S. K., Harvim, P., Saviour, A. W., Obeng, B. A. Generalized Euler method for modeling measles with fractional differ ential equations. Int. J. Innovative Research and Development, (2015), 4.
  • [19] Tartof, S. Y., Slezak, J. M., Fischer, H., Hong, V., Ackerson, B. K., Ranasinghe, O. N., & McLaughlin, J. M., Effectiveness of mRNA BNT162b2 COVID-19 vaccine up to 6 months in a large integrated health system in the USA: a retrospective cohort study. The Lancet, 398(10309), (2021), 1407-1416.
  • [20] O¨ zko¨se, F., Yavuz, M., Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey. Computers in biology and medicine, 141, (2022), 105044.
  • [21] Joshi, H., Jha, B. K., Yavuz, M. Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data. Mathematical Biosciences and Engineering, 20(1), (2023), 213-240.
  • [22] O¨ zko¨se, F., Yavuz, M., S¸ enel, M. T., Habbireeh, R. Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom. Chaos, Solitons & Fractals, 157, (2022), 111954.
  • [23] Yavuz, M., Cos¸ar, F. O¨ ., Gu¨nay, F., O¨ zdemir, F. N. A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign. Open Journal of Modelling and Simulation, 9(3), (2021), 299-321.
  • [24] Ahmad, S., Qiu, D., ur Rahman, M. Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator. Mathematical Modelling and Numerical Simulation with Applications, 2(4), (2022), 228-243.
  • [25] Demir, I., Kirisci, M. Forecasting COVID-19 disease cases using the SARIMA-NNAR hybrid model. Universal Journal of Mathematics and Applications, 5(1), (2022), 15-23.
  • [26] Joshi, H., Yavuz, M., Townley, S., Kumar Jha, B. Stability Analysis of a Non-singular Fractional-order COVID-19 Model with Nonlinear Incidence and Treatment Rate., (2023), Physica Scripta.
  • [27] C¸ akan, U¨ . Stability Analysis of a Mathematical Model SI u I a QR for COVID-19 with the Effect of Contamination Control (Filiation) Strategy. Fundamental Journal of Mathematics and Applications, 4(2), (2021), 110-123.
  • [28] Yavuz, M., Cos¸ar, F. O¨ ., Usta, F. A novel modeling and analysis of fractional-order COVID-19 pandemic having a vaccination strategy. In AIP Conference Proceedings (Vol. 2483, No. 1, p. 070005). AIP Publishing LLC.,(2022, November).
  • [29] P´erez, A. G., Oluyori, D. A. A model for COVID-19 and bacterial pneumonia coinfection with community-and hospital-acquired infections., (2022), arXiv preprint arXiv:2207.13265.
  • [30] Haq, I. U., Ali, N., Nisar, K. S. An optimal control strategy and Gr¨unwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model. Mathematical Modelling and Numerical Simulation with Applications, 2(2), (2022), 108-116.
  • [31] Yavuz, M., Haydar, W. Y. A. A new mathematical modelling and parameter estimation of COVID-19: a case study in Iraq. AIMS Bioengineering, 9(4), (2022), 420-446.
There are 31 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Articles
Authors

Zafer Öztürk 0000-0001-5662-4670

Halis Bilgil

Sezer Sorgun

Publication Date October 31, 2023
Submission Date March 1, 2022
Acceptance Date September 12, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

APA Öztürk, Z., Bilgil, H., & Sorgun, S. (2023). Fractional SIQRV Model for COVID-19 and Numerical Solutions. Konuralp Journal of Mathematics, 11(2), 131-140.
AMA Öztürk Z, Bilgil H, Sorgun S. Fractional SIQRV Model for COVID-19 and Numerical Solutions. Konuralp J. Math. October 2023;11(2):131-140.
Chicago Öztürk, Zafer, Halis Bilgil, and Sezer Sorgun. “Fractional SIQRV Model for COVID-19 and Numerical Solutions”. Konuralp Journal of Mathematics 11, no. 2 (October 2023): 131-40.
EndNote Öztürk Z, Bilgil H, Sorgun S (October 1, 2023) Fractional SIQRV Model for COVID-19 and Numerical Solutions. Konuralp Journal of Mathematics 11 2 131–140.
IEEE Z. Öztürk, H. Bilgil, and S. Sorgun, “Fractional SIQRV Model for COVID-19 and Numerical Solutions”, Konuralp J. Math., vol. 11, no. 2, pp. 131–140, 2023.
ISNAD Öztürk, Zafer et al. “Fractional SIQRV Model for COVID-19 and Numerical Solutions”. Konuralp Journal of Mathematics 11/2 (October 2023), 131-140.
JAMA Öztürk Z, Bilgil H, Sorgun S. Fractional SIQRV Model for COVID-19 and Numerical Solutions. Konuralp J. Math. 2023;11:131–140.
MLA Öztürk, Zafer et al. “Fractional SIQRV Model for COVID-19 and Numerical Solutions”. Konuralp Journal of Mathematics, vol. 11, no. 2, 2023, pp. 131-40.
Vancouver Öztürk Z, Bilgil H, Sorgun S. Fractional SIQRV Model for COVID-19 and Numerical Solutions. Konuralp J. Math. 2023;11(2):131-40.
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