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A fractional order vaccination model for COVID-19 incorporating environmental transmission: a case study using Nigerian data

Yıl 2023, Cilt: 1 Sayı: 1, 78 - 110, 30.04.2023

Anne Ojoma Atede Andrew Omame , Simeon Chioma Inyama

https://doi.org/10.59292/bulletinbiomath.2023005

Öz

In this work, a fractional-order vaccination model for the novel Coronavirus 2019 (COVID-19) incorporating environmental transmission is considered and analyzed using tools of fractional calculus. The Laplace transform technique and the fixed point theorem lay out the model solutions' existence and uniqueness. The solutions' positivity and boundedness are also demonstrated. Additionally, the stability of the model's equilibrium points is discussed using the fractional-order system stability theory. The model is fitted using the data sets for the Pfizer vaccination program in Nigeria from April 1, 2021, to June 10, 2021. In conclusion, simulation results for various fractional parameter values are presented. It has been observed that increasing fractional-order values has distinct effects on the various model compartments, for $R_0 < 1$ and $R_0 > 1$, respectively.

Anahtar Kelimeler

Fractional derivative stability COVID-19 environmental transmission simulation

Kaynakça

  • Kahn, J.S. and McIntosh, K. History and recent advances in coronavirus discovery. The Pediatric Infectious Disease Journal, 24(11), S223-S227, (2005).
  • Bhargava HD, WebMD Medical Reference, August 15, (2021).
  • WMCH Wuhan Municipal Health and Health Commission’s Briefing on the Current Pneumonia Situation in our City, February 1, (2020).
  • World Health Organization (WHO), URL: https://www.who.int/health-topics/coronavirus, (2021). (Access Date: February 2023).
  • Viner, R.M., Mytton, O.T., Bonell, C., Melendez-Torres, G.J., Ward, J., et al. Susceptibility to SARS-CoV-2 infection among children and adolescents compared with adults: a systematic review and meta-analysis. JAMA Pediatrics, 175(2), 143-156, (2021).
  • Koh, W.C., Naing, L., Chaw, L., Rosledzana, M.A., Alikhan, M.F., Jamaludin, S.A., et al. What do we know about SARS-CoV-2 transmission? A systematic review and meta-analysis of the secondary attack rate and associated risk factors. PLoS one, 15(10), e0240205, (2020).
  • https://www.ncdc.gov.ng/coronavirus, (2021). (Access Date: November 2022).
  • Ahmed, I., Modu, G.U., Yusuf, A., Kumam, P. and Yusuf, I. A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes. Results in Physics, 21, 103776, (2021).
  • Omame, A., Abbas, M. and Onyenegecha, C.P. A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative. Chaos, Solitons & Fractals, 153, 111486, (2021).
  • Bugalia, S., Bajiya, V.P., Tripathi, J.P., Li, M.T. and Sun, G.Q. Mathematical modeling of COVID-19 transmission: the roles of intervention strategies and lockdown. Mathematical Biosciences and Engineering, 17(5), 5961-5986, (2020).
  • Iboi, E.A., Sharomi, O., Ngonghala, C.N., & Gumel, A.B. Mathematical modeling and analysis of COVID-19 pandemic in Nigeria. Mathematical Biosciences and Engineering, 17(6), 7192-7220, (2020).
  • Okuonghae, D. and Omame, A. Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria. Chaos, Solitons & Fractals, 139, 110032, (2020).
  • Baba, B. A. and Bilgehan, B. Optimal control of a fractional order model for the COVID–19 pandemic. Chaos, Solitons & Fractals, 144, 110678, (2021).
  • Aba Oud, M.A., Ali, A., Alrabaiah, H., Ullah, S., Khan, M.A. and Islam, S. A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load. Advances in Difference Equations, 2021, 106, (2021).
  • Rezapour, S., Mohammadi, H. and Samei, M.E. SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order. Advances in Difference Equations, 2020, 490, (2020).
  • Baleanu, D., Mohammadi, H. and Rezapour, S. A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative. Advances in Difference Equations, 2020, 229, (2020).
  • Huang, C., Wang, J., Chen, X. and Cao, J. Bifurcations in a fractional-order BAM neural network with four different delays. Neural Networks, 141, 344-354, (2021).
  • Xu, C., Mu, D., Liu, Z., Pang, Y., Liao, M. and Aouiti, C. New insight into bifurcation of fractional-order 4D neural networks incorporating two different time delays. Communications in Nonlinear Science and Numerical Simulation, 118, 107043, (2023).
  • Xu, C., Liu, Z., Li, P., Yan, J. and Yao, L. Bifurcation mechanism for fractional-order threetriangle multi-delayed neural networks. Neural Processing Letters, (2022).
  • Xu, C., Zhang, W., Aouiti, C., Liu, Z. and Yao, L. Bifurcation insight for a fractional-order stagestructured predator–prey system incorporating mixed time delays. Mathematical Methods in the Applied Sciences, (2023).
  • Sene, N. SIR epidemic model with Mittag-Leffer fractional derivative. Chaos, Solitons & Fractals, 137, 109833, (2020).
  • Omame, A., Abbas, M. and Abdel-Aty, A.H. Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives. Chaos, Solitons & Fractals, 162, 112427, (2022).
  • Omame, A., Abbas, M. and Onyenegecha, C.P. A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus. Results in Physics, 37, 105498, (2022).
  • Omame, A., Okuonghae, D., Nwajeri, U.K. and Onyenegecha, C.P. A fractional-order multivaccination model for COVID-19 with non-singular kernel. Alexandria Engineering Journal, 61(8), 6089-6104, (2022).
  • Omame, A., Nwajeri, U.K., Abbas, M. and Onyenegecha, C.P. A fractional order control model for Diabetes and COVID-19 co-dynamics with Mittag-Leffler function. Alexandria Engineering Journal, 61(10), 7619-7635, (2022).
  • Omame, A., Isah, M.E., Abbas, M., Abdel-Aty, A.H. and Onyenegecha, C.P. A fractional order model for Dual Variants of COVID-19 and HIV co-infection via Atangana-Baleanu derivative. Alexandria Engineering Journal, 61(12), 9715-9731, (2022).
  • Ogunrinde, R.B., Nwajeri, U.K., Fadugba, S. E., Ogunrinde, R.R. and Oshinubi, K.I. Dynamic model of COVID-19 and citizens reaction using fractional derivative. Alexandria Engineering Journal, 60(2), 2001-2012, (2021).
  • Atangana, A. and Secer, A. A note on fractional order derivatives and table of fractional derivatives of some special functions. Abstract and Applied Analysis, 2013, 279681, (2013).
  • Gorenflo, R., Mainardi, F. Fractional Calculus. In: Carpinteri, A., Mainardi, F. (eds) Fractals and Fractional Calculus in Continuum Mechanics. International Centre for Mechanical Sciences, vol 378. Springer, Vienna, (1997).
  • Liu, K., Feckan, M. and Wang, J. Hyers–Ulam stability and existence of solutions to the generalized Liouville–Caputo fractional differential equations. Symmetry, 12(6), 955, (2020).
  • https://www.populationpyramid.net/nigeria/2021/ (Access Date: February 2023).
  • United States Food and Drug Administration, https://www.fda.gov/media/144245/download, (2021), (Access Date: January 2023).
  • Nwajeri, U.K., Omame, A. and Onyenegecha, C.P. Analysis of a fractional order model for HPV and CT co-infection. Results in Physics, 28, 104643, (2021).
  • Diethelm, K. and Freed, A.D. The FracPECE subroutine for the numerical solution of differential equations of fractional order. Forschung und Wissenschaftliches Rechnen, 57-71, (1998).
  • McCall, J. Genetic algorithm for modeling and optimization. Journal of Computational and Applied Mathematics, 184(1), 205-222, (2005).

Yıl 2023, Cilt: 1 Sayı: 1, 78 - 110, 30.04.2023

Anne Ojoma Atede Andrew Omame , Simeon Chioma Inyama

https://doi.org/10.59292/bulletinbiomath.2023005

Öz

Kaynakça

  • Kahn, J.S. and McIntosh, K. History and recent advances in coronavirus discovery. The Pediatric Infectious Disease Journal, 24(11), S223-S227, (2005).
  • Bhargava HD, WebMD Medical Reference, August 15, (2021).
  • WMCH Wuhan Municipal Health and Health Commission’s Briefing on the Current Pneumonia Situation in our City, February 1, (2020).
  • World Health Organization (WHO), URL: https://www.who.int/health-topics/coronavirus, (2021). (Access Date: February 2023).
  • Viner, R.M., Mytton, O.T., Bonell, C., Melendez-Torres, G.J., Ward, J., et al. Susceptibility to SARS-CoV-2 infection among children and adolescents compared with adults: a systematic review and meta-analysis. JAMA Pediatrics, 175(2), 143-156, (2021).
  • Koh, W.C., Naing, L., Chaw, L., Rosledzana, M.A., Alikhan, M.F., Jamaludin, S.A., et al. What do we know about SARS-CoV-2 transmission? A systematic review and meta-analysis of the secondary attack rate and associated risk factors. PLoS one, 15(10), e0240205, (2020).
  • https://www.ncdc.gov.ng/coronavirus, (2021). (Access Date: November 2022).
  • Ahmed, I., Modu, G.U., Yusuf, A., Kumam, P. and Yusuf, I. A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes. Results in Physics, 21, 103776, (2021).
  • Omame, A., Abbas, M. and Onyenegecha, C.P. A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative. Chaos, Solitons & Fractals, 153, 111486, (2021).
  • Bugalia, S., Bajiya, V.P., Tripathi, J.P., Li, M.T. and Sun, G.Q. Mathematical modeling of COVID-19 transmission: the roles of intervention strategies and lockdown. Mathematical Biosciences and Engineering, 17(5), 5961-5986, (2020).
  • Iboi, E.A., Sharomi, O., Ngonghala, C.N., & Gumel, A.B. Mathematical modeling and analysis of COVID-19 pandemic in Nigeria. Mathematical Biosciences and Engineering, 17(6), 7192-7220, (2020).
  • Okuonghae, D. and Omame, A. Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria. Chaos, Solitons & Fractals, 139, 110032, (2020).
  • Baba, B. A. and Bilgehan, B. Optimal control of a fractional order model for the COVID–19 pandemic. Chaos, Solitons & Fractals, 144, 110678, (2021).
  • Aba Oud, M.A., Ali, A., Alrabaiah, H., Ullah, S., Khan, M.A. and Islam, S. A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load. Advances in Difference Equations, 2021, 106, (2021).
  • Rezapour, S., Mohammadi, H. and Samei, M.E. SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order. Advances in Difference Equations, 2020, 490, (2020).
  • Baleanu, D., Mohammadi, H. and Rezapour, S. A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative. Advances in Difference Equations, 2020, 229, (2020).
  • Huang, C., Wang, J., Chen, X. and Cao, J. Bifurcations in a fractional-order BAM neural network with four different delays. Neural Networks, 141, 344-354, (2021).
  • Xu, C., Mu, D., Liu, Z., Pang, Y., Liao, M. and Aouiti, C. New insight into bifurcation of fractional-order 4D neural networks incorporating two different time delays. Communications in Nonlinear Science and Numerical Simulation, 118, 107043, (2023).
  • Xu, C., Liu, Z., Li, P., Yan, J. and Yao, L. Bifurcation mechanism for fractional-order threetriangle multi-delayed neural networks. Neural Processing Letters, (2022).
  • Xu, C., Zhang, W., Aouiti, C., Liu, Z. and Yao, L. Bifurcation insight for a fractional-order stagestructured predator–prey system incorporating mixed time delays. Mathematical Methods in the Applied Sciences, (2023).
  • Sene, N. SIR epidemic model with Mittag-Leffer fractional derivative. Chaos, Solitons & Fractals, 137, 109833, (2020).
  • Omame, A., Abbas, M. and Abdel-Aty, A.H. Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives. Chaos, Solitons & Fractals, 162, 112427, (2022).
  • Omame, A., Abbas, M. and Onyenegecha, C.P. A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus. Results in Physics, 37, 105498, (2022).
  • Omame, A., Okuonghae, D., Nwajeri, U.K. and Onyenegecha, C.P. A fractional-order multivaccination model for COVID-19 with non-singular kernel. Alexandria Engineering Journal, 61(8), 6089-6104, (2022).
  • Omame, A., Nwajeri, U.K., Abbas, M. and Onyenegecha, C.P. A fractional order control model for Diabetes and COVID-19 co-dynamics with Mittag-Leffler function. Alexandria Engineering Journal, 61(10), 7619-7635, (2022).
  • Omame, A., Isah, M.E., Abbas, M., Abdel-Aty, A.H. and Onyenegecha, C.P. A fractional order model for Dual Variants of COVID-19 and HIV co-infection via Atangana-Baleanu derivative. Alexandria Engineering Journal, 61(12), 9715-9731, (2022).
  • Ogunrinde, R.B., Nwajeri, U.K., Fadugba, S. E., Ogunrinde, R.R. and Oshinubi, K.I. Dynamic model of COVID-19 and citizens reaction using fractional derivative. Alexandria Engineering Journal, 60(2), 2001-2012, (2021).
  • Atangana, A. and Secer, A. A note on fractional order derivatives and table of fractional derivatives of some special functions. Abstract and Applied Analysis, 2013, 279681, (2013).
  • Gorenflo, R., Mainardi, F. Fractional Calculus. In: Carpinteri, A., Mainardi, F. (eds) Fractals and Fractional Calculus in Continuum Mechanics. International Centre for Mechanical Sciences, vol 378. Springer, Vienna, (1997).
  • Liu, K., Feckan, M. and Wang, J. Hyers–Ulam stability and existence of solutions to the generalized Liouville–Caputo fractional differential equations. Symmetry, 12(6), 955, (2020).
  • https://www.populationpyramid.net/nigeria/2021/ (Access Date: February 2023).
  • United States Food and Drug Administration, https://www.fda.gov/media/144245/download, (2021), (Access Date: January 2023).
  • Nwajeri, U.K., Omame, A. and Onyenegecha, C.P. Analysis of a fractional order model for HPV and CT co-infection. Results in Physics, 28, 104643, (2021).
  • Diethelm, K. and Freed, A.D. The FracPECE subroutine for the numerical solution of differential equations of fractional order. Forschung und Wissenschaftliches Rechnen, 57-71, (1998).
  • McCall, J. Genetic algorithm for modeling and optimization. Journal of Computational and Applied Mathematics, 184(1), 205-222, (2005).
Toplam 35 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Biyolojik Matematik, Uygulamalı Matematik (Diğer)
Bölüm Research Articles
Yazarlar

Anne Ojoma Atede 0000-0001-8978-9826

Andrew Omame 0000-0002-1252-1650

Simeon Chioma Inyama 0000-0002-8582-5890

Yayımlanma Tarihi 30 Nisan 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 1 Sayı: 1

Kaynak Göster

APA Atede, A. O., Omame, A., & Inyama, S. C. (2023). A fractional order vaccination model for COVID-19 incorporating environmental transmission: a case study using Nigerian data. Bulletin of Biomathematics, 1(1), 78-110. https://doi.org/10.59292/bulletinbiomath.2023005
 Kapak Resmi İndir