A fractional order vaccination model for COVID-19 incorporating environmental transmission: a case study using Nigerian data
DOI:
https://doi.org/10.59292/bulletinbiomath.2023005Keywords:
Fractional derivative, stability, COVID-19, environmental transmission, simulationAbstract
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 R0 < 1 and R0 > 1, respectively.
References
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).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Anne Atede, Andrew Omame, Simeon C Inyama
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles published in the Bulletin of Biomathematics are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in the Bulletin of Biomathematics, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
