Mathematical Assessment of Covid-19 Transmission Dynamic with Intervention via: ABC Fractional Operator
DOI:
https://doi.org/10.62054/ijdm/0102.05Keywords:
ABC-Operator, Covid-19, Intervention, Stability AnalysisAbstract
A Covid-19 model in terms of the ABC operator with intervention is developed and used to study the disease transmission dynamics. The model showed stability when the basic reproduction number is less than unity, indicating that each existing infection causes less than one new infection, resulting in a decline in cases. A stable system and a basic reproduction number R0 value greater than unity suggest exponential growth of the disease. The model was fitted using NCDC data from March 4 to April 30; 2022 and the sensitivity analysis reveals effective contact rates and transmissibility of asymptomatic individuals as the most sensitive parameters. Numerical simulations reveal that increased effective contact rate (social distancing) increases virus spread, while increased face mask compliance reduces exposure and infection rates. Hence wearing face masks reduces respiratory droplet transmission, reducing the need for quarantine and reducing infection rates
References
Sun, T.-C., DarAssi, M.H., Alfwzan, W.F., Khan, M.A., Alshahrani, A.S., Alqahtani, S., S. (2023).
Muhammad, T. Mathematical Modeling of COVID-19 with Vaccination Using Fractional
Derivative: A Case Study. Fractal Fract. 7, 234. https://doi.org/10.3390/fractalfract7030234
Iboi E. A., Ngonghala, C. N., & Gumel, A. B. (2020). Will an imperfect vaccine curtail the COVID-19 pandemic in the U.S.? Infectious Disease Modelling, 5, 510–524. https://doi.org/10.1016/j.idm.2020.07.006
Abioye A. I., Peter, O. J., Ogunseye, H. A., Oguntolu, F. A., Oshinubi, K., Ibrahim, A. A., & Khan, I. (2021). Mathematical model of COVID-19 in Nigeria with optimal control. Results in Physics, 28, 104598. https://doi.org/10.1016/j.rinp.2021.104598
Atangana A. & Baleanu D. (2016). New fractional derivatives with nonlocal and non-singular kernel theory and application to heat transfer model, Therm. Sci., 20, 763–769.
Caputo M. & Fabrizio M. (2015). A new definition of fractional derivatives without singular kernel, Prog. Fract. Differ. Appl., 1. 1–13.
Atangana A. Bonyah E. & Elsadany A., A. (2020). A fractional order optimal 4D chaotic financial model with Mittag-Leffler law, Chinese J. Phys., 65, 38–53. http://dx.doi.org/10.1016/j.cjph.2020.02.003 doi: 10.1016/j.cjph.2020.02.003
Choi, S. K., Kang, B., & Koo, N. (2014). Stability for Caputo Fractional Differential Systems. Abstract and Applied Analysis, 2014, 1–6. https://doi.org/10.1155/2014/631419
Akinyemi AI & Isiugo-Abanihe U. C. (2014). Demographic dynamics and development in nigeria. African Population Studies. 27:239–48.
Baba, I. A., Ahmed, I., Al-Mdallal, Q. M., Jarad, F., & Yunusa, S. (2022). Numerical and theoretical analysis of an awareness COVID-19 epidemic model via generalized Atangana-Baleanu fractional derivative. Journal of Applied Mathematics and Computational Mechanics, 21(1), 7–18. https://doi.org/10.17512/jamcm.2022.1.01
Okyere, S., Ackora-Prah, J., Abdullah, S., Adarkwa, S. A., Owusu, F. K., Bonsu, K., Fokuo, M. O., & Yeboah, M. A. (2023). Analysis of Turberculosis-COVID-19 Coinfection Using Fractional Derivatives. International Journal of Mathematics and Mathematical Sciences, 2023, 1–14. https://doi.org/10.1155/2023/2831846
Ega, T. T., & Ngeleja, R. C. (2022). Mathematical Model Formulation and Analysis for COVID-19 Transmission with Virus Transfer Media and Quarantine on Arrival. Computational and Mathematical Methods, 2022, 1–16. https://doi.org/10.1155/2022/2955885
Sun, T. C., DarAssi, M. H., Alfwzan, W. F., Khan, M. A., Alqahtani, A. S., Alshahrani, S. S., & Muhammad, T. (2023). Mathematical Modeling of COVID-19 with Vaccination Using Fractional Derivative: A Case Study. Fractal and Fractional, 7(3), 234. https://doi.org/10.3390/fractalfract7030234
Sinan, M., & Alharthi, N. H. (2023). Mathematical Analysis of Fractal-Fractional Mathematical Model of COVID-19. Fractal and Fractional, 7(5), 358. https://doi.org/10.3390/fractalfract7050358
Worldometers. COVID-19 Coronavirus Pandemic. 2021. Available online: https://www.worldometers.info/coronavirus/(accessed on 8 July 2023).
Alam, M.T., Sohail, S.S., Ubaid, S., Ali, Z., Hijji, M., Saudagar, A.K.J. & Muhammad, K. (2022). It’s your turn, are you ready to get vaccinated? Towards an exploration of vaccine hesitancy using sentiment analysis of Instagram posts. Mathematics, 10, 4165.
Xu, J. & Tang, Y. (2021) Bayesian framework for multi-wave COVID-19 epidemic analysis using empirical vaccination data. Mathematics, 10, 21.
Nguyen, P.H., Tsai, J.F., Lin, M.H. & Hu, Y.C. (2021). A hybrid model with spherical fuzzy-AHP, PLS-SEM and ANN to predict vaccination intention against COVID-19. Mathematics 2021, 9, 3075.
Ferguson, N., Laydon, D., Nedjati Gilani, G., Imai, N., Ainslie, K., Baguelin, M. & Perez, Z.C. (2020). Impact of Non-Pharmaceutical Interventions (NPIs) to Reduce COVID-19 Mortality and Healthcare Demand; Imperial College London: London, UK.
Brauer, F. (2005). The Kermack-McKendrick epidemic model revisited. Math. Biosci. 2005, 198, 119–131.
Cortés-Carvajal, P.D., Cubilla-Montilla, M. & González-Cortés, D.R. (2022). Estimation of the instantaneous reproduction number and its confidence interval for modeling the COVID-19 pandemic. Mathematics. 10, 287.
Peng, L., Yang, W., Zhang, D., Zhuge, C. & Hong, L. (2020). Epidemic analysis of COVID-19 in China by dynamical modeling. arXiv:2002.06563.
Jia, J., Ding, J., Liu, S., Liao, G., Li, J., Duan, B., Wang, G. & Zhang, R. (2020). Modeling the control of COVID-19: Impact of policy interventions and meteorological factors. Electron. J. Differ. Equ. 23, 1–24.
Castilho, C., Gondim, J.A.M., Marchesin, M. & Sabeti, M. (2020). Assessing the efficiency of different control strategies for the COVID-19 epidemic. Electron. J. Differ. Equ. 64, 1–17.
Prem, K., Liu, Y., Russell, T.W., Kucharski, A.J., Eggo, R.M., Davies, N. & Klepac, P. (2020). The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: A modelling study. Lancet Public Health. 5, e261–e270.
Hou, C., Chen, J., Zhou, Y., Hua, L., Yuan, J., He, S., Guo, Y., Zhang, S., Jia, Q., Zhao, C. et al. (2020). The effectiveness of quarantine of Wuhan city against the corona virus disease 2019 (COVID-19): A well-mixed SEIR model analysis. J. Med. Virol. 92, 841–848.
NCDC, (2020). Nigeria Center for Disease Control. [Online]. Available: http://covid19. ncdc.gov.ng/. Accessed 7 September 2020.
Madubueze C., E, Kimbir A., R & Aboiyar T. (2018). Global Stability of Ebola Virus Disease Model with Contact Tracing and Quarantine. Appl Appl Math.13 (1):382–403.
Kim Y., Lee S., Chu C., Choe S., Hong S. & Shin Y. (2016). The characteristics of Middle Eastern respiratory syndrome coronavirus transmission dynamics in South Korea. Osong Public Health Res Perspectives. 7(1):49–55.
World Health Organization, (2020). Coronavirus Disease (COVID-19) Technical Guidance. Available from: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/ technical-guidance.
Podlubny, I. (1999). Fractional differential equations, 198 academic press. San Diego, California, USA.
Hossein, K. & Mohsen, J. (2018). Optimal control of a fractional-order model for the HIV/AIDS epidemic. Int. J. Biomath. 11(7):1850086.
Choi, S. K., Kang, B. & Koo, N. (2014). Stability for Caputo Fractional Differential Systems. Ab- stract and Applied Analysis, 16. https://doi.org/10.1155/2014/631419.
Hassan, T. S., Elabbasy, E. M., Matouk, A., Ramadan, R. A., Abdulrahman, A. T. & Odi- naev I. (2022). RouthHurwitz Stability and Quasiperiodic Attractors in a Fractional-Order Model for Awareness Programs: Applications to COVID-19 Pandemic. Discrete Dynamics in Na- ture and Society; 115. https://doi.org/10.1155/2022/1939260
LaSalle, J. P. Stability theory for ordinary equations. J Differ Equ. 4(1968): 57-65.
Toufik, M. & Atangana, A. (2017). New numerical approximation of fractional derivative with non- local and non-singular kernel: Application to chaotic models. The European Physical Journal Plus. 132(10). https://doi.org/10.1140/epjp/i2017-11717-0
Atangana, A. & Igret Araz, S. (2021) New Numerical Scheme with Newton Polynomial: Theory, Methods and Applications. Academic Press, Elsevier, 2021. ISBN 978-0323854481.
Vasily, E. T. (2018) Generalized Memory: fractional calculus approach. Fractal fract. 2(4):23.
Atangana, A. (2021). Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?. Adv Differ Equ. 403 (2021).
https://doi.org/10.1186/s13662-021-03494-7.
Van den Driessche, P. & Watmough, P. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci, 180: 29–48.
Ahmed, I., Baba, I. A., Yusuf, A., Kumam, P., & Kumam, W. (2020). Analysis of Caputo fractional-order model for COVID-19 with lockdown. Advances in Difference Equations, 2020(1). https://doi.org/10.1186/s13662-020-02853-0
Downloads
Published
Issue
Section
License
Copyright (c) 2024 International Journal of Development Mathematics (IJDM)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors are solely responsible for obtaining permission to reproduce any copyrighted material contained in the manuscript as submitted. Any instance of possible prior publication in any form must be disclosed at the time the manuscript is submitted and a
copy or link to the publication must be provided.
The Journal articles are open access and are distributed under the terms of the Creative
Commons Attribution-NonCommercial-NoDerivs 4.0 IGO License, which permits use,
distribution, and reproduction in any medium, provided the original work is properly cited.
No modifications or commercial use of the articles are permitted.
