APPLICATION OF NON-STANDARD FINITE DIFFERENCE METHOD ON COVID-19 MATHEMATICAL MODEL WITH FEAR OF INFECTION
Abstract
This study presents a novel application of Non -Standard Finite Difference (NSFD) Method to solve a COVID-19 epidemic mathematical model with the impact of fear due to infection. The mathematical model is governed by a system of first-order non-linear ordinary differential equations and is shown to possess a unique positive solution that is bounded. The proposed numerical scheme is used to obtain an approximate solution for the COVID-19 model. Graphical results were displayed to show that the solution obtained by NSFD agrees well with those obtained by the Runge-Kutta-Fehlberg method built-in Maple 18.
References
Aba Oud, M. A., Ali, A., Alrabaiah, H., Ullah, S., Khan, M. A., & Islam, S.(2021). A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load. Advances in Difference Equations, 2021(1): 1-19. DOI: https://doi.org/10.1186/s13662-021-03265-4
Adewole, M. O., Onifade, A. A., Abdullah, F. A., Kasali, F., & Ismail, A. I.(2021). Modelling the Dynamics of COVID-19 in Nigeria. International journal of applied and computational mathematics, 7(3):1-25. DOI: https://doi.org/10.1007/s40819-021-01014-5
Ahmed, H. A. O. (2011). Construction and analysis of efficient numerical methods to solve mathematical models of TB and HIV co-infection (Doctoral dissertation, University of the Western Cape).
Akinyemi, S. T., Oyelowo, Yemisi., Ibrahim, M. O. & Adamu, B. (2023). Approximate Solution of a Fractional-Order Ebola Virus Disease Model with Contact Tracing and Quarantine. Applied Mathematics and Computational Intelligence (AMCI), 12(1), 30–42.
Ashgi, R., Pratama, M. A. A., & Purwani, S. (2021). Comparison of Numerical Simulation of Epidemiological Model between Euler Method with 4th Order Runge Kutta Method. International Journal of Global Operations Research, 2(1): 37-44. DOI: https://doi.org/10.47194/ijgor.v2i1.67
Butt, A. I. K., Rafiq, M., Ahmad, W., & Ahmad, N. (2023). Implementation of computationally efficient numerical approach to analyze a Covid-19 pandemic model. Alexandria Engineering Journal, 69:341-362. DOI: https://doi.org/10.1016/j.aej.2023.01.052
Costa, G. M. R., Lobosco, M., Ehrhardt, M., & Reis, R. F. (2023). Mathematical Analysis and a Nonstandard Scheme for a Model of the Immune Response against COVID-19.1-21. Available at https : //www.imacm.uni -wuppertal.de/fileadmin/imacm/preprints/2023/imacm2302.pdf
Cui,Q., Xu, J., Zhang, Q. and Wang, K.(2014).An NSFD scheme for SIR epidemic models of childhood diseases with constant vaccination strategy. Advances in Difference Equations, 2014(172):1-15. DOI: https://doi.org/10.1186/1687-1847-2014-172
Derrick, W. R. and Grossman, S. I. (1987). A first course in differential equations with applications. West Publishing Company.
Diagne, M. L., Rwezaura, H., Tchoumi, S. Y., & Tchuenche, J. M. (2021). A mathematical model of COVID-19 with vaccination and treatment. Computational and Mathematical Methods in Medicine, 2021:1-16. DOI: https://doi.org/10.1155/2021/1250129
Dietz, K., & Heesterbeek, J. A. P. (2002). Daniel Bernoulli’s epidemiological model revisited. Mathematical Biosciences, 180(2): 1-21. DOI: https://doi.org/10.1016/S0025-5564(02)00122-0
Egbelowo, O. (2018). Nonlinear elimination of drugs in one-compartment pharmacokinetic models: nonstandard finite difference approach for various routes of administration. Mathematical and Computational Applications, 23(2):1-21. DOI: https://doi.org/10.3390/mca23020027
Egbelowo, O. F., & Hoang, M. T. (2021). Global dynamics of target-mediated drug disposition models and their solutions by nonstandard finite difference method. Journal of Applied Mathematics and Computing, 66: 621-643. DOI: https://doi.org/10.1007/s12190-020-01452-2
Elaiw, A. M., Aljahdali, A. K., & Hobiny, A. D. (2023). Dynamical Properties of Discrete-Time HTLV-I and HIV-1 within-Host Coinfection Model. Axioms, 12(2):1-26. DOI: https://doi.org/10.3390/axioms12020201
Foppa, I. M. (2017). A Historical Introduction to Mathematical Modeling of Infectious Diseases: Seminal Papers in Epidemiology. Academic Press, Amsterdam.
Garba, S. M., Lubuma, J. M and Tsanou, B. (2020). Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa. Mathematical Bioscience, 328(2):1-16 DOI: https://doi.org/10.1016/j.mbs.2020.108441
Gu, Y., Khan, M., Zarin, R., Khan, A., Yusuf, A., & Humphries, U. W. (2023). Mathematical analysis of a new nonlinear dengue epidemic model via deterministic and fractional approach. Alexandria Engineering Journal, 67:1-21. DOI: https://doi.org/10.1016/j.aej.2022.10.057
Ibrahim (2022). Application of Optimal Control Theory on a Covid-19 Mathematical Model. Seminar presented at the University of Usmanu Danfodio University
Kambali, P. N., Abbasi, A., & Nataraj, C. (2023). Nonlinear dynamic epidemiological analysis of effects of vaccination and dynamic transmission on COVID-19. Nonlinear Dynamics, 111(1): 951-963. DOI: https://doi.org/10.1007/s11071-022-08125-8
Mehdizadeh K, M., Rashidi, M. M., Shokri, A., Ramos, H., & Khakzad, P. (2022). A Nonstandard Finite Difference Method for a Generalized Black-Scholes Equation. Symmetry, 14(1):1-13. DOI: https://doi.org/10.3390/sym14010141
Mehdizadeh K, M., Shokri, A., Wang, Y., Bazm, S., Navidifar, G., & Khakzad, P. (2023). Qualitatively Stable Schemes for the Black-Scholes Equation. Fractal and Fractional, 7(2):1-14 DOI: https://doi.org/10.3390/fractalfract7020154
Mickens, R.E. and Washington, T. (2012). A note on an NSFD scheme for a mathematical model of respiratory virus transmission. J. Differ. Equ. Appl, 8: 525-529. DOI: https://doi.org/10.1080/10236198.2010.515590
Miller, J. J., & O’Riordan, E. (2020). Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics. Biomath, 9(2):1-12. DOI: https://doi.org/10.11145/j.biomath.2020.08.227
Mohammed, S. J., & Mohammed, M. A. (2021, May). Runge-kutta numerical method for solving nonlinear influenza model. In Journal of Physics:Conference Series, 1879(2):1-15. DOI: https://doi.org/10.1088/1742-6596/1879/3/032040
Nana-Kyere, S., Boateng, F. A., Jonathan, P., Donkor, A., Hoggar, G. K.,Titus, B. D., & Adu, I. K. (2022). Global Analysis and Optimal Control Model of COVID-19. Computational and Mathematical Methods in Medicine, 2022:1-20. DOI: https://doi.org/10.1155/2022/9491847
Ochi, P. O., Agada, A. A., Timothy, J., Urum, T. G., Ochi, H. T., & Nworah, D. A. (2023). Stability Analysis Of A Shigella Infection Epidemic Model At Endemic Equilibrium. Fudma Journal of Sciences, 7(3), 48-64. DOI: https://doi.org/10.33003/fjs-2023-0703-1706
Onwubuoya, C., Nwanze, D. E., Erejuwa, J. S., & Akinyemi, S. T. (2018). An Approximate Solution of a Computer Virus Model with Antivirus using Modifed Differential Transform Method. International Journal of Engineering Research & Technology, 7(4): 154-161. DOI: https://doi.org/10.17577/IJERTV7IS040077
Onwubuoya, C., Akinyemi, S. T., Odabi, O. I., & Odachi, G. N. (2018). Numerical simulation of a computer virus transmission model using euler predictor corrector method. IDOSR Journal of Applied Sciences, 3(1):16-28.
Paul, A. K., & Kuddus, M. A. (2022). Mathematical analysis of a COVID-19 model with double dose vaccination in Bangladesh. Results in Physics, 35:1-13. DOI: https://doi.org/10.1016/j.rinp.2022.105392
Peter, O. J., Shaikh, A. S., Ibrahim, M. O., Nisar, K. S., Baleanu, D., Khan, I., &Abioye, A. I. (2020). Analysis and dynamics of fractional order mathematical model of COVID-19 in Nigeria using atangana-baleanu operator. Computers, Materials and Continua, 66(2):1-10. DOI: https://doi.org/10.32604/cmc.2020.012314
Rabiu, M. and Akinyemi, S.T. (2016). Global Analysis of Dengue Fever in a Variable Population.. Journal of the Nigerian Association of Mathematical Physics, 33:363-376.
Raza, A., Chu, Y. M., Bajuri, M. Y., Ahmadian, A., Ahmed, N., Rafiq, M., & Salahshour, S. (2022). Dynamical and nonstandard computational analysis of heroin epidemic model. Results in Physics, 34:1-12 DOI: https://doi.org/10.1016/j.rinp.2022.105245
Riyapan, P., Shuaib, S. E., Intarasit, A., & Chuarkham, K. (2021). Applications of the Differential Transformation Method and Multi-Step Differential Transformation Method to Solve a Rotavirus Epidemic Model.Mathematics and Statistics, 9(1):71-80. DOI: https://doi.org/10.13189/ms.2021.090112
Srivastav, A. K., Tiwari, P. K., Srivastava, P. K., Ghosh, M., & Kang, Y. (2021). A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministicvs. stochastic. Mathematical Biosciences and Engineering, 18(1): 182-213. DOI: https://doi.org/10.3934/mbe.2021010
Sweilam, N. H., Soliman, I. A., & Al-Mekhlafi, S. M. (2017). Nonstandard finite difference method for solving the multi-strain TB model. Journal of the Egyptian Mathematical Society, 25(2): 129-138. DOI: https://doi.org/10.1016/j.joems.2016.10.004
ur Rehman, M. A., Kazim, M., Ahmed, N., Raza, A., Rafiq, M., Akg¨ ul, A.,... & Zakarya, M. (2023). Positivity preserving numerical method for epidemic model of hepatitis B disease dynamic with delay factor. Alexandria Engineering Journal, 64: 505-515, DOI: https://doi.org/10.1016/j.aej.2022.09.013
WHO. (2021a). WHO lists two additional COVID-19 vaccines for emergencyuse and COVAX roll-out: AstraZeneca/Oxford-developed vaccines to reach countries in the coming weeks . https://www.who.int/news/item/15-02-2021-who-lists-two- additional-covid-19-vaccines-for emergency-use-and-covaxroll-out (Accessed 28th July, 2021).
Worldometer. (2022). https://www.worldometers.info/world-population/nigeriapopulation. (Accessed online on the 4th of May, 2022).
Zafar, Z. U. A., Inc, M., Tchier, F., & Akinyemi, L. (2023). Stochastic suicide substrate reaction model. Physica A: Statistical Mechanics and its Applications 610: 1-20. DOI: https://doi.org/10.1016/j.physa.2022.128384
Copyright (c) 2023 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
