Open Access

ARTICLE

A Detailed Mathematical Analysis of the Vaccination Model for COVID-19

Abeer S. Alnahdi^1,*, Mdi B. Jeelani¹, Hanan A. Wahash², Mansour A. Abdulwasaa^3,4

1 Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
2 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India
3 Department of Statistics, Taiz University, Taiz, Yemen
4 Department of Statistics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India

* Corresponding Author: Abeer S. Alnahdi. Email:

(This article belongs to this Special Issue: Advanced Numerical Methods for Fractional Differential Equations)

Computer Modeling in Engineering & Sciences 2023, 135(2), 1315-1343. https://doi.org/10.32604/cmes.2022.023694

Received 09 May 2022; Accepted 30 June 2022; Issue published 27 October 2022

Abstract

This study aims to structure and evaluate a new COVID-19 model which predicts vaccination effect in the Kingdom of Saudi Arabia (KSA) under Atangana-Baleanu-Caputo (ABC) fractional derivatives. On the statistical aspect, we analyze the collected statistical data of fully vaccinated people from June 01, 2021, to February 15, 2022. Then we apply the Eviews program to find the best model for predicting the vaccination against this pandemic, based on daily series data from February 16, 2022, to April 15, 2022. The results of data analysis show that the appropriate model is autoregressive integrated moving average ARIMA (1, 1, 2), and hence, a forecast about the evolution of theCOVID-19 vaccination in 60 days is presented. The theoretical aspect provides equilibrium points, reproduction number , and biologically feasible region of the proposed model. Also, we obtain the existence and uniqueness results by using the Picard-Lindel method and the iterative scheme with the Laplace transform. On the numerical aspect, we apply the generalized scheme of the Adams-Bashforth technique in order to simulate the fractional model. Moreover, numerical simulations are performed dependent on real data of COVID-19 in KSA to show the plots of the effects of the fractional-order operator with the anticipation that the suggested model approximation will be better than that of the established traditional model. Finally, the concerned numerical simulations are compared with the exact real available date given in the statistical aspect.

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Keywords

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