MATHEMATICAL AND NUMERICAL ANALYSIS OF SIQR EPIDEMIC MODEL OF MEASLES DISEASE DYNAMICS

Muhammad Aziz-Ur Rehman, Anum Farooq Rana, Nauman Ahmed, Ali Raza, Amnah S. Al-Johani, Abdullah Mohamed, Muhammad Sajid Iqbal, Muhammad Rafiq and Ilyas Khan
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Muhammad Aziz-Ur Rehman: Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Anum Farooq Rana: Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Nauman Ahmed: ��Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
Ali Raza: ��Department of Mathematics, National College of Business Administration & Economics, Lahore, Pakistan§Department of Mathematics, Government Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore, Pakistan
Amnah S. Al-Johani: �Mathematics Department, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Abdullah Mohamed: ��University Research Centre, Future University in Egypt, New Cairo 11745, Egypt
Muhammad Sajid Iqbal: ��Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
Muhammad Rafiq: *Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan
Ilyas Khan: ��†Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-17

Abstract: Measles is a highly transmissible disease in children around the world. According to the World Health Organization (WHO), 73% of deaths of children were due to measles in 2018. This study describes the physical solution of the SIQR model for measles spread under the effect of natural delay amongst different compartments. By three different numerical techniques, the efficacies of solutions of the underlying system have been compared and a clear preference of nonstandard finite-difference (NSFD) scheme over the rest has been established. It has also been observed, on principle, that the NSFD formulation recovers all the essential traits of a continuous model namely the boundedness, positivity and stability of equilibriums of populations. The numerical results have also been supported by a very strong classical analysis of the model where the existence of a solution vector in explicit subsets of the function spaces has been guaranteed which leads to optimization of fixed-point methods.

Keywords: Measles Disease; SIQR Model; Numerical Modeling; Positivity; Optimal Existence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401545

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