Mathematical Modeling with Two Strains to Investigate Evolution of COVID-19 from Computational and Theoretical Perspectives

Authors

  • Muhammad Riaz University of Malakand
  • Zeeshan Ali National Yunlin University of Science and Technology Douliu Taiwan
  • Rahim Ud Din Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
  • Sadique Ahmad EIAS Data Science and Block Chain Laboratory, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
  • Kamaleldin Abodayeh Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia
  • Muhammad Sarwar Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6001

Keywords:

$SEI_1I_2HRD$ model,, Two strain model,, NSFD scheme, , COVID-19, Disease, Sensitivity Analysis, Stability Analysis and Reproduction Number., Effective reproduction number, Fractional numerical analysis

Abstract

The respiratory disease COVID-19 is brought on by a mutagenic {ribonucleic acid (RNA)} virus. Variants with various traits that could potentially impact transmissibility started to appear globally in December 2020. We develop and examine a computational model of two-strain COVID-19 transmission behaviors in order to deal with this novel aspect of the disease. After a theoretical analysis, enough criteria are derived for the stability of the model's equilibrium. The model contains single-strain 1 and variant 2 endemic equilibria as well as disease-free and endemic equilibria. The global stability of the model equilibrium is demonstrated using the Lyapunov function. For each strain, we separately compute the basic reproductive numbers $\mathscr{R}_{01} <1$, and $\mathscr{R}_{02}<1$. To determine the realistic values of the model parameters, the actual data from South Africa for the period of three months, are taken into consideration.
Sensitivity study employing the {partial rank correlation coefficient technique (PRCC)} to look into the key variables that affect $\mathscr{R}_{01} <1$, or $\mathscr{R}_{02}<1$  decrease or increase. We show the numerical simulation of the model using {non-standard finite difference scheme (NSFDS)} and Caputo fractional derivative for distinct non-integer order. The world health organizations (WHO) recommends {standard operating procedures (SOPs)} to minimize infection in the population. Based on these recommendations, some graphical results for the model with sensitive parameters are provided.

Author Biographies

  • Kamaleldin Abodayeh, Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia

    Full professor in Mathematics in Prince Sultan University Riyadh KSA

  • Muhammad Sarwar, Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia

    Associate Professor, Department of Mathematics University of Malakand Chakdara, Dir(L), Pakistan

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Published

2025-05-01

Issue

Section

Mathematical Modeling and Numerical Analysis

How to Cite

Mathematical Modeling with Two Strains to Investigate Evolution of COVID-19 from Computational and Theoretical Perspectives. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6001. https://doi.org/10.29020/nybg.ejpam.v18i2.6001