Mathematical modeling and analysis of the SARS-Cov-2 disease with reinfection

Asghar Atifa; Muhammad Altaf Khan; Kulpash Iskakova; Fuad S Al-Duais; Irshad Ahmad

doi:10.1016/j.compbiolchem.2022.107678

Mathematical modeling and analysis of the SARS-Cov-2 disease with reinfection

Comput Biol Chem. 2022 Jun:98:107678. doi: 10.1016/j.compbiolchem.2022.107678. Epub 2022 Apr 6.

Authors

Asghar Atifa¹, Muhammad Altaf Khan², Kulpash Iskakova³, Fuad S Al-Duais⁴, Irshad Ahmad⁵

Affiliations

¹ COMSATS University Islamabad, Lahore Campus, Pakistan.
² Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa. Electronic address: altafdir@gmail.com.
³ Department of Physics and Mathematics, Kazakh National Pedagogical University, Almaty, Kazakhstan.
⁴ Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al Aflaj, Saudi Arabia; Administration Department, Administrative Science College, Thamar University, Thamar, Yemen.
⁵ College of Applied Medical Sciences, Department of Medical Rehabilitation Sciences, King Khalid University, Abha, Saudi Arabia.

Abstract

The COVID-19 infection which is still infecting many individuals around the world and at the same time the recovered individuals after the recovery are infecting again. This reinfection of the individuals after the recovery may lead the disease to worse in the population with so many challenges to the health sectors. We study in the present work by formulating a mathematical model for SARS-CoV-2 with reinfection. We first briefly discuss the formulation of the model with the assumptions of reinfection, and then study the related qualitative properties of the model. We show that the reinfection model is stable locally asymptotically when R₀<1. For R₀≤1, we show that the model is globally asymptotically stable. Further, we consider the available data of coronavirus from Pakistan to estimate the parameters involved in the model. We show that the proposed model shows good fitting to the infected data. We compute the basic reproduction number with the estimated and fitted parameters numerical value is R₀≈1.4962. Further, we simulate the model using realistic parameters and present the graphical results. We show that the infection can be minimized if the realistic parameters (that are sensitive to the basic reproduction number) are taken into account. Also, we observe the model prediction for the total infected cases in the future fifth layer of COVID-19 in Pakistan that may begin in the second week of February 2022.

Keywords: Estimation of parameters; Mathematical model with reinfection; Numerical results and discussion; Stability analysis.

MeSH terms

Basic Reproduction Number
COVID-19*
Humans
Models, Theoretical
Reinfection
SARS-CoV-2