Mathematical modeling and optimal control of the COVID-19 dynamics

Zhong-Hua Shen; Yu-Ming Chu; Muhammad Altaf Khan; Shabbir Muhammad; Omar A Al-Hartomy; M Higazy

doi:10.1016/j.rinp.2021.105028

Mathematical modeling and optimal control of the COVID-19 dynamics

Results Phys. 2021 Dec:31:105028. doi: 10.1016/j.rinp.2021.105028. Epub 2021 Nov 27.

Authors

Zhong-Hua Shen¹, Yu-Ming Chu², Muhammad Altaf Khan³, Shabbir Muhammad^{4

5}, Omar A Al-Hartomy⁶, M Higazy^{7

8}

Affiliations

¹ School of Mathematics, Hangzhou Normal University, Hangzhou 311121, PR China.
² Department of Mathematics, Huzhou University, Huzhou 313000, PR China.
³ Institute for Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa.
⁴ Research Center for Advanced Materials Science (RCAMS), King Khalid University, P.O. Box 9004, Abha, Saudi Arabia.
⁵ Department of Physics,College of Science, King Khalid University, Abha, P.O. Box 9004, Saudi Arabia.
⁶ Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
⁷ Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt.
⁸ Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.

Abstract

We are considering a new COVID-19 model with an optimal control analysis when vaccination is present. Firstly, we formulate the vaccine-free model and present the associated mathematical results involved. Stability results for $R_{0} < 1$ are shown. In addition, we frame the model with the vaccination class. We look at the mathematical results with the details of the vaccine model. Additionally, we are considering setting controls to minimize infection spread and control. We consider four different controls, such as prevention, vaccination control, rapid screening of people in the exposed category, and people who are identified as infected without screening. Using the suggested controls, we develop an optimal control model and derive mathematical results from it. In addition, the mathematical model with control and without control is resolved by the forward-backward Runge-Kutta method and presents the results graphically. The results obtained through optimal control suggest that controls can be useful for minimizing infected individuals and improving population health.

Keywords: COVID-19; Numerical results; Optimal control; Real data; Stability analysis; Vaccination.