Stability analysis and optimal control of Covid-19 pandemic SEIQR fractional mathematical model with harmonic mean type incidence rate and treatment

Muhammad Sinan; Amjad Ali; Kamal Shah; Taghreed A Assiri; Taher A Nofal

doi:10.1016/j.rinp.2021.103873

Stability analysis and optimal control of Covid-19 pandemic SEIQR fractional mathematical model with harmonic mean type incidence rate and treatment

Results Phys. 2021 Mar:22:103873. doi: 10.1016/j.rinp.2021.103873. Epub 2021 Jan 30.

Authors

Muhammad Sinan¹, Amjad Ali², Kamal Shah³, Taghreed A Assiri⁴, Taher A Nofal⁵

Affiliations

¹ Department of Mathematics and Statistics, University of Swat, 18000 Khyber Pakhtunkhwa, Pakistan.
² Department of Mathematics, Govt P.G Jahanzeb College Swat, 18000 Khyber Pakhtunkhwa, Pakistan.
³ Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000 Khyber Pakhtunkhwa, Pakistan.
⁴ Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia.
⁵ Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.

Abstract

In the present work, we investigated the transmission dynamics of fractional order SARS-CoV-2 mathematical model with the help of Susceptible $S (t)$ , Exposed $E (t)$ , Infected $I (t)$ , Quarantine $Q (t)$ , and Recovered $R (t)$ . The aims of this work is to investigate the stability and optimal control of the concerned mathematical model for both local and global stability by third additive compound matrix approach and we also obtained threshold value by the next generation approach. The author's visualized the desired results graphically. We also control each of the population of underlying model with control variables by optimal control strategies with Pontryagin's maximum Principle and obtained the desired numerical results by using the homotopy perturbation method. The proposed model is locally asymptotically unstable, while stable globally asymptotically on endemic equilibrium. We also explored the results graphically in numerical section for better understanding of transmission dynamics.

Keywords: 26A33; 34A08; 93A30; Basic reproduction number; Fractional optimal control; Homotopy perturbation method; Next generation matrix; Stability analysis; Third additive compound matrix.