Modeling the pandemic trend of 2019 Coronavirus with optimal control analysis

BiBi Fatima; Gul Zaman; Manar A Alqudah; Thabet Abdeljawad

doi:10.1016/j.rinp.2020.103660

Modeling the pandemic trend of 2019 Coronavirus with optimal control analysis

Results Phys. 2021 Jan:20:103660. doi: 10.1016/j.rinp.2020.103660. Epub 2020 Dec 9.

Authors

BiBi Fatima¹, Gul Zaman¹, Manar A Alqudah², Thabet Abdeljawad^{3

4}

Affiliations

¹ Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan.
² Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
³ Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
⁴ Department of Medical Research, China Medical University, Taichung 40402, Taiwan.

Abstract

In this work, we propose a mathematical model to analyze the outbreak of the Coronavirus disease (COVID-19). The proposed model portrays the multiple transmission pathways in the infection dynamics and stresses the role of the environmental reservoir in the transmission of the disease. The basic reproduction number $R_{0}$ is calculated from the model to assess the transmissibility of the COVID-19. We discuss sensitivity analysis to clarify the importance of epidemic parameters. The stability theory is used to discuss the local as well as the global properties of the proposed model. The problem is formulated as an optimal control one to minimize the number of infected people and keep the intervention cost as low as possible. Medical mask, isolation, treatment, detergent spray will be involved in the model as time dependent control variables. Finally, we present and discuss results by using numerical simulations.

Keywords: (COVID-19); Next generation matrix method; Numerical simulation; Optimal control analysis; Pandemic model; Stability analysis.