Title: Time optimal control for an epidemic system with isolation and quadratic treatment

Authors: Soovoojeet Jana; Anupam Khatua; Tapan Kumar Kar; Manotosh Mandal

Addresses: Department of Mathematics, Ramsaday College, Amta-711401, Howrah, West Bengal ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India ' Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk-721636, West Bengal, India

Abstract: This paper aims to explore the use of the time-optimal control problem to eradicate infectious diseases. In the first part, an SIS-type epidemic system including isolation and quadratic treatment control is proposed. The dynamical characteristics of the system are studied, considering the control variable fixed. Next, in the second part, a time-optimal control problem is formulated to reach the disease-free state in the minimum possible time. The control problem is solved by employing Pontryagin's maximum principle, and the explicit expression of the optimal time is derived for the developed model system.

Keywords: epidemic model; isolation; quadratic treatment; global stability; time optimal control.

DOI: 10.1504/IJDSDE.2022.126532

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.4, pp.361 - 370

Received: 26 Mar 2020
Accepted: 24 May 2021
Published online: 28 Oct 2022 *

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