Title: Optimal control of behaviour and treatment in a nonautonomous SIR model

Authors: Samhita Das; Pritha Das; Parthasakha Das

Addresses: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India

Abstract: In this paper, we have considered a nonautonomous susceptible, infected, removed (SIR) model with saturation incidence rate for disease transmission. The global dynamical properties like permanence and global stability of the system as well as extinction of disease are analytically and numerically studied. The impact of behavioural patterns of individuals on disease control is validated along with possible applications. Furthermore, Pontryagin's Maximum Principle is used to characterise optimal level of the two controls, treatment and awareness level. Our objective is to minimise the infected population as well as the cost of applied control. The controls at optimal level are found to achieve different levels of impact on infection. It is observed that the combined impact of treatment and awareness exhibits more effective result in disease control compared to their single application. Based on observation, the strategy regarding the implementation of awareness and treatment is suggested.

Keywords: nonautonomous SIR model; saturation incidence rate; permanence; extinction; optimal control; awareness; treatment.

DOI: 10.1504/IJDSDE.2021.115178

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.2, pp.108 - 130

Received: 24 Nov 2018
Accepted: 24 May 2019

Published online: 15 May 2021 *

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