A review of optimal control strategies to inhibit contagious infectious diseases

Using mathematical models to describe infectious diseases and then how to control and eliminate them by vaccines or other treatments, is a great help to public health organizations. Eradication of this category of diseases is possible when treatments are prescribed at the right time and with the right amount and process; In this regard, optimal control theory has been applied as a successful tool. The main purpose of this article is to review the existing literature considering such strategies in dealing with infectious diseases in the form of the famous basic model SIR. For this purpose, this study, deals with the way to use the control functions and how to explain the provided solutions, indeed the aims are to investigate susceptible, infected, and recovered populations in terms of the required goals, among the performed activities by evaluation and analyzing. Based on the number of used control variables in the treatment model, which indicate different methods of simultaneous prevention, including vaccination, treatment of infection, quarantine, and like or, the type of model, this study has been categorized and the results are presented. Also, in this review, the methods of implementing models from a numerical computation point of view and reality have also been discussed and time delay, stochastic, and discrete-time models in the case of SIR are also investigated. This review would help the researchers in order to have knowledge about the subject and activities carried out to continue research in this area are very helpful.