MATHEMATICAL MODELING AND COMPUTING, Vol. 10, No. 3, pp. 841–853 (2023) M athematical M odeling C omputing Optimal control strategy for the administration of the third vaccine dose in the treatment of pandemic COVID-19 Khalouﬁ I., Benfatah Y., Laﬁf M., Ghazaoui A., Rachik M. Laboratory of Analysis, Modeling and Simulation, 20670, Casablanca, Morocco (Received 11 September 2022; Revised 9 January 2023; Accepted 10 January 2023) In this paper, we propose a mathematical model of COVID-19 infection, taking into ac- count the division of the population according to vaccination criteria. Our goal is to demonstrate the positive eﬀect of receiving the third dose of the Corona vaccine. We pro- posed two strategies to limit the spread of the COVID-19 pandemic respectively awareness programs on the importance of the third dose of the vaccine and the delivery of treatment to infected individuals who have health problems. Pontryagin’s maximum principle is ap- plied in order to characterize the optimal controls, and the optimality system is resolved using an iterative approach. At last, numerical simulations are executed to verify the theoretical analysis using MATLAB. Keywords: optimal control; mathematical model; COVID-19; the third dose — Corona vaccine. 2010 MSC: 93C15, 34H05, 37N35 DOI: 10.23939/mmc2023.03.841 1. Introduction Commensurate with the World Health Organization (WHO), the severe acute respiratory syndrome corona virus 2 (SARS-CoV-2) otherwise called new corona virus (2019-nCoV) is reckoned as the ety- mology of a contagious disease denominated as (COVID-19). As part of its response to the outbreak, WHO has stopped up its Research and Development (R&D) Program to hasten elaboration of di- agnostics, vaccines and medicines. Beside a wide variety of organizations involved in development, from largest pharma companies to academic centers and non-proﬁt groups. Hence, vaccination for the susceptible host is predominantly contemplated as the only reliable procedure to control SARS-CoV-2. However, the sense of exigency in rummaging vaccines was not shared across all demographics. Vaccine hesitancy emerges as ubiquitous phenomenon threatening the global health. This refusal although accessibility of vaccination services is altered by a variety of determinants as conﬁdence (belief in vaccination safety, eﬃcacy, and the proﬁciency of healthcare systems), convenience (accessibility, competitiveness and distribution of vaccines in a well-provided conditions), and complacency (points out the deﬁcient awareness of the pandemic risk; wherefore, vaccination interpreted as unwarranted process) [1]. A survey of the United Kingdom ascertained a representative UK sample and elicited the join between vaccine knowledge and vaccination willingness. Thus, results perceived the crucial aspect in vaccine hesitancy among respondents which was anxiety rather than familiarity with vaccines. In modern society, mass media and social networks involve an immense inﬂuence on perceived knowledge regarding vaccines along with vaccination refusal, based on irresponsible anti-vaccination propaganda sparked by misleading information. Henceforward, rumors and homemade remedies were perceptibly propagated on social platforms, adjoining mass distribution of worldwide post describing vaccine severe side eﬀects, the latter forced vaccination and overestimation of the number of vaccinated people [2]. A large community-based study concerning COVID-19 vaccine hesitancy in the United States, discerned that almost 22% of respondents delayed acceptance of vaccination predicated on assortment of criteria as ethnicity, sex, educational status, ﬁnancial position, and zone of habitation. Subsequently, political aﬃliations beside presumed COVID-19 threat were observed as a vital aspects of vaccine hesitancy [3]. c  2023 Lviv Polytechnic National University 841