Abstract
In this paper, we propose a mathematical model that describes the effect of rumors on the success of vaccination programs against Covid-19 in an environment infected by the coronavirus. The aim of this study is to highlight the role of addressing the spread of rumors regarding vaccination risks and booster doses in the success of vaccination programs and in achieving herd immunity. Additionally, we formulate an optimal control problem by proposing several strategies, including awareness and anti-rumor programs, to assist country officials in achieving successful vaccination programs with optimal effort. The existence of optimal controls is investigated, and Pontryagin's maximum principle is used to characterize them. The optimality system is solved using an iterative method. Finally, we conduct numerical simulations to verify the theoretical analysis using Matlab.
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