In this paper, we propose and analyze a prey–predator model with the functional response of Beddington–DeAngelis and the fear effect that have infection only in prey populations. We determine existence criteria of several equilibria, and the stability at different equilibria are presented. We exert pesticide control over prey and additional food control over predators, the optimal control is obtained by the Pontryagin maximum principle. We confirm that adding controls to the predator and prey yields better results. Further we enrich our analysis with the inclusion of the existence and uniqueness of the optimal control. Finally, some numerical results to illustrate our analysis are presented.
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