ALI, Linda2025-11-172025-11-172025-06-03http//localhost:8080/jspui/handle/123456789/13518In this memory, we have made a detailed study of the inverse problem and in particular the observation problem and analyzed an epidemiological model of the type SIS using optimal con- trol methods with the aim of identifying unknown coefficients such as transition and recovery coefficients . The inverse problem is transformed into an optimal control problem in which a cost function is defined that minimizes the difference between the model results and the observed data at the final time and is often represented by differential or integral equations, where the results of the theory such as existence and necessary conditions for optimality are proved .eninverse problem; control problem; observability; optimal control .Thesis