Breast Cancer Epidemic Model and Optimal Control

The breast cancer represents one of the most frequent disease diagnosed worldwide; with the modern im- provements in medicine and technology a fast detection of tumor could allow a total recovery. In this paper, it is proposed a compartmental epidemiological model in which the female population is partitioned depend- ing on the condition with respect to the tumor diagnosis. The model is identified referring to the population of a region of Italy, using real data; increasing levels of control are introduced, from noninvasive prevention to combination of surgery and chemotherapy. In the framework of optimal control, aiming at reducing the number of severe cases and of women dead by tumor, a suitable combination of control effort is determined, considering constraints in the containment measures. Numerical results stress the importance of prevention that at the very beginning increases the number of discovered positive diagnosis, and, successively, signifi- cantly contains the fatal consequences of breast cancer on the population by reducing the late diagnosis.