Alzheimer’s disease is a neurodegenerative condition marked by the gradual and irreversible deterioration of brain cells. Normally, after oxidative stress, ATM proteins move to the nucleus to detect and repair DNA double-strand breaks. Recent research, however, reveals that in Alzheimer’s-affected cells, ATM proteins form structures called perinuclear ATM crowns, influenced by the APOE protein, which prevents their migration to the nucleus. We propose a mathematical model to describe perinuclear ATM crown formation using a system of nonlinear differential equations, aiming to assess the potential of irradiation and antioxidants as preventive and therapeutic interventions. Our model shows that irradiation or antioxidants alone cannot eliminate the perinuclear ATM crown, although antioxidants may play a preventive role if the crown has not yet formed. To dissolve an existing crown, a combined treatment with irradiation and antioxidants is necessary. Ultimately, this model serves as an initial framework for understanding disease progression and evaluating possible treatment strategies.