Modeling breast cancer and its optimal control

Abstract

Breast cancer is the most common cancer among womenfolk, impacting above 1.5 million women every year, and correspondingly roots the utmost number of cancer-related deaths among women. In 2015, 570,000 women died from the disease that is about 15% of all cancer deaths amongst womenfolk. Although the disease rates are higher amongst womenfolk in more industrialized regions, rates are increasing in nearly every region globally. In this paper, a model of the disease is developed. Conditions are derived for the existence of disease free equilibrium. Stability analysis of the model shows that that disease free equilibrium is both locally asymptotically stable and globally asymptotically stable. Optimal control theory is applied to the model and Pontrygain’s Maximum Principle is applied for analysis of the control. To this end, three control strategies were incorporated into disease transmission model. The impact of using possible combinations of the three control strategies was investigated