Optimal control strategies for SGLT2 inhibitors as a novel anti-tumor agent and their effect on human breast cancer cells with the effect of time delay and hyperglycemia

Breast cancer is the most frequent cancer in the world, and it continues to have a significant impact on the total number of cancer deaths. Recently, oncology findings hint at the role of excessive glucose in cancer progression and immune cells' suppression. Sequel to this revelation is ongoing researches on possible inhibition of glucose flow into the tumor micro-environment as therapeutics for malignant treatment. In this study, the effect of glucose blockage therapeutics such as SGLT-2 inhibitors drug on the dynamics of normal, tumors and immune cells interaction is mathematically studied. The asymptomatic nature of the breast cancer is factored into the model using time delay. We first investigate the boundedness and non-negativity of the solution. The condition for existence of critical equilibrium point is determined, and its global stability conditions are derived using Lyapunov function. This revealed that a timely administration of the SGLT-2 inhibitors drug can eliminate tumor cells. Secondly, we determine the sufficient and necessary conditions for optimal control strategy of SGLT-2 inhibitors so as to avert side effects on normal cells using a Pontryagin's Minimum Principle. The results showed that if the ingestion rate of the inhibitor drug is equal to the digestion rate, the tumor cells can be completely eliminated within 9 months without side effects. The analytical results were numerically verified and the qualitative views of interacting cells dynamics is showcased.