A study on cancer-obesity-treatment model with quadratic optimal control approach for better outcomes

In this study, we propose a cancer-obesity-treatment model under the control parameters: IL-2 therapy, ACI therapy, and nutritional diet. We analyze the proposed model and examine the existence and stability of the equilibrium points for the cases: with and without treatment cases. Further, to reduce the number of cancer cells and minimize the toxicity effect of the drug dose on other healthy cells, we consider an optimal control problem over a finite time interval under the treatment control parameters. To understand the treatment effect, we present simulation results for our proposed model considering different treatment strategies: no treatment; only IL-2 therapy; a combination of IL-2 therapy and ACI therapy; and a combination of IL-2 therapy, ACI therapy, and nutritional diet. Our results demonstrate that we could achieve an optimal treatment schedule for cancer management by controlling all three treatment parameters. •A cancer obesity-treatment model under some control parameters: IL-2 therapy, ACI therapy, and nutritional diet is proposed.•Discussed the proposed model without treatment.•Further, to reduce the number of cancer cells and minimize the toxicity effect of the drug dose on other healthy cells, we consider an optimal control problem over a finite time interval under the treatment control parameters.•Finally, to understand the treatment effect, we present simulation results for our proposed model.•Our results demonstrate that we could achieve an optimal treatment schedule for cancer management by controlling all three treatment parameters.