An optimally controlled chemotherapy treatment for cancer eradication

In the present study, we developed a modified immune-tumor-normal cell model, considering Lotka-Volterra-type competitions between the cell populations and the chemotherapy drugs. The local stability of the model has been examined at each equilibrium point. Also, the global stability of the model at tumor-free equilibrium has been looked at, and a range of drug administration rates has been found for which the tumor-free state is asymptotically stable globally. Also, the growth of tumor cells was kept to a minimum by setting up an optimal control policy for how drugs are given. We found that the optimal control strategy helped eliminate tumor cells with fewer adverse side effects because it kept the number of normal and immune cells high. The optimal control strategy also reduces the time needed for the treatment strategy. Finally, numerical simulations are performed to verify some of our theoretical results.