Optimal strategy in cancer chemotherapy for exponential model of cell population growth

The problem of optimal cancer chemotherapy is reconsidered. The cumulative negative toxic effect of the drug is minimized for the assumed destruction result at the end of the therapy. The control function to be optimized is time-dependent dose of the drug. A exponential model of growth of the cancer cell population is employed. It is known that for constant intrinsic rate the solution of the problem is ununique - different strategies give the same result of the therapy. If intrinsic rate is a variable monotonic function of time the solution of the problem is unique and it is of "bang-bang" type with one switching point. The method of extremization of linear integrals via Green's theorem is applied.