On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems

Motivated by our prior work on a Triple Negative breast cancer cell line, the focus of this paper is controller synthesis for cancer treatment, through the use of drug scheduling and a switched dynamical system model. Here we study a cyclic schedule of $d$ drugs with maximal waiting times between drug inputs, where each drug is applied once per cycle in any order. We suppose that some of the $d$ drugs are highly toxic to normal cells and that these drugs can shrink the live cancer cell population. The remaining drugs are less toxic to normal cells and can only reduce the growth rate of the live cancer cell population. Also, we assume that waiting time bounds related to toxicity, or to the onset of resistance, are available for each drug. A cancer cell population is said to be stable if the number of live cells tends to zero, as time becomes sufficiently large. In the absence of modeling error, we derive conditions for exponential stability. In the presence of modeling error, we prove exponential stability and derive a settling time, under certain mathematical conditions on the error. We conclude the paper with a numerical example that uses models which were identified on Triple Negative breast cancer cell line data.