For tumors close to their environmental carrying capacity, a cost was not required. Tumor cells were divided into sensitive and resistant populations and we model their competition using a system of two ordinary differential equations based on the Lotka–Volterra model. In this article, we study a general, but simple, mathematical model to investigate whether the presence of a cost is necessary for adaptive therapy to extend the time to progression beyond that of a standard-of-care continuous therapy. A plausible candidate for such a selection criterion is the fitness cost of resistance. As such, it is urgent to understand the characteristics of a cancer that determine whether or not it will respond well to adaptive therapy. Motivated by promising results in prostate cancer, there is growing interest in extending this approach to other neoplasms. Adaptive therapy seeks to exploit intratumoral competition to avoid, or at least delay, the emergence of therapy resistance in cancer.
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