Wouldn’t it be better to use both treatments simultaneously, if possible? Sometimes, but if there is a single mechanism that can provide resistance to both (i.e. cross-resistance), then the sequential two-strike extinction therapy approach may beat combination therapy. See paper for more details!

Instead, continuing the treatment slightly longer, even though it is no longer shrinking the cancer population, would be optimal in such cases, because continued selection for cells resistant to the first drug may remove preexisting resistance to the second drug. Here’s another example:

Unfortunately, even under our relatively simple model switching at t_min will not work for everyone. If by chance there is even a small fraction of cells resistant to the second drug (red line, note the log scale) at the time of the “second-strike” the treatment will fail:

Often this is due to a genetic adaptation to the treatment. If this adaptation emerges and spreads through the cancer cell population rapidly enough (orange line), the population (blue line) will avoid extinction. This is an example of evolutionary rescue.