Tumor growth project, part 2
Group members:
For the second part of the tumor growth project, we imagine a cancerous tumor was detected after it reached a sizable mass, containing $c=10,000,000$ cells. At that point, to fight the cancer, a drug is administered to kill the cancer cells, increasing their death rate by a factor of three, so that the probability per day of a cancer cell dying becomes $\mu =0.015$.
However, the fear is that the application of the drug may lead to the emergence of cancer cells that are resistant to the drug. Given the presence of a drug, there is a tiny chance that, upon cell division, one of the daughter cells might contain a mutation that produces drug resistance. The probability that a division produces one drug-resistant cell is $m = 10^{ -8 }$. Since the drug-resistant cells don't respond to the drug, their probability of death per day is $0.005$, as was the case for all cancer cells before the drug was administered.