Evolution of resistance and progression to disease during clonal expansion of cancer

Inspired by previous work of Iwasa et al. (2006) and Haeno et al. (2007), we consider an exponentially growing population of cancerous cells that will evolve resistance to treatment after one mutation or display a disease phenotype after two or more mutations. We prove results about the distribution of the first time when kk mutations have accumulated in some cell, and about the growth of the number of type-kk cells. We show that our results can be used to derive the previous results about a tumor grown to a fixed size.