Dynamics of cancer recurrence

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16 Scopus citations


Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as initial tumor size, mutation rates and growth kinetics of drugsensitive and resistance cells. To study this phenomenon we characterize the dynamics of escape from extinction of a subcritical branching process, where the establishment of a clone of escape mutants can lead to total population growth after the initial decline. We derive uniform in-time approximations for the paths of the escape process and its components, in the limit as the initial population size tends to infinity and the mutation rate tends to zero. In addition, two stochastic times important in cancer recurrence will be characterized: (i) the time at which the total population size first begins to rebound (i.e., become supercritical) during treatment, and (ii) the first time at which the resistant cell population begins to dominate the tumor.

Original languageEnglish (US)
Pages (from-to)1437-1468
Number of pages32
JournalAnnals of Applied Probability
Issue number4
StatePublished - Aug 2013


  • Branching processes
  • Cancer
  • Population genetics


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