Cancer is a somatic evolutionary process characterized by the accumulation of mutations,
which contribute to tumor growth, clinical progression, immune escape, and drug resistance …

Cancer is a disease in which cells accumulate genetic aberrations that are believed to
confer a clonal advantage over cells in the surrounding tissue. However, the quantitative …

The theory of branching processes is an area of mathematics that describes situations in
which an entity exists for a time and then may be replaced by one, two, or more entities of a …

Most physical and other natural systems are complex entities that are composed of a large
number of interacting individual elements. It is a surprising fact that they often obey the so …

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic
intervention, given the constant selective pressure toward drug resistance. Mathematical …

With rare exceptions, human tumors arise from single cells that have accumulated the
necessary number and types of heritable alterations. Each such cell leads to dysregulated …

In this chapter, we will use multitype branching processes with mutation to model cancer.
With cancer progression, resistance to therapy, and metastasis in mind, we will investigate τ …

Therapeutic resistance arises as a result of evolutionary processes driven by dynamic
feedback between a heterogeneous cell population and environmental selective pressures …

In order to analyze data from cancer genome sequencing projects, we need to be able to
distinguish causative, or “driver,” mutations from “passenger” mutations that have no …

An explicit solution for a general two-type birth–death branching process with one-way
mutation is presented. This continuous time process mimics the evolution of resistance to …