Branching processes and their application in family trees and tumour growth

Abstract

Branching processes are stochastic processes that model populations over time. We first look at a branching process model for the family tree that can be applied to human family lines in discrete time (generations). We also look at a branching process model that describes the evolution of cells, using asymptotic theorems to calculate limiting distributions of certain variables of this process. Lastly, we use lung tumour data and compare the limiting functions to our own simulations.