Study level

  • PhD
  • Master of Philosophy
  • Honours
  • Vacation research experience scheme


Topic status

We're looking for students to study this topic.

Research centre


Dr Elliot Carr
Senior Lecturer
Division / Faculty
Faculty of Science
Professor Scott McCue
Division / Faculty
Faculty of Science
Professor Matthew Simpson
Division / Faculty
Faculty of Science


Branching processes are stochastic mathematical models used to study a range of biological processes, including tissue growth and disease transmission.

This project will implement a simple stochastic branching process to generate simulations of biological growth, and then consider differential equation-based description of the stochastic model.

Using computation we will compare the two models, and use phase plane and perturbation analysis to analyze the resulting traveling wave solutions.

Research activities

Research activities include:

  • building stochastic simulation algorithms and visualise the resulting simulations
  • constructing conservation arguments leading to a differential equation description
  • solving differential equations and comparing the numerical solutions with data from the stochastic simulations
  • phase plane analysis to understand travelling wave solutions.


  • New stochastic simulation algorithms.
  • New partial differential equation models that describe the banching process and tissue growth.
  • New mathematical analysis of travelling wave solutions of the partial differential equation models.

Skills and experience

You should have:

  • strong computational skills (e.g. MATLAB, Julia)
  • undergraduate training in differential equations (e.g. MXB225 or MXB322).


You may be eligible to apply for a research scholarship.

Explore our research scholarships



Contact the supervisor Professor Matthew Simpson for more information.