Branching processes, stochastic simulations and travelling waves

Overview

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.

Outcomes

• 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).

Scholarships

You may be eligible to apply for a research scholarship.

Explore our research scholarships

Keywords

• mathematical modelling
• computational mathematics
• mathematical biology

Contact

Contact the supervisor Professor Matthew Simpson for more information.