Giulia Belluccini

Short description of my project

We are seeking to understand the dynamics of T cell populations. From a mathematical point of view, many biological processes are modelled using Markov chains, therefore the underlying hypothesis is that interevent times are exponentially distributed.

However, recent works showed that this assumption is not appropriate for such processes where cell proliferation plays a key role. Indeed, the history-dependence nature of the cell cycle breaks the Markov property.

Multi-stage representations for cell proliferation are able to overcome this problem using Erlang distributions.

In this scenario, my project consists of two main parts:

• use a more general family of distributions, called Phase Type distributions, to represent the cell cycle;
• generalise the idea of multi-stage representations for cell proliferation to a model which involves also cell death and is able to track the number of divisions that the cell has undergone.