Workshop - "Stochastic simulations in branching processes"

In this workshop, we will explore different strategies often used to simulate stochastic systems. We will focus on biological systems with intrinsic noise, i.e., in which the individuals involved are governed by rules with some degree of randomness. In particular, we will explore different applications of branching processes, including disease modelling, resistance evolution and cancer evolution. We will cover different algorithms found in the literature of stochastic processes. We will mainly focus on:

• Gillespie algorithm (also known as kinetic Monte Carlo): a standard method used to simulate continuous-time Markov chains with constant rates. This algorithm generates exact realisations of the system dynamics.
   
• Lewis' thinning algorithm: a modified version of the Gillespie algorithm suitable for systems with time-dependent rates.
   
• tau-leaping algorithm: an approximate method based on the Gillespie algorithm. This algorithm works in discrete-time and allows for a more efficient simulation in larger systems.

We will provide the necessary theoretical background on stochastic processes to apply each algorithm.

Prerequisites

Participants need basic knowledge of probability theory and of a programming language (Python, C++, R, etc.).

Program

Day 1 (new schedule)

13:00 - 15:00: Theoretical session 1: Background in probability theory; theory and applications of the Gillespie algorithm

15:00 - 15:20: Break

15:20 - 17:00: Practical session 1: Implementation of the Gillespie algorithm and exercises

Day 2

14:00 - 16:00: Theoretical session 2: Theory and applications of Lewis' thinning algorithm and the tau-leaping algorithm

16:00 - 16:20: Break

16:20 - 18:00: Practical session 2: Implementation of the tau-leaping algorithm and exercises

During the practical sessions, participants will implement stochastic algorithms with a programming language of their choice; however, we will use Python in our explanations. We will provide the necessary material for these sessions in advance. Please bring your laptop on both days. 

This workshop will take place in person in the interim Lecture Hall if conditions permit.

For planning purposes, please register by November 26. The maximum number of participants is 25.