Phase transitions in stochastic systems. This project aims to understand models of physical and biological phenomena in the presence of uncertainty/randomness. Such models often exhibit phase transitions if a variable defining the model is modified. For example, a population explosion can occur if the average number of offspring per individual is larger than one, while macroscopic defects can occur in a material if the density of microscopic defects is larger than some threshold. This research c ....Phase transitions in stochastic systems. This project aims to understand models of physical and biological phenomena in the presence of uncertainty/randomness. Such models often exhibit phase transitions if a variable defining the model is modified. For example, a population explosion can occur if the average number of offspring per individual is larger than one, while macroscopic defects can occur in a material if the density of microscopic defects is larger than some threshold. This research could lead to strategies for directing physical and biological systems towards preferred states or phases, and better prediction of adverse events such as fracturing of Antarctic sea ice.Read moreRead less
Epidemics in large populations: long-term and near-critical behaviour. The project aims to prove qualitative and quantitative results concerning aspects of the long-term behaviour of near-critical epidemics, including the probability and duration of a large outbreak, and the total number of people infected. This project is a theoretical study of stochastic models of epidemics in large populations. The project will focus on emerging epidemics, where the average number of contacts, infection and r ....Epidemics in large populations: long-term and near-critical behaviour. The project aims to prove qualitative and quantitative results concerning aspects of the long-term behaviour of near-critical epidemics, including the probability and duration of a large outbreak, and the total number of people infected. This project is a theoretical study of stochastic models of epidemics in large populations. The project will focus on emerging epidemics, where the average number of contacts, infection and recovery rates are such that the basic reproduction number of the disease is near the critical value 1. The project will plan to both analyse particular epidemic models and develop new methodologies applicable in broader contexts. The mathematical predictions will be tested through simulations and comparison to real-world data. The significant outcome of the project should be the advancement in mathematical understanding of infectious disease spread, eventually leading to improved epidemic surveillance and control, and resulting in more effective protection of public health, improved quality of life, and obvious economic benefits.Read moreRead less