Analysis of diffusion driven instability in the Oregonator using "Common Lyapunov Functions”; Elragig & Townley, Math. Bioscience, 2012.

Analysis of diffusion driven instability in the Oregonator using "Common Lyapunov Functions”; Elragig & Townley, Math. Biosciences, 2012.

Simulated incidence timeseries of a 4-strain pathogen system showing irregular, epidemiological dynamics; Lourenco & Recker, PLoS Comp. Biol., 2013.

Simulated incidence timeseries of a 4-strain pathogen system showing irregular, epidemiological dynamics; Lourenco & Recker, PLoS Comput. Biol., 2013.

Simulated epidemic impact for various vaccination strategies for a foot-and-mouth disease outbreak in the UK; Tildesley et al., Nature, 2006.

Simulated epidemic impact for various vaccination strategies for a foot-and-mouth disease outbreak in the UK; Tildesley et al., Nature, 2006.

Schooling fish collectively sensing a darkness field; Berdahl, Torney et al. Science, 2013.

Schooling fish collectively sensing a darkness field; Berdahl, Torney et al., Science, 2013.

Evolution of an antigenic switching network optimised over two fitness traits; Recker et al., PLoS Pathogen, 2011.

Evolution of an antigenic switching network optimised over two fitness traits; Recker et al., PLoS Pathogen, 2011.

Research interests

Our research applies mathematics to the study of a diverse range of issues with a common aim of understanding, and mitigating against, the effects of environmental change. With strong links to the life and environmental sciences and engineering our research focuses on the following areas of interest.

Ecological modelling

Ecological systems involve complex, interacting dynamics and motivate a rich and diverse range of mathematical modelling and analyses. We are developing systems-based tools to understand transient dynamics in ecological models and their impact on conservation, invasion and life history.

In collaboration with experimentalists, we study how animals make decisions and move within their environments or how environmental conditions influence the spread of diseases. Theoretically we aim to understand how individual behaviour affect population dynamics and macro-scale ecological processes such as predator-prey interaction, migration and dispersal.

Epidemiology and infectious disease

Infectious diseases of humans and livestock are a major concern for global public health and a burden on the global economy. The particular ways in which disease causing agents, or pathogens, interact with their respective hosts and the environment underlie the dynamics of individual infections, transmission events between individuals all the way to epidemic outbreaks and pandemic spread.

Our research combines mathematical modelling with the fields of ecology, evolution and epidemiology to investigate these multi-scale interactions and the effects they have on the emergence, spread, persistence and management of infectious diseases.

Evolutionary dynamics

Evolution is the mechanism by which natural populations adapt and famously is the unifying principle without which nothing in biology makes sense. The mathematical study of evolution has a long history. Research in the Centre applies and develops this theory to understand the evolution of collective behaviour and animal grouping, the evolution of traits (including pathogen fitness and virulence), the evolutionary dynamics of resistance and host-pathogen interactions and the impact, and evolution, of non-genetic effects, including maternal effects.

Mathematics of complexity and control

Natural systems are complex and often unpredictable. By employing mathematical tools from fields such as complexity science, control theory, network science and statistical physics, we study how these systems function and persist. Common principles apply across multiple scales, from the behaviour of animals, to the resilience of ecosystems or the functioning of distributed technologies.

In an engineering context we apply these theories to the complex dynamics arising in renewable energy. As renewable energy is centred around localized power sources, (tidal, wave or wind based) there are a range of mathematical challenges relating to prediction, optimization, and synchronization to the global electricity network and distributed consumption.

A Butterfly Effect: a small initial difference may make a great transient change, although both solutions tend to a stable orbit; Rüffer, van de Wouw & Mueller, Syst. Control Lett., 2013

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