People, animals and plants can be infected by a diverse range of viruses, bacteria and other microbes. Many of these infections cause diseases that limit lifespan, quality of life and productivity. Consequently, the prevention, management and control of infectious diseases is an essential component of socio-economic development and stability. We use mathematical models to explore how nonlinear interactions between multiple drivers of transmission affect the way epidemics develop, and how they might be controlled.
Many of our models are based on systems ordinary or partial differential equations. But we also use discrete-time, stochastic and network-based formulations. We study the dynamics of these models with analytic and numerical methods, dynamical systems theory, stochastic process theory and control theory, alongside computer simulation.
We have used mathematical modelling to study how people's daily commuting patterns affect the risk of dengue epidemics, how host specialisation and immunological interaction drives the diversity of Borrelia bacteria in wildlife populations, and how the management of parasitic worms in grazing livestock is affected by the non-uniform distribution of parasite load. We have developed mathematical theory that offers insight into how seasonal factors affect the prevention of wildlife diseases, and how optimal and adaptive control techniques can be used to manage epidemics.