I use mathematical models to describe how infectious diseases spread in (typically human) populations and how pathogens evolve, for example in the case of emerging of resistance to drugs. Although I have worked also on spread of infection on networks, the areas of main interest to me at present involve infections in the context of:
- Populations with a social structure (e.g. age classes, households, schools, etc.)
- Multiscale models (i.e. within-host dynamics and between-host transmission)
- Statistical methods for parameter estimation
The model construction process per se is already a third of the journey. The second third is the analysis of the model, and I try to work at the boundary between models that are analytically tractable and models that need to be studied via large stochastic simulations. Because my work is driven by a biologically relevant question, I typically use any mathematical tool that turns out to be useful for the problem, but most commonly:
- Ordinary differential equations (ODEs)
- Integral equations
- Stochastic processes
- Individual-based stochastic simulations
The third part of the journey is to estimate model parameters, so more recently I am developing a growing interest in Bayesian statistics, and more general in data science.
In such an interdisciplinary field, a surprising amount of time is spent clarifying poorly defined concepts. I am particularly interested in comparing the behaviour of a range of different models and the assumptions on which they rely, in order to ensure as much as possible that the model predictions do actually reflect the system at hand, rather than being an artefact of the particular mathematical representation used.