Modelling approaches
These cover a spectrum that includes the following.
- Temporal models are mostly based on compartmental SEIR (Susceptible, Exposed, Infected and Removed) models for epidemics but with additional complexities of:
- dual sources of inoculum;
- quenching as hosts become resistant to infection;
- and host dynamics that depend upon infection load.
- Stochastic models include allowance for:
- demographic stochasticity (chance effects in transmission from infected to susceptible individuals under otherwise identical conditions);
- environmental stochasticity (when transmission parameters are influenced by local or global changes in environmental variables).
- Spatially-implicit models seek to capture some of the spatial aspects of epidemics within a temporal model by using:
- non-linear mixing terms between susceptibles and infected;
- moment closure and pair-approximation methods.
- Spatially-explicit models include:
- individual-based models, for example, for susceptibles on a lattice often with local mixing;
- reaction-advection-diffusion and dispersal-kernel models;
- metapopulation models that comprise coupled sub-populations such as fields or different regions.
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Mathematical techniques
The group uses a range of mathematical techniques to model epidemic and other ecological processes. These include:
- ordinary and partial differential equations including asymptotic and perturbation theory for model reduction;
- stochastic differential equations;
- probability theory;
- individual-based models for spatial epidemics;
- optimisation and control theory;
- percolation theory and other methods from statistical physics.
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Statistical techniques
One of the principal characteristics of the group’s work is the close interaction between modelling, experimentation and statistical inference to test models and to estimate epidemiological parameters.
We are particularly interested in the role of error structure in epidemic dynamics and in the estimation of variance and higher moments. Examples of recent and current work include:
- Markov chain Monte Carlo techniques to estimate parameters for spatio-temporal models of epidemics;
- Bayesian methods to estimate parameters for replicate epidemics with treatment effects;
- Bayesian methods to estimate parameters for stochastic compartmental models;
- Likelihood methods for estimation of a range of epidemiological parameters.
Links with experimentation and testing models against data
The mathematical and experimental programmes are strongly linked. For example, theoretical work on the consequences of seasonality for epidemics in agricultural crops is accompanied by experiments on R. solani infecting radish seedlings in easily-controllable microcosms. Similarly, modelling of the growth of fungi in soil evolves in concert with the experimental techniques in soil physics to control the spatial structures through which micro-organisms spread along with techniques which make it possible to visualise fungi in that environment. Other work on the regional spread of diseases, draw on extensive field data from collaborating organisations and our own archives. Current and previous examples include:
- Rhizomania disease of sugar beet
- Dutch elm disease
- Citrus canker disease
- Fungicide resistance
- Biological control of Sclerotinia disease
- Bubonic plague
- Seal distemper disease
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Keeling, M.J. & Gilligan, C. A. (2000) Nature 407, 903-906.
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Kleczkowski, A., Bailey, D. J. & Gilligan, C. A. (1996) Proc. R. Soc. Lond. Ser. B. 263, 777-783. Gibson, G. J., Kleczkowski, A. & Gilligan, C. A. (2004) PNAS, 101 (12120-12124).
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Gibson, G. J., Gilligan, C. A. & Kleczkowski, A. (1999) Proc. R. Soc. Lond. Ser. B. 266, 1743-1753. Truscott, J. T. & Gilligan, C. A. (2003) PNAS 100, 9067-9072.
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Truscott, J. E., Gilligan, C. A. & Webb, C. R. (2000) Bull. Math. Biol. 62, 377-393.
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Park, A. W., Gubbins, S. & Gilligan, C. A. (2003) Ecol. Lett. 5, 747-755.
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 Gubbins, S. & Gilligan, C. A. (1997) Philos. Trans. R. Soc. Lond. Ser. B. 352, 1935-1949
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