Fitting transmission models

Theme Co-ordinator: Richard White

Complex mathematical models are now being used in many scientific disciplines and are becoming increasingly common in basic science, climate modelling, communicable and non-communicable disease epidemiology and public health.  The utility of mathematical models for prediction and planning relies on how well they are calibrated to empirical data and how well the models can be analysed to test the robustness of model predictions.  However, the development of methods to robustly calibrate and analyse complex mathematical models has greatly lagged behind their application.

One of the key reasons that complex mathematical model calibration is uncommon is that most formal methods (including distance-based and likelihood-based measures) require that models are run many times.  This poses a considerable problem for complex models as they may require many minutes or even hours for a single scenario.  The problem is compounded for stochastic models because hundreds or thousands of realisations are required for each scenario.  Current standard methods for formal sensitivity and uncertainty analysis are also impractical for complex models because of the heavy computational burden. Model simplification, although desirable, is not appropriate if a complex model is required to satisfactorily address the research question and it increases the probability of model inadequacy.  As the number of model parameters increases, the number of runs required for an adequate exploration of the parameter space increases rapidly. Robust fitting and uncertainty analysis of complex models with dozens of parameters is often impossible, even with increasing computer power and advances in parallelisation.

Fortunately, in recent years there have been important methodological developments in Bayesian Emulation and Approximate Bayesian Computation that show considerable potential for the calibration and analysis of complex mathematical models.

This Centre theme will focus on developing methods to robustly calibrate and analyse complex mathematical transmission models.  We are currently focussing on Bayesian Emulation and Approximate Bayesian Computation methods, but other fun stuff is bound to emerge…

For more information on the mathematical modelling of infectious diseases please visit the website of the LSHTM Centre for the Mathematical Modelling of Infectious Diseases.