Parameter Estimation and Site-Specific Calibration of Disease Transmission Models

Abstract

The use of mathematical models for developing management options for controlling infectious diseases at a local scale requires that the structure and parameters of the model reflect the realities of transmission at that scale. Data available to inform local models are generally sparse and come from diverse sources and in diverse formats. These characteristics of the data and the complex structure of transmission models, result in many different parameter sets which mimic the local behavior of the system to within the resolution of field data, even for a model of fixed structure. A Bayesian approach is described, at both a practical and a theoretical level, which involves the assignment of prior parameter distributions and the definition of a semi-quantitative goodness of fit criteria which are essentially priors on the observable outputs. Monte Carlo simulations are used to generate samples from the posterior parameter space. This space is generally much more constrained than the prior space, but with a highly complex multivariate structure induced by the mathematical model. In applying the approach to a model of schistosomiasis transmission in a village in southwestern China, calibration of the model was found to be sensitive to the effective reproductive number, R _eff . This finding has implications both for computation time for the Monte Carlo analysis and for the specification of field data to efficiently calibrate the model for transmission control.