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An approximate diffusion process for environmental stochasticity in infectious disease transmission modelling.

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De Angelis, Daniela 


Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe, mechanistically, changes in extrinsic environmental factors including public behaviour and seasonal fluctuations. An elegant approach to capturing environmental stochasticity is to model the force of infection as a stochastic process. However, inference in this context requires solving a computationally expensive "missing data" problem, using data-augmentation techniques. We propose to model the time-varying transmission-potential as an approximate diffusion process using a path-wise series expansion of Brownian motion. This approximation replaces the "missing data" imputation step with the inference of the expansion coefficients: a simpler and computationally cheaper task. We illustrate the merit of this approach through three examples: modelling influenza using a canonical SIR model, capturing seasonality using a SIRS model, and the modelling of COVID-19 pandemic using a multi-type SEIR model.


Acknowledgements: The authors acknowledge Gareth Roberts, Chris Jewell and Simon Spencer for the helpful discussions at a Bayes4Health meeting where an initial version of this work was presented. The authors also like to thank Angelos Alexopoulos and Colin Starr for discussions and feedback on some aspects of this work.


Humans, Pandemics, COVID-19, Stochastic Processes, Influenza, Human, Models, Biological

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PLoS Comput Biol

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Public Library of Science (PLoS)
Medical Research Council (MC UU 00002/11)