Inference for partially observed epidemic dynamics guided by Kalman filtering techniques

Mercredi 22 avril 15:30-16:30 - Maud DELATTRE - AgroParisTech/INRAE

Résumé : Estimating the parameters governing epidemic dynamics, such as the transmission rate, from available data is a major issue in order to provide reliable predictions of these dynamics and of the impact of control strategies. In this context, several difficulties occur : all the components of the system dynamics are not observed, and data are available at discrete times with measurement errors. Diffusion processes with small diffusion coefficient are a convenient set-up for modelling epidemics
the small diffusion coefficient being related to the population size. To estimate the key epidemic parameters, we therefore propose to consider time-dependent diffusion processes on R^p satisfying a stochastic differential equation.
In practical applications on epidemic dynamics, it often occurs that some coordinates of the process are not observed and, when observed, measurement errors are systematically present. We are then concerned with the estimation of the parameters when the diffusion process is discretely observed with noise and with sampling step on a finite time interval and when some components of the process cannot be observed. We propose a procedure derived from Kalman filtering approaches to compute estimates of the parameters based on approximate likelihoods. Our approach is original because
it combines the framework of diffusions with small diffusion coefficient with approximate likelihood methods and Kalman filtering, the latter being little exploited for the inference of epidemic dynamics partially observed and with errors.
We carry out simulation studies to assess the performances of the proposed methods. Applications to real epidemic data are still in progress.

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