Gaussian process approximations for fast inference from infectious disease data.

Area of Science:

• Epidemiology
• Computational Biology
• Statistical Modeling

Background:

• Stochastic individual-based models (IBMs) are crucial for understanding epidemic dynamics.
• Approximating these complex models is essential for efficient inference and analysis.
• Gaussian processes offer a flexible approach for model approximation.

Purpose of the Study:

• To present a flexible framework for deriving and quantifying the accuracy of Gaussian process (GP) approximations for non-linear stochastic individual-based models (IBMs) of epidemics.
• To apply this framework to the SIR (Susceptible-Infectious-Recovered) and SEIR (Susceptible-Infectious-Exposed-Recovered) models.
• To demonstrate the utility of the framework for parameter inference and inferring unobserved epidemic processes.

Main Methods:

• Development of a Gaussian process approximation framework for stochastic IBMs.
• Application and validation of the framework using SIR and SEIR epidemic models.
• Implementation of maximum likelihood inference for model parameters using population estimates.

Main Results:

• The framework accurately quantifies the performance of Gaussian process approximations for epidemic models.
• Efficient maximum likelihood inference for model parameters is achieved using population data.
• Simultaneous inference of underlying parameters and unobserved epidemic processes is demonstrated.

Conclusions:

• The presented framework provides a robust method for approximating and analyzing epidemic models.
• Gaussian process approximations facilitate rapid and accurate parameter estimation in epidemiological studies.
• The approach enhances the understanding of epidemic dynamics by enabling inference of both observable and unobservable components.