Using a latent Hawkes process for epidemiological modelling.

Area of Science:

• Epidemiology and Public Health
• Computational Biology
• Statistical Modeling

Background:

• Accurate modeling of infectious disease spread, like COVID-19, is crucial for public health interventions.
• Existing epidemic models often lack the ability to trace infection origins or accurately predict near-future cases.
• There is a need for advanced modeling techniques that incorporate temporal dynamics and individual-level infection pathways.

Purpose of the Study:

• To introduce a novel epidemic model for infectious disease spread, specifically COVID-19.
• To utilize a latent Hawkes process with temporal covariates to model infection dynamics.
• To enable the estimation of infection origins and the prediction of future case numbers.

Main Methods:

• Developed a novel epidemic model based on a latent Hawkes process with temporal covariates.
• Modeled reported COVID-19 cases using a probability distribution driven by the Hawkes process.
• Proposed a Kernel Density Particle Filter (KDPF) for inferring latent cases, reproduction number, and predicting new cases.

Main Results:

• The proposed Hawkes process model successfully captures infection transmission pathways.
• The Kernel Density Particle Filter (KDPF) demonstrated effective inference of latent cases and reproduction number.
• The model showed strong performance on synthetic data and real-world COVID-19 data from UK local authorities.
• Benchmarking confirmed the model's superiority over alternative approaches.

Conclusions:

• The novel latent Hawkes process model provides a robust framework for understanding and predicting infectious disease spread.
• The Kernel Density Particle Filter (KDPF) is an efficient and effective tool for real-time epidemic analysis.
• This approach enhances epidemic modeling by enabling the estimation of infection sources and improving short-term forecasting.