Towards uncertainty quantification and inference in the stochastic SIR epidemic model

Area of Science:

• Epidemiology
• Computational Biology
• Statistical Modeling

Background:

• Markov jump processes are crucial for modeling epidemic dynamics.
• Estimating parameters with partial observation data presents significant challenges.
• Stochastic SIR models are widely used but require robust inference methods.

Purpose of the Study:

• To develop a novel Bayesian inference method for Markov jump processes in epidemic modeling.
• To address parameter estimation challenges arising from partial state variable observations.
• To provide accurate estimations and predictions for epidemic scenarios.

Main Methods:

• Utilized van Kampen's inverse-size expansion to approximate state variable moments.
• Developed an approximate likelihood function using a Generic Discrete distribution.
• Implemented full Bayesian inference with informative priors.

Main Results:

• The novel method provides accurate parameter estimations for epidemic models.
• The approach is effective for both low and high count data scenarios.
• Successful application demonstrated on synthetic data and Dengue fever case studies.

Conclusions:

• The proposed Bayesian inference method offers a robust solution for epidemic modeling with partial observations.
• This technique enhances the predictive power of epidemiological models.
• The findings have implications for public health surveillance and intervention strategies.