Parameter estimation of stochastic SEIR epidemic model using particle MCMC.

Area of Science:

• Epidemiology
• Computational Statistics
• Mathematical Biology

Background:

• Infectious disease dynamics are complex and require accurate parameter estimation for effective prediction.
• Stochastic Susceptible-Exposed-Infected-Recovered (SEIR) models are crucial for understanding disease spread.
• Existing parameter estimation methods can be computationally intensive and less efficient.

Purpose of the Study:

• To develop a novel Bayesian inference algorithm for parameter estimation in stochastic SEIR models.
• To enhance the efficiency of parameter estimation using a gradient-based proposal mechanism.
• To predict the extinction and persistence of infectious diseases.

Main Methods:

• Bayesian inference utilizing Gaussian processes for posterior distribution construction.
• Particle Markov Chain Monte Carlo (pMCMC) for efficient sampling.
• A novel gradient-based proposal mechanism for improved sampling efficiency.
• Application to real-world COVID-19 data from Iceland.

Main Results:

• The proposed algorithm demonstrates efficient convergence to the stationary distribution, even with multiple parameters.
• Numerical simulations confirm the algorithm's effectiveness in parameter estimation.
• Theoretical properties of the stochastic SEIR model are discussed.
• Successful application to COVID-19 data highlights practical utility.

Conclusions:

• The novel Bayesian algorithm offers an efficient and effective approach for parameter estimation in stochastic SEIR models.
• This method aids in predicting infectious disease dynamics, crucial for public health strategies.
• The algorithm's efficiency and applicability are validated through simulations and a real-world case study.