Approximation of epidemic models by diffusion processes and their statistical inference.

Area of Science:

• Epidemiology
• Mathematical Biology
• Statistical Inference

Background:

• Markov jump processes are standard for modeling epidemics but challenging with incomplete data.
• Diffusion processes can approximate these models, especially with large populations.
• Existing inference methods for diffusion processes have limitations with time-dependent systems.

Purpose of the Study:

• To develop a novel framework for estimating epidemic model parameters using diffusion process statistics.
• To generalize existing approximation and inference results to non-autonomous and time-dependent systems.
• To provide a computationally efficient analytical method for parameter estimation.

Main Methods:

• Generalizing diffusion process approximation of density-dependent Markov jump processes to non-autonomous systems.
• Extending inference methods for discretely observed diffusion processes to time-dependent diffusions.
• Developing consistent and asymptotically Gaussian estimators, including a non-asymptotic correction term.

Main Results:

• Achieved consistent and asymptotically Gaussian estimates for key epidemic model parameters.
• Demonstrated good performance and robustness of estimators through simulations on SIR and SEIR models.
• Validated the method's effectiveness for realistic observation numbers and population sizes.

Conclusions:

• The proposed analytical framework offers an efficient alternative to simulation-intensive methods for epidemic data inference.
• The estimators exhibit favorable asymptotic properties and practical performance.
• This work lays the groundwork for a generic inference method applicable to incompletely observed epidemic data.