An approximate diffusion process for environmental stochasticity in infectious disease transmission modelling.

Area of Science:

• Epidemiology and Biostatistics
• Mathematical Modeling of Infectious Diseases
• Computational Biology

Background:

• Accurate modeling of infectious disease transmission is challenged by non-stationarity, heterogeneity, and environmental factors like public behavior and seasonality.
• Current methods often struggle to mechanistically incorporate these extrinsic influences, necessitating advanced statistical techniques.
• Stochastic processes offer an elegant way to capture environmental variability in transmission dynamics.

Purpose of the Study:

• To develop a computationally efficient method for modeling infectious disease transmission dynamics that accounts for environmental stochasticity.
• To replace computationally expensive data-augmentation techniques with a simpler inference of expansion coefficients.
• To demonstrate the applicability of the proposed method across various epidemiological models and real-world scenarios.

Main Methods:

• Proposed modeling the time-varying transmission potential as an approximate diffusion process using a path-wise series expansion of Brownian motion.
• This approximation bypasses the need for 'missing data' imputation, a common bottleneck in stochastic modeling.
• Inference is achieved by estimating the expansion coefficients, a computationally less intensive task.

Main Results:

• The proposed method offers a computationally cheaper alternative to traditional data-augmentation techniques for stochastic inference.
• The approach successfully models infectious disease dynamics, as demonstrated through applications to influenza (SIR model), seasonality (SIRS model), and COVID-19 (multi-type SEIR model).
• This method effectively captures the influence of environmental factors on disease transmission.

Conclusions:

• The novel diffusion process approximation provides an efficient and effective framework for modeling infectious disease transmission dynamics.
• This approach enhances the ability to incorporate environmental stochasticity and changing transmission patterns into epidemiological models.
• The method holds significant potential for improving real-time forecasting and public health interventions for various infectious diseases.