Stochastic transmission in epidemiological models.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Stochastic Processes

Background:

• Empirical evidence indicates time-varying transmission coefficients in SEIR-like models, exhibiting random patterns, mean-reversion, and jumps.
• Traditional SEIR models often assume constant or smoothly varying transmission rates, which may not capture real-world disease dynamics.

Purpose of the Study:

• To propose and analyze a novel SEIR-like epidemiological model incorporating jump-diffusion stochastic processes for the transmission coefficient.
• To investigate the theoretical properties, including existence, uniqueness, and asymptotic behavior, of the proposed stochastic model.
• To evaluate the forecasting performance of the stochastic model against variations using real-world COVID-19 data.

Main Methods:

• Development of an SEIR-like model parameterized by jump-diffusion stochastic processes for the transmission coefficient.
• Theoretical analysis including proof of existence and uniqueness of solutions and study of asymptotic behavior.
• Comparative analysis of forecasting performance against model variations using reported COVID-19 infection data from New York City.

Main Results:

• The proposed jump-diffusion stochastic process effectively parameterizes the time-evolving transmission coefficient.
• Theoretical analysis confirmed the existence, uniqueness, and asymptotic properties of the model solutions.
• The model demonstrated fairly accurate forecasting of COVID-19 scenarios, even with its inherent simplicity.

Conclusions:

• Stochastic transmission, particularly incorporating random jumps and mean-reversion, significantly enhances the accuracy of epidemiological forecasts.
• The proposed jump-diffusion SEIR-like model offers a robust framework for understanding and predicting infectious disease dynamics.
• This approach provides valuable insights for public health strategies by improving the reliability of disease spread predictions.