Modeling correlated uncertainties in stochastic compartmental models.

Area of Science:

• Epidemiology
• Mathematical Biology
• Statistical Physics

Background:

• Compartmental models are crucial for understanding communicable disease dynamics.
• Uncertainty in contact rates is often modeled using stochastic fluctuations, typically white noise.
• White noise approximations can lead to underestimation of disease severity and unrealistic transitions.

Purpose of the Study:

• To develop a more accurate stochastic model for communicable disease contact rates.
• To investigate the impact of temporal correlations in social behavior on disease dynamics.
• To compare the performance of Ornstein-Uhlenbeck (OU) process-based models against white noise models using real-world pandemic data.

Main Methods:

• Modeled contact rates as a Markov process incorporating temporal correlations using the Ornstein-Uhlenbeck (OU) process.
• Applied the OU process to Susceptibles-Infected-Susceptibles (SIS) and Susceptibles-Exposed-Infected-Removed (SEIR) compartmental models.
• Validated models against US COVID-19 data from the Johns Hopkins University database.
• Derived analytical solutions for the SIS model's stationary probability density and used Monte Carlo simulations for the SEIR model.

Main Results:

• White noise models systematically underestimate disease spread due to unrealistic noise-induced transitions.
• The OU process effectively hinders unrealistic transitions, providing more robust disease spread estimations.
• Analytical solutions for the SIS model reveal asymptotic behavior influenced by reproduction number, noise intensity, and correlation time.
• SEIR model simulations using the OU process show improved accuracy compared to white noise models.

Conclusions:

• The Ornstein-Uhlenbeck process is a more appropriate model for stochastic contact rates in communicable disease dynamics than white noise.
• Accurate modeling of temporal correlations in social behavior is essential for reliable epidemiological predictions.
• This approach offers a framework for quantifying uncertain parameters in diverse biological systems and improving pandemic response strategies.