Large-deviations of disease spreading dynamics with vaccination

Area of Science:

• Epidemiology
• Computational modeling
• Statistical physics

Background:

• Understanding disease dynamics is crucial for public health interventions.
• Contact network structure significantly influences epidemic spread.
• Vaccination strategies aim to mitigate disease transmission.

Purpose of the Study:

• To numerically simulate disease spread using a Susceptible-Infected-Recovered (SIR) model on small-world networks.
• To investigate the impact of random and high-degree vaccination strategies on the probability density function (pdf) of cumulative infections.
• To analyze the size-dependence of pdfs and typical/extreme infection courses using large-deviation theory.

Main Methods:

• Numerical simulation of SIR model on small-world contact networks.
• Application of a 1/t Wang-Landau algorithm for large-deviation analysis to obtain low-probability pdfs.
• Analysis of empirical rate functions to study size-dependence.
• Investigation of time series structures conditioned on cumulative infection values.

Main Results:

• The study quantifies the probability density function (pdf) of cumulative infections under different vaccination strategies.
• A large-deviation approach, specifically the 1/t Wang-Landau algorithm, was successfully applied to determine pdfs at extremely low probabilities (10^-80).
• Analysis of empirical rate functions revealed size-dependent behaviors within the large-deviation framework.
• Distinct time series structures were identified for typical, mild, and severe infection courses.

Conclusions:

• Both random and high-degree vaccination strategies significantly alter the probability distribution of cumulative infections.
• The 1/t Wang-Landau algorithm is effective for characterizing rare epidemic events.
• Understanding the relationship between network structure, vaccination strategy, and epidemic outcomes is essential for effective disease control.