Novel moment closure approximations in stochastic epidemics

Area of Science:

• Mathematical modeling
• Epidemiology
• Computational statistics

Background:

• Moment closure approximations offer analytic insights into non-linear stochastic population models.
• Existing closure schemes struggle with highly skewed distributions and population extinctions.

Purpose of the Study:

• Introduce novel second- and third-order moment closure approximations.
• Address limitations of current methods for stochastic SI and SIS epidemic models.

Main Methods:

• Developed a beta-binomial distribution-based second-order approximation for the skewed SI model.
• Created a mixture distribution approximation for the SIS model, including a probability mass for extinction.
• Investigated third-order mixture approximations using log-normal and beta-binomial distributions.

Main Results:

• The beta-binomial approximation accurately captures skewness in the SI model.
• Mixture approximations successfully predict transient dynamics and extinction in the SIS model.
• New approximations outperform existing methods in capturing population dynamics.

Conclusions:

• Novel moment closure approximations provide accurate analytic predictions for stochastic epidemic models.
• These methods enhance understanding of disease dynamics, particularly in scenarios with high skewness or extinction risk.
• The developed approximations can be used for parameter estimation via likelihood functions.