Computation of epidemic final size distributions

Area of Science:

• Epidemiology
• Computational Biology
• Mathematical Modeling

Background:

• Accurate computation of epidemic final size is crucial for public health planning.
• Existing methods can be computationally intensive or lack stability for complex models.
• Markovian models offer a framework for stochastic epidemic simulation.

Purpose of the Study:

• To develop a novel, efficient, and numerically stable methodology for computing epidemic final size distributions.
• To extend this methodology to various complex epidemic models.
• To provide a computationally transparent approach for analyzing epidemic dynamics.

Main Methods:

• Exploitation of a specific representation of the stochastic epidemic process.
• Derivation of computationally efficient and numerically stable algorithms.
• Adaptation of the method for SIR, phase-type infectious period, and waning immunity models.

Main Results:

• A new methodology for efficient computation of epidemic final size distributions.
• Demonstrated computational efficiency and numerical stability.
• Successful extension of the method to models beyond the basic SIR framework.

Conclusions:

• The developed methodology offers a significant advancement in calculating epidemic final sizes.
• The approach is broadly applicable to Markovian models requiring hitting probability calculations.
• This work provides a transparent and extendable framework for epidemic modeling.