Second Quantization Approach to Stochastic Epidemic Models

TL;DR

This paper introduces a second quantization method using field theory to derive master equations for stochastic epidemic models, demonstrated on a hepatitis C virus model with dynamic population size.

Contribution

It applies a second quantization approach to epidemic modeling, providing a new framework for deriving population dynamics equations in stochastic models.

Findings

Derived closed master equations for multivariate epidemic models.

Applied the method to a hepatitis C virus epidemic model.

Showed how population size variability can be incorporated.

Abstract

We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of closed master equations describing the population dynamics of multivariate stochastic epidemic models. In order to do that, we introduce an SIR-inspired stochastic model for hepatitis C virus epidemic, from which we obtain the time evolution of the mean number of susceptible, infected, recovered and chronically infected individuals in a population whose total size is allowed to change.