Randomized migration processes between two epidemic centers

TL;DR

This paper models epidemic spread between two centers using stochastic Markov processes, deriving explicit formulas and approximations to analyze outbreak dynamics and moments in large populations.

Contribution

It introduces a Markov chain model for epidemic migration between centers, providing explicit formulas and a mean field approximation for large networks.

Findings

Explicit formulas for migration process distribution

Dependence of outbreak parameters on initial conditions

Effective approximation method for large populations

Abstract

Epidemic dynamics in a stochastic network of interacting epidemic centers is considered. The epidemic and migration processes are modelled by Markov's chains. Explicit formulas for probability distribution of the migration process are derived. Dependence of outbreak parameters on initial parameters, population, coupling parameters is examined analytically and numerically. The mean field approximation for a general migration process is derived. An approximate method allowing computation of statistical moments for networks with highly populated centres is proposed and tested numerically.