# Equivalence between non-Markovian and Markovian dynamics in epidemic spreading processes

## TL;DR

This paper presents a formalism that reduces non-Markovian epidemic spreading processes on networks to equivalent Markovian models, capturing complex temporal effects with a single parameter, applicable across various network topologies.

## Contribution

The authors introduce a formalism that simplifies non-Markovian epidemic dynamics to Markovian processes using an effective infection rate, independent of network topology.

## Key findings

- Non-Markovian effects are captured by a single effective infection rate.
- The formalism is validated on different network types through simulations.
- An analytic approximation for the effective infection rate is provided.

## Abstract

A general formalism is introduced to allow the steady state of non-Markovian processes on networks to be reduced to equivalent Markovian processes on the same substrates. The example of an epidemic spreading process is considered in detail, where all the non-Markovian aspects are shown to be captured within a single parameter, the effective infection rate. Remarkably, this result is independent of the topology of the underlying network, as demonstrated by numerical simulations on two-dimensional lattices and various types of random networks. Furthermore, an analytic approximation for the effective infection rate is introduced, which enables the calculation of the critical point and of the critical exponents for the non-Markovian dynamics.