Non-Markovian SIR epidemic spreading model

TL;DR

This paper introduces a non-Markovian SIR epidemic model that incorporates realistic features like incubation and recovery periods, providing a more accurate framework for modeling diseases such as COVID-19.

Contribution

The paper develops a generalized non-Markovian SIR model with analytical epidemic thresholds, extending classical models to include realistic disease progression functions.

Findings

Model reduces to classical Markovian case with specific functions

Epidemic threshold derived analytically for arbitrary functions

Model successfully applied to Italy's COVID-19 first wave

Abstract

We introduce non-Markovian SIR epidemic spreading model inspired by the characteristics of the COVID-19, by considering discrete- and continuous-time versions. The incubation period, delayed infectiousness and the distribution of the recovery period are modeled with general functions. By taking corresponding choice of these functions, it is shown that the model reduces to the classical Markovian case. The epidemic threshold is analytically determined for arbitrary functions of infectivity and recovery and verified numerically. The relevance of the model is shown by modeling the first wave of the epidemic in Italy, in the spring, 2020.