Real-time growth rate for general stochastic SIR epidemics on unclustered networks

TL;DR

This paper develops a comprehensive theoretical framework to analyze the early exponential growth rate of epidemics on large, unclustered networks, incorporating various infectivity profiles and validating with simulations.

Contribution

It introduces a general theory for early epidemic growth on configuration model networks, including analytical, numerical, and Monte Carlo methods for diverse infectivity assumptions.

Findings

Explicit formulas for the Malthusian parameter under different assumptions.

Impact of network structure on epidemic growth dynamics quantified.

Benchmark results for validating large-scale epidemic simulations.

Abstract

Networks have become an important tool for infectious disease epidemiology. Most previous theoretical studies of transmission network models have either considered simple Markovian dynamics at the individual level, or have focused on the invasion threshold and final outcome of the epidemic. Here, we provide a general theory for early real-time behaviour of epidemics on large configuration model networks (i.e. static and locally unclustered), in particular focusing on the computation of the Malthusian parameter that describes the early exponential epidemic growth. Analytical, numerical and Monte-Carlo methods under a wide variety of Markovian and non-Markovian assumptions about the infectivity profile are presented. Numerous examples provide explicit quantification of the impact of the network structure on the temporal dynamics of the spread of infection and provide a benchmark for validating results of large scale simulations.