Epidemic reproduction numbers in spatial networks

TL;DR

This paper introduces a network-based framework to analyze how spatial structure influences epidemic reproduction numbers, revealing differences from traditional homogeneous mixing assumptions and emphasizing the importance of contact network structure.

Contribution

It provides a novel network-based approach to compare reproduction numbers in spatially structured populations versus homogeneous ones, highlighting the impact of network topology.

Findings

Reproduction numbers differ significantly between homogeneous and spatially structured populations.

In spatial networks, the effective reproduction number converges to unity over time.

Network structure influences the competition among infectious nodes, affecting epidemic dynamics.

Abstract

The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not hold in real-world populations where the contact patterns deviate from that assumption. In this paper, we present a network-based framework to compare reproduction numbers in populations with and without spatial structure, while other parameters of the disease remain fixed. Using this framework, we show that in homogeneously mixed populations, in the absence of external interventions, the effective reproduction number decreases exponentially as the susceptible population declines. In contrast, in spatially structured populations, the basic reproduction number is smaller, and the effective reproduction number initially decreases faster but eventually converges to unity. We show that the reproduction number is determined by the level of competition between infectious nodes, which is governed by the network structure. Our results suggest that without knowledge of the network structure, reproduction numbers may not be informative for parameterizing the contagiousness of the disease or predicting the behavior of epidemic spreading.