Epidemics on a stochastic model of temporal network

TL;DR

This paper introduces a stochastic model of temporal networks to study how epidemic spread dynamics are affected by heterogeneous versus homogeneous contact timing, revealing stage-dependent differences in infection growth rates.

Contribution

It presents a simple stochastic model of temporal networks that isolates the effect of contact timing heterogeneity on epidemic growth, without underlying network topology.

Findings

Heterogeneous contact timing accelerates early epidemic spread.

Homogeneous contact timing leads to slower initial growth but faster overall reach.

Epidemic growth dynamics depend on the stage of infection and contact pattern heterogeneity.

Abstract

Contacts between individuals serve as pathways where infections may propagate. These contact patterns can be represented by network structures. Static structures have been the common modeling paradigm but recent results suggest that temporal structures play different roles to regulate the spread of infections or infection-like dynamics. On temporal networks a vertex is active only at certain moments and inactive otherwise such that a contact is not continuously available. In several empirical networks, the time between two consecutive vertex-activation events typically follows heterogeneous activity (e.g. bursts). In this chapter, we present a simple and intuitive stochastic model of a temporal network and investigate how epidemics co-evolves with the temporal structures, focusing on the growth dynamics of the epidemics. The model assumes no underlying topological structure and is only constrained by the time between two consecutive events of vertex activation. The main observation is that the speed of the infection spread is different in case of heterogeneous and homogeneous temporal patterns but the differences depend on the stage of the epidemics. In comparison to the homogeneous scenario, the power law case results in a faster growth in the beginning but turns out to be slower after a certain time, taking several time steps to reach the whole network.