Epidemic threshold and control in a dynamic network

TL;DR

This paper develops a dynamic network model for SIS epidemics, using an improved compartmental framework to accurately predict epidemic thresholds and analyze the effects of network evolution on disease spread.

Contribution

It introduces a novel ODE-based approach for SIS epidemics on dynamic networks, capturing epidemic thresholds and timescale effects more accurately than previous models.

Findings

ODE model agrees well with stochastic simulations

Accurate epidemic threshold prediction across parameters

Identifies static and homogeneous mixing limits

Abstract

In this paper we present a model describing Susceptible-Infected-Susceptible (SIS) type epidemics spreading on a dynamic contact network with random link activation and deletion where link ac- tivation can be locally constrained. We use and adapt a improved effective degree compartmental modelling framework recently proposed by Lindquist et al. [J. Lindquist et al., J. Math Biol. 62, 2, 143 (2010)] and Marceau et al. [V. Marceau et al., Phys. Rev. E 82, 036116 (2010)]. The resulting set of ordinary differential equations (ODEs) is solved numerically and results are compared to those obtained using individual-based stochastic network simulation. We show that the ODEs display excellent agreement with simulation for the evolution of both the disease and the network, and is able to accurately capture the epidemic threshold for a wide range of parameters. We also present an analytical R0 calculation for the dynamic network model and show that depending on the relative timescales of the network evolution and disease transmission two limiting cases are recovered: (i) the static network case when network evolution is slow and (ii) homogeneous random mixing when the network evolution is rapid. We also use our threshold calculation to highlight the dangers of relying on local stability analysis when predicting epidemic outbreaks on evolving networks.