Edge-based compartmental modelling of an SIR epidemic on a dual-layer static-dynamic multiplex network with tunable clustering

TL;DR

This paper develops an edge-based compartmental model for SIR epidemics on a dual-layer static-dynamic multiplex network with tunable clustering, capturing complex real-world contact heterogeneities.

Contribution

It introduces a novel dual-layer network model with tunable clustering and dynamic edges, deriving equations for epidemic spread and the basic reproduction number.

Findings

Model equations converge to existing models in limiting cases.

Validation shows good agreement with stochastic simulations.

Alterations in network parameters significantly affect epidemic dynamics.

Abstract

The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a dual-layer static-dynamic multiplex network. The static network layer affords tunable clustering and describes an individual's permanent community structure. The dynamic network layer describes the transient connections an individual makes with members of the wider population by imposing constant edge rewiring. We follow the edge-based compartmental modelling approach to derive equations describing the evolution of a susceptible - infected - recovered (SIR) epidemic spreading through this multiplex network of individuals. We derive the basic reproduction number, measuring the expected number of new infectious cases caused by a single infectious individual in an otherwise susceptible population. We validate model equations by showing convergence to pre-existing edge-based compartmental model equations in limiting cases and by comparison with stochastically simulated epidemics. We explore the effects of altering model parameters and multiplex network attributes on resultant epidemic dynamics. We validate the basic reproduction number by plotting its value against associated final epidemic sizes measured from simulation and predicted by model equations for a number of setups. Further, we explore the effect of varying individual model parameters on the basic reproduction number. We conclude with a discussion of the significance and interpretation of the model and its relation to existing research literature. We highlight intrinsic limitations and potential extensions of the present model and outline future research considerations, both experimental and theoretical.