A class of pairwise models for epidemic dynamics on weighted networks

TL;DR

This paper develops pairwise models for SIS and SIR epidemic dynamics on weighted networks, analyzing how different weight distributions affect epidemic thresholds and basic reproductive ratios through theoretical and simulation approaches.

Contribution

It introduces a general pairwise modeling framework for weighted networks, considering both random and fixed weight distributions, and evaluates their impact on epidemic thresholds and R0.

Findings

Equal weights maximize R0 in both network models.

Random weight distribution leads to higher R0 than fixed weights.

Pairwise models closely match simulation results across parameters.

Abstract

In this paper, we study the $SIS$ (susceptible-infected-susceptible) and $SIR$ (susceptible-infected-removed) epidemic models on undirected, weighted networks by deriving pairwise-type approximate models coupled with individual-based network simulation. Two different types of theoretical/synthetic weighted network models are considered. Both models start from non-weighted networks with fixed topology followed by the allocation of link weights in either (i) random or (ii) fixed/deterministic way. The pairwise models are formulated for a general discrete distribution of weights, and these models are then used in conjunction with network simulation to evaluate the impact of different weight distributions on epidemic threshold and dynamics in general. For the $SIR$ dynamics, the basic reproductive ratio $R_0$ is computed, and we show that (i) for both network models $R_{0}$ is maximised if all weights are equal, and (ii) when the two models are equally matched, the networks with a random weight distribution give rise to a higher $R_0$ value. The models are also used to explore the agreement between the pairwise and simulation models for different parameter combinations.