Note on ‘Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-Free Networks’

In a recent paper entitled ‘Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-Free Networks’ by Huang et al., the authors attempted to establish a key characteristic of epidemic dynamics in a scale-free network when properly accounting for the cost of transmitting the infection at each node and the resources available for transmission to that node. The main input parameter is the effective rate of spreading the infection, i.e. the instantaneous rate at which the infection is spread to an uninfected node via a single link to an infected node. The primary result is the existence of a positive critical threshold for the infection-spreading rate at or below which the epidemic dies out and above which the epidemic is spread through the network and ultimately reaches a steady-state non-vanishing condition. Some flaws in the authors’ proof of this result are discussed, and an alternative derivation is provided that sheds additional light on the transient and steady-state behavior of the system. The alternative derivation may be adapted to the analysis of other scale-free networks with different features.