  This brief note highlights a largely overlooked similarity between the SIR
ordinary differential equations used for epidemics on the configuration model
of a Poisson network and the classical mass-action SIR equations introduced
nearly a century ago by Kermack and McKendrick. We demonstrate that the decline
pattern in susceptibles is identical for both models. This equivalence carries
practical implications: the susceptibles decay curve, often referred to as the
epidemic or incidence curve, is frequently used in empirical studies to
forecast epidemic dynamics. Although the curves for susceptibles align
perfectly, those for infections do differ. Yet, the infection curves tend to
converge and become almost indistinguishable in high-degree networks. In
summary, our analysis suggests that under many practical scenarios, it is
acceptable to use the classical SIR model as a close approximation to the
Poisson SIR network model.
