A Tutorial Model for the Role of Superspreaders in Pandemic Outbreaks

Popular media have spread widely the concepts behind SIR and related differential-equation models for pandemic spread, and in particular the role of the basic reproduction number R₀. However, deterministic models of this sort tend to underestimate the variability of outbreaks, in part because stochastic effects cannot be ignored. Specifically, a huge variability of the infectivity of COVID-infected individuals has been documented, yet the "overdispersion parameter" k quantifying it is hardly ever mentioned even in semipopular accounts. I will give a simple implementation of this idea suitable for an undergraduate-level project. A straightforward Gillespie simulation of the model showcases the dramatic effects of different k values in models with the same R₀, and motivates some public-policy conclusions. This material is publicly available as a module that can be introduced into any biological physics course.