Understanding the R0 of Epidemics

Resumo

A fundamental parameter in the epidemiology of infections is the so-called basic reproduction number,
R0, loosely defined as the number of new infections an infected individual will subsequently cause. This parameter
is central to traditional SIR models and plays a key role in dictating transmission dynamics. However, R0 is
typically ill-defined since it does not specify the time interval over which such secondary infections will occur.
In SIR models, R0 also has a different interpretation depending on the assumed kinetics of infection. In this
paper, we borrow concepts from a recent publication [1] to provide explicit expressions for R0 in terms of key
physio-chemical, environmental, and operational parameters, including the spatial population density, which is
fundamental to the health policy of spatial distancing. We then explore how R0 varies depending on the kinetics
assumed, motivated by the special case of interactions in enclosed environments for which the SIR model needs to
be reformulated. We consider, as a special case, super-spreader events, where we show that if one were to use the
SIR model, the effective value of R0 will be a significantly large, albeit decreasing, function of the duration of the
event, suggesting a delta-function-like behavior. We comment on a possible extension of the SIR model to capture
different infection kinetics by introducing an additional dimensionless number m, which represents the one-to-m
collision mechanism expected for the spread of infections in enclosed or high-density environments.