The myth of R_0 and Ebola infectiousness

2014 October 17
by Daniel Lakeland

$$R_0$$ or (the basic reproduction number) is a parameter used in mathematical models of infection. It’s in theory the time integrated average number of people who will be infected by each new case. An $$R_0 < 1$$ suggests the infection will die out, and greater than 1 suggests it will spread. But $$R_0$$ is a tricky thing to calculate. Wikipedia gives references to how it’s calculated, and in fact it seems to be that these different methods of calculation give different results even with a given infection, and likely comparison across diseases is not indicative of something that can really be compared accurately.

But beyond the difficulty of actually calculating such a parameter, there’s the uncertainty involved when an epidemic moves from one environment, where you’ve got a lot of data (say West African Ebola), to another environment which has very different social dynamics and where you have very little data (Say Ebola in International Airline Travel). Bayesian methods can be used to help give a sense of the uncertainty in the parameter once you’ve got enough cases to do calculations… But I’m going to hope we will have to rely primarily on prior data in the Ebola outbreak. Unfortunately, we are going to have to put a wide prior on $$R_0$$ in the global case, because we just don’t know how highly mobile and interacting societies compare to West African villages in the spread of this disease.


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