Contagion: How to Model It and What R-nought (R0) Actually Means

The 2011 film Contagion, starring the spectacularly ill-fated Gwyneth Paltrow, is a dramatization of a viral pandemic starting in pretty analagous circumstances to the current Wuhan Coronavirus (2019-nCoV) outbreak. It’s a good film, and is a great introduction to the work of Centers for Disease Control (CDCs) that monitor the spread – the epidemiology – of the disease. There are two scenes where R-nought, or R0, are described:

Despite the blogger character in the clip describing the spread, using a R0 of 2, as being a problem you can do on a napkin, it takes a little more thinking about. He also seems a bit confused about R0, talking about growth from 2 to 4 to 16, to 256, to 65,536 each day. That’s not what R0 is – it is not a rate, and actually if the rate was 2, this would mean 2 to 4 to 8 to 16 to 32 etc., each time doubling the number. It is possible that he is thinking that there are two generations each per day, but that’s not whatR0 is.

So, on to the professionals:

The CDC epidemiologist in the clip is more on point (despite having sloppy notation with no subscripts). This is better – it shows the reproduction number for the infection – note again, this is not a rate – no time dimension is involved – it basically shows the number of cases on average each case generates.

This population modelling – so called SIR (Susceptible, Infected, Recovered) system dynamics modelling – is just one of several approaches that can be used to model contagion across a population. My recent paper ‘Spatial Transmission Models: A Taxonomy and Framework’ sets out a review of what they are and the advantages and disadvantages of each. In brief, we can model the population numbers, the individual agents that carry the virus, the network of contacts between infected individuals, or the regions or cells in which individuals are located (city districts, for example). The paper is available to read by clicking on the link here.

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