Anecdotally, we have found that most biologists believe that there is one and only one R 0 value for a given disease and, in order to verify an R 0 is correct, all that is required is to check that it has a threshold at 1. We have demonstrated here that R 0 is not a unique concept. Indeed, it is straightforward to construct simple variations that satisfy the threshold criterion at 1. Furthermore, since multiple methods calculate multiple thresholds, it follows that the vast majority of them cannot be the average number of secondary infections. However, the nonuniqueness is not the only problem associated with the concept, as we will demonstrate. Figure 4 : The changing face of R 0 . All expressions for R 0 were generated from the same model, using standard techniques. As the death rate varies, all have the property that if R 0 > 1 then an outbreak will occur, whereas if R 0 < 1, then the disease will be eradicated. However, aside from the common threshold at R 0 = 1, none of these expressions are equal to each other. The curve labelled "Jacobian" illustrates R 0,J , as given by (18) . The curve labelled "Adding and subtracting 9" illustrates the value R 0,9 as given by (20) . The curve labelled "Next generation" illustrates R 0,N , as given by (25) . The curve labelled "Constant term of the characteristic polynomial" illustrates R 0,C , as given by (19) . The curve labelled "Exponential" illustrates R 0,e , as given by (21) . 