then a 0 = 0 is a threshold if a j ≥ 0 for all j. More generally, the Routh-Hurwitz condition allows the coefficients to take on other signs, under certain restrictions, but the nonconstant coefficients all being positive is a sufficient condition. Another sufficient condition is that a j ≥ 0 under the constraint a 0 = 0 (so that the largest eigenvalue at a 0 = 0 is 0). This method is significantly easier to use than finding the largest eigenvalue, although verifying that a 0 = 0 necessarily corresponds to the largest eigenvalue can become complicated for some models. However, similar to the above, rearranging a 0 = 0 to produce R 0,C = 1 is not a unique process and does not always produce the average number of secondary infections.