It follows that a threshold is λ max = 0, where λ max is the largest eigenvalue of the Jacobian matrix (or the largest real part if the eigenvalues are complex). However, for a system of n differential equations, this requires solving an nth order polynomial, which may be impossible. Furthermore, rearranging the condition λ max = 0 to produce a threshold R 0,J = 1 is not a unique process and does not always produce the average number of secondary infections.