Kamgang and Sallet [44] used the special structure of Metzler matrices (real, square matrices with nonnegative off-diagonal entries) to define T 0 , an analytical threshold condition. T 0 is a function of the parameters of the system such that if T 0 < 1, the disease-free equilibrium is locally asymptotically stable, and if T 0 > 1, the disease-free equilibrium is unstable. T 0 has an association with R 0 , although it is a stronger condition; however, it has no direct biological interpretation. The algorithm for deriving T 0 , although highly mathematical in nature, allows computation of a threshold for high-dimensional epidemic models.