where s(K) is the maximal real part of all eigenvalues of K, the Jacobian matrix evaluated at the disease-free equilibrium; K represents the change of status of infected individuals in different regions. The model has the property that the disease will be eradicated if T 0 < 1 but will persist if T 0 > 1. The paper stresses that this quantity should be understood only as a threshold condition for eradication; the model from which it derives does not quantify the transient dynamics, the timecourse of the infection or the prevalence of the disease. However, they showed that the simpler version of the model has the same eradication threshold (T 0 ) as more realistic, nonlinear models. The mathematical analysis results, together with a simple cost analysis, used the threshold nature of R 0 to show that eradication of AIDS is feasible, using the tools that we have currently to hand, but action needs to occur immediately and globally.