These numbers allow a disease to be classified as mild (R I 0 < R 0 < R II 0 ) or severe (R III 0 < R 0 < R IV 0 ). Hosack et al. [46] noted that R 0 does not necessarily address the dynamics of epidemics in a model that has an endemic equilibrium. They used the concept of reactivity to derive a threshold index for epidemicity, E 0 , which gives the maximum number of new infections produced by an infective individual at a disease-free equilibrium. They also showed that the relative influence of parameters on E 0 and R 0 may differ and lead to different strategies for control.