the basic reproduction number R0 is a key concept, the public health cornerstone used to
determine the minimum effort required to eliminate an infection when the model doesn't exhibit the existence of multiple endemic equilibria. However, in the last two decades several
models exhibited bistable endemic states, where backward bifurcation and hysteresis phenomena are shown to exist. In such cases, R0 < 1 is a necessary but not sufficient condition for eliminating the infection. For a model with backward bifurcation, it has been shown in that the ratio R0=R0 could be interpreted as a reproduction number and so, reducing
this ratio to below one ensures an effective control of the infection. Thus, if we solve the
inequality Rc;2=Rc;2 < 1 in terms of the probability p, we get