Fig. 5

The effect of protection function \(b_2\) on stopping the epidemic for the set of parameters (39), where for \(\alpha _0=0.2\), we get \(\mathfrak {R}_0\approx 1.78\) and for \(\alpha _0=2.6\), we get \(\mathfrak {R}_0\approx 0.89\). Clearly, the situation forwards from the epidemic for \(\alpha _0=0.2\) to the extinction of disease for \(\alpha _0=2.6\).