Figure 3

The time series of model (3) in the special case (12), with Figures (d), (e), and (f) representing (respectively) \(S(t)\), \(I(t)\), and \(R(t)\). The parameters of the model are \(b = 10\), \(\mu = 0.65 \), \(\beta = 0.2 \), \(c = 0.77 \), \(\gamma = 0.75 \), \(h=1.5\), \(d=0.4\), \(p=0.4\), \(\epsilon =0.2\), \(\xi = 10\), and \(a=0\). In this case \(\mathcal{R}_{0}=0.5969< 1\)