Figure 4

Let us consider system (15) with \(n=2\) and the following local parameters values: \(\sigma _{j}^{E}=0.8\), \(\gamma _{j}^{E}=0.5\) and \(\beta _{j}=0.75\), \(j\in \{1,2\}\), so \(A=0.5\); \(\sigma _{1}^{I}=0.85\), \(\sigma _{2}^{I}=0.75\), \(\gamma _{1}^{I}=0.3\), and \(\gamma _{2}^{I}=0.15\). The shaded triangle contains the values of \(m^{E}_{1}\) and \(m^{I}_{1}\), stable equilibrium proportions of exposed and infectious individuals in patch 1, that ensure \(\overline{\mathcal{R}}_{0}<1\) in system (21) and, therefore, the disease eradication in system (15). The blue line corresponds to \(\overline{\mathcal{R}}_{0}=1\)