Figure 1

The curves of \(c^{*}(k)\). Let \(F(S,I)=\beta S*I\), \(\alpha =1\), \(\beta =3\), \(S_{0}=1\), \(\gamma =1.5m\) and \(\tau =1\) be fixed. Additionally, \(d_{2}=4\) and \(d_{3}=7\). We can see that the minimal wave speed \(c^{*}\) of the first, second, and third models converges to the minimal wave speed of the local reaction case as \(k=\frac{1}{\rho }\rightarrow \infty \)