Figure 1

Numerical simulations of system (17) which display the persistence of the system, when \(\mathcal{R}_{0}^{s}>1\) with \(\alpha=0.12\), \(a=0.08\), \(c=0.3\), \(r=1\), \(\mu=0.9\), \(\delta=0.39\), \(K=1\), \(\sigma _{1}=\sigma_{2}=0.001\), and \(\tau_{1}=\tau_{2}=0.1\). However, the right banner illustrates that the predator population dominates the prey population as time goes when α is increased to \(\alpha=1.2\)