Figure 2

A computer simulation of the impulsive differential equations (1a)–(1f). The solution of the system is permanent. Here, \({a_{1}}=0.38\), \({a_{2}}=0.1\), \({a_{3}}=0.247\), \({b_{1}}=0.25\), \({b_{2}}=0.1\), \({b_{3}}=0.1\), \({k_{1}}=0.3\), \({k_{2}}=0.017\), \(\alpha =0.5\), \(\gamma =0.9\), \(\delta =0.2\), \(T=60\), \(x(0)=5\), \(y(0)=5\), and \(z(0)=5\) in which all conditions in Theorem 2 are satisfied