## Permanence and complexity of the eco-epidemiological model with impulsive perturbation.(English)Zbl 1166.92039

The authors study existence and local stability of periodic solutions for the system with impulses: $ds/dt=r(s+i)(1-(s+i)/k)-bsi,$
$di/dt=bsi-miy/(a+i)-ci,\qquad dy/dt=emi/(a+i)-d)y,$ They investigate the effects of impulsive immigration on the system and give conditions for extinction of the infected prey and permanence of the system.

### MSC:

 92D40 Ecology 92D30 Epidemiology 34A37 Ordinary differential equations with impulses 34C25 Periodic solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations

### Keywords:

permanence, stability
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### References:

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