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.


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
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