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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
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References:

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