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.
\[ di/dt=bsi-miy/(a+i)-ci,\qquad dy/dt=emi/(a+i)-d)y, \] They investigate the effects of impulsive immigration on the system and give conditions for extinction of the infected prey and permanence of the system.
Reviewer: Leonid Berezanski (Beer-Sheva)
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, stabilityReferences:
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