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Zbl 1166.92039
Sun, Shulin; Chen, Lansun
Permanence and complexity of the eco-epidemiological model with impulsive perturbation. (English)
[J] Int. J. Biomath. 1, No. 2, 121-132 (2008). ISSN 1793-5245; ISSN 1793-7159/e

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.
[Leonid Berezanski (Beer-Sheva)]

MSC 2000:: *92D40 Ecology
92D30 Epidemiology
34A37 Differential equations with impulses
34C25 Periodic solutions of ODE
34D05 Asymptotic stability of ODE

Keywords: permanence, stability

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