Sun, Shulin; Chen, Lansun Permanence and complexity of the eco-epidemiological model with impulsive perturbation. (English) Zbl 1166.92039 Int. J. Biomath. 1, No. 2, 121-132 (2008). 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. Reviewer: Leonid Berezanski (Beer-Sheva) Cited in 13 Documents 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 PDF BibTeX XML Cite \textit{S. Sun} and \textit{L. Chen}, Int. J. Biomath. 1, No. 2, 121--132 (2008; Zbl 1166.92039) Full Text: DOI OpenURL References: [1] DOI: 10.1016/0022-247X(74)90267-4 · Zbl 0281.92012 [2] Anderson R. M., Infectious Diseases of Humans, Dynamics and Control (1991) [3] Bainov D. D., Impulsive Differential Eqations: Periodic Solutions and Applications (1993) [4] DOI: 10.1016/S0895-7177(97)00240-9 · Zbl 1185.34014 [5] DOI: 10.1016/S0362-546X(98)00126-6 · Zbl 0922.34036 [6] DOI: 10.1016/S0895-7177(02)00177-2 · Zbl 1025.92011 [7] DOI: 10.1016/S0960-0779(02)00114-5 · Zbl 1033.92026 [8] DOI: 10.1016/j.tpb.2006.06.007 · Zbl 1112.92053 [9] DOI: 10.1142/0906 [10] DOI: 10.1016/S0960-0779(02)00408-3 · Zbl 1085.34529 [11] DOI: 10.1093/imamci/15.3.269 · Zbl 0949.93069 [12] DOI: 10.1086/283092 [13] DOI: 10.1016/j.ecolmodel.2006.05.030 [14] DOI: 10.1016/S0025-5564(97)10016-5 · Zbl 0928.92027 [15] Shulgin B., Bull. Math. Biol. 60 pp 1– [16] DOI: 10.1007/s002850100097 · Zbl 1007.34031 [17] DOI: 10.1016/S0025-5564(01)00049-9 · Zbl 0978.92031 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.