Permanence and complexity of the eco-epidemiological model with impulsive perturbation. (English) Zbl 1166.92039

Sun, Shulin; Chen, Lansun

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)

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

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