IJPAM: Volume 70, No. 7 (2011)

ANALYSIS OF AN ECO-EPIDEMICAL MODEL WITH
IVLEV FUNCTIONAL RESPONSE AND
IMPULSIVE PERTURBATION

Jianwen Jia$^1$, Bo Wu$^2$, Ruiqing Shi$^3$
$^{1,2,3}$School of Mathematics and Computer Science
Shanxi Normal University
Shanxi, Linfen, 041004, P.R. CHINA


Abstract. In this paper,an impulsive predator-prey model with disease in the predator is investigated for the purpose of integrated pest management. We consider an Ivlev-type functional response and assume that the periods of releasing natural enemies and spraying pesticide are different. We get the sufficient conditions for the local asymptotic stability of pest-eradication periodic solution by applying the Floquet theorem. We also get the sufficient condition for the permanence of the system, which means if the releasing amount of natural enemies and the spraying amount of pesticide satisfy the condition, then the prey and the predator will coexist.

Received: March 7, 2011

AMS Subject Classification: 34K45, 49N25

Key Words and Phrases: eco-epidemiological model, stability, impulsive, permanent, local asymptotic stability

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 7