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A impulsive infective transmission SI model for pest control
Author(s) -
Zhang Hong,
Xu Weijian,
Chen Lansun
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.834
Subject(s) - floquet theory , pest analysis , mathematics , pest control , stability theory , integrated pest management , control theory (sociology) , stability (learning theory) , perturbation (astronomy) , comparison theorem , stability theorem , transmission (telecommunications) , control (management) , ecology , computer science , mathematical analysis , biology , physics , botany , telecommunications , artificial intelligence , quantum mechanics , nonlinear system , machine learning , cauchy distribution
Abstract In this paper, we propose a model with impulsive control of epidemics for pest management. By using Floquet's theorem, small‐amplitude perturbation skills and comparison theorem, we show that there exists a globally asymptotically stable susceptible pest‐eradication periodic solution when the release amount of infective pests is larger than some critical value. However, when the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial periodic susceptible pest‐eradication solution loses its stability. Further, the existence of a positive periodic endemic solution and other rich dynamics are also studied by numerical simulation. Therefore, we can use the amount of release of infective pests to control susceptible pests at desirable low levels. Copyright © 2007 John Wiley & Sons, Ltd.