Dynamic models of pest propagation and pest control

doi:10.1088/1674-1056/20/8/088201

中国物理B ›› 2011, Vol. 20 ›› Issue (8): 88201-088201.doi: 10.1088/1674-1056/20/8/088201

Dynamic models of pest propagation and pest control

尹铭, 林振权, 柯见洪

Department of Physics, Wenzhou University, Wenzhou 325035, China

收稿日期:2010-12-19 修回日期:2011-03-16 出版日期:2011-08-15 发布日期:2011-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104).

Dynamic models of pest propagation and pest control

Yin Ming(尹铭), Lin Zhen-Quan(林振权)^†, and Ke Jian-Hong(柯见洪)

Department of Physics, Wenzhou University, Wenzhou 325035, China

Received:2010-12-19 Revised:2011-03-16 Online:2011-08-15 Published:2011-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104).

摘要/Abstract

摘要： This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel I(k)=Ik and a fragmentation rate kernel L(i,j)=L, we find that the total number M₀^A(t) and the total mass of the pest aggregates M₁^A(t) both increase exponentially with time if L ≠ 0. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel J₁(k)=J₁k, it is found that only when I<J₁B₀ (B₀ is the concentration of catalyst aggregates) can the pests be killed off. Otherwise, the pest aggregates can survive. In the model of pest control with a natural enemy, a pest aggregate loses one of its individuals and the number of natural enemies increases by one. For this system, we find that no matter how many natural enemies there are at the beginning, pests will be eliminated by them eventually.

关键词: kinetic evolution behaviour, pest propagation, pest control, scaling law

Abstract: This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel $I(k)=Ik$ and a fragmentation rate kernel $L(i,j)=L$, we find that the total number $M^A_0(t)$ and the total mass of the pest aggregates $M^A_1(t)$ both increase exponentially with time if $L\neq0$. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel $J_1(k)=J_1k$, it is found that only when $I<J_1B_0$ ($B_0$ is the concentration of catalyst aggregates) can the pests be killed off. Otherwise, the pest aggregates can survive. In the model of pest control with a natural enemy, a pest aggregate loses one of its individuals and the number of natural enemies increases by one. For this system, we find that no matter how many natural enemies there are at the beginning, pests will be eliminated by them eventually.

Key words: kinetic evolution behaviour, pest propagation, pest control, scaling law

中图分类号: (Chemical kinetics and dynamics)

82.20.-w

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 68.43.Jk (Diffusion of adsorbates, kinetics of coarsening and aggregation) 89.75.Da (Systems obeying scaling laws)

尹铭, 林振权, 柯见洪. Dynamic models of pest propagation and pest control[J]. 中国物理B, 2011, 20(8): 88201-088201.

Yin Ming(尹铭), Lin Zhen-Quan(林振权), and Ke Jian-Hong(柯见洪). Dynamic models of pest propagation and pest control[J]. Chin. Phys. B, 2011, 20(8): 88201-088201.

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Dynamic models of pest propagation and pest control

Dynamic models of pest propagation and pest control

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