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Chin. Phys. B, 2011, Vol. 20(8): 088201    DOI: 10.1088/1674-1056/20/8/088201

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
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.
Keywords:  kinetic evolution behaviour      pest propagation      pest control      scaling law  
Received:  19 December 2010      Revised:  16 March 2011      Accepted manuscript online: 
PACS:  82.20.-w (Chemical kinetics and dynamics)  
  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)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104).

Cite this article: 

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 2011 Chin. Phys. B 20 088201

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