Dynamic models of pest propagation and pest control

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

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) = I k

and a fragmentation rate kernel

L (i, j) = L

, we find that the total number

M_{0}^{A} (t)

and the total mass of the pest aggregates

M_{1}^{A} (t)

both increase exponentially with time if

L \neq 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

J_{1} (k) = J_{1} k

, it is found that only when

I < J_{1} B_{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

[1]	Chandrasekhar S 1943 Rev. Mod. Phys. 15 1
[2]	Friedlander S K 1977 Smoke, Dust and Haze: Fundamental of Aerosol Behaviour (New York: Wiley)
[3]	Drake R L 1972 Topics of Current Aerosol Research ed. Hidy G M and Brook J R (New York: Pergamon) p. 201
[4]	Pruppacher H and Klett J 1998 Microphysics of Cloudsand Precipitations (Dordrecht: Kluwer)
[5]	Flory P J 1941 J. Am. Chem. Soc. 63 3083
[6]	Stockmayer W H 1943 J. Chem. Phys. 11 45
[7]	Scott W T 1968 J. Atmos. Sci. 25 54
[8]	Ziff R M 1980 J. Stat. Phys. 23 241
[9]	Ben-Naim E and Krapivsky P L 2004 Phys. Rev. E 69 050901 (R)
[10]	Kessler D A and Shnerb N M 2007 Phys. Rev. E 76 010901 (R)
[11]	Wang H, Lin Z, Gao Y and Xu C 2009 Chin. Phys. B 18 3577
[12]	Schelling T 1971 J. Math. Soc. 1 16
[13]	Krapivsky P L, Rodgers G J and Redner S 2001 Phys. Rev. Lett. 86 5401
[14]	Krapivsky P L and Redner S 2001 Phys. Rev. E 63 066123
[15]	Albert R and Barabasi B A 2002 Rev. Mod. Phys. 74 47
[16]	Dorogovtsev S N and Mendes J F F 2002 Adv. Phys. 51 1079
[17]	Kang K and Redner S 1984 Phys. Rev. A 30 2833
[18]	Racz Z 1985 Phys. Rev. A 32 1129
[19]	Vicsek T and Family F 1984 Phys. Rev. Lett. 52 1669
[20]	Vicsek T, Meakin P and Family F 1985 Phys. Rev. A 32 1122
[21]	Family F, Meakin P and Deutch J M 1986 Phys. Rev. Lett. 57 727
[22]	Family F and Meakin P 1989 Phys. Rev. A 40 3836
[23]	Song S and Poland D 1992 Phys. Rev. A 46 5063
[24]	Krapivsky P L 1993 Physica A 198 135
[25]	Ben-Naim E and Krapivsky P L 1995 Phys. Rev. E 52 6066
[26]	Ke J and Lin Z 2002 Phys. Rev. E 65 051107
[27]	Ke J, Lin J and Lin Z 2003 Chin. Phys. Lett. 20 1390
[28]	Ke J, Chen X and Lin Z 2010 Chin. Phys. B 19 026802
[29]	Li J , Lin B and Huang Y 2008 Chin. Phys. B 17 473
[30]	Stanley M H R, Amaral L A N, Buldyrev S V, Havlin S, Leschhorn H, Maass P, Salinger M A and Stanley H E 1996 Nature 379 804
[31]	Stanley H E, Amaral L A N, Canning D, Gopikrishnan P, Lee Y and Liu Y 1999 Physica A 269 156
[32]	Fu D, Pammolli F, Buldyrev S V, Riccaboni M, Matia K, Yamasaki K and Stanley H E 2005 Proc. Natl. Acad. Sci. USA 102 18801
[33]	Plerou V, Amaral L A N, Gopikrishnan P, Meyer M and Stanley H E 1996 Nature 400 433
[34]	Pammolli F, Fu D, Buldyrev S V, Riccaboni1 M, Matia K, Yamasaki K and Stanley H E 2007 Eur. Phys. J. B 57 127
[35]	Buldyrev S V, Pammolli F, Riccaboni M, Yamasaki K, Fu D, Matia K and Stanley H E 2007 Eur. Phys. J. B 57 131
[36]	Ispolatov S, Krapivsky P L and Redner S 1998 Eur. Phys. J. B 2 267
[37]	Leyvraz F and Redner S 2002 Phys. Rev. Lett. 88 068301
[38]	Lin Z and Ke J 2003 Phys. Rev. E 67 031103
[39]	Lin Z, Ke J and Ye G 2005 Commun. Theor. Phys. 43 837
[40]	Lin Z, Ke J and Ye G 2006 Phys. Rev. E 74 046113
[41]	Wang H, Lin Z and Ke J 2007 Phys. Rev. E 75 046108
[42]	Ke J, Lin Z, Zheng Y, Chen X and Lu W 2006 Phys. Rev. Lett. 97 028301
[43]	Ben-Naim E and Redner S 2005 J. Stat. Mech. L11002
[44]	Ben-Naim E, Vazquez F and Redner S 2006 Eur. Phys. J. B 49 531
[45]	Yang S, Zhu S, Ke J and Lin Z 2008 Commun. Theor. Phys. 50 787
[46]	Chen D, Sun Y, Lin Z and Ke J 2009 Commun. Theor. Phys. 52 1139

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