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Several types of infertility under the control of rodent population dynamics model

Author: ZhangMeiMing
Tutor: ZhangFengQin
School: University of North
Course: Applied Mathematics
Keywords: Infertility control Density-dependence Stability Second addi-tive compound matrix Competitive reproduction interference
CLC: S443
Type: Master's thesis
Year: 2011
Downloads: 28
Quote: 0
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Abstract


Presently, a lot of ?eld trials have been done on the infertility control of bandicoot.However, theoretical analysis for the dynamics of the bandicoot is scarce, especially for thecase with virus-vectored immunocontraception control. In this paper, under the assumptionthat the rodent density is not large enough to cause disasters, we use di?erential equationsto establish models on sterile technique. In detail:Firstly, we propose a stage-structured bandicoot model on female infertility control. Westudy the boundedness of solutions, analyze the local stability of the equilibrium points byapplying the Routh-Hurwitz criterion, demonstrate the dynamics with numerical simulation.Secondly, we build several models on bandicoot with virus-vectored immunocontracep-tion control. The ?rst one has no sex distinction but the other two have. For the ?rstmodel, we obtain the globally asymptotic stability. For the latter two models, we considerthe boundedness of solutions and the local stability of the equilibrium points, simulate thedynamics numerically. Based on the theoretical results, we suggest strategies on infertilitycontrol.Finally, we establish a model with both impulsive and virus-vectored immunocontracep-tion controls. First we prove the globally asymptotic stability of the bandicoot-eradicationperiodic solution by using the Floquet theory and impulsive comparison theorem. Then weobtain su?cient conditions on the permanence.

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CLC: > Agricultural Sciences > Plant Protection > Birds and animals harm and its prevention > Rodents
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