A Mathematical Model for the Spatial Spread and Biocontrol of the Asian Longhorned Beetle
A Mathematical Model for the Spatial Spread and Biocontrol of the Asian Longhorned Beetle
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DOI：
10.1137/130939304
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发表时间：
2014-06
期刊：
影响因子：
--
通讯作者：
S. A. Gourley;Y. Lou
中科院分区：
文献类型：
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作者：
S. A. Gourley;Y. Lou
我们提出了一个数学模型，四个耦合的延迟微分方程，控制亚洲天牛光肩星天牛由它的天敌之一，圆柱形树皮甲虫Dastarcus longulus或其他具有类似特征的捕食者。这是一个捕食者与猎物在幼虫而不是成虫水平上的相互作用，这产生了有趣的建模挑战。我们只指定A的出生率。并计算控制剂D的出生率。longulus的幼虫的消耗量。光肩星天牛的生物量和利用生物量转化的思想。我们证明了平衡点的稳定性和D. longulus，并对D. longulus或任何类似的控制剂，以有效地控制A.光翅亚目害虫如A.光肩星天牛会破坏它的栖息地，必须不断寻找新的寄主树木。尽管我们的模型没有明确的空间...
We propose a mathematical model, of four coupled delay differential equations, for control of the Asian longhorned beetle Anoplophora glabripennis by one of its natural predators, the cylindrical bark beetle Dastarcus longulus or another predator with similar characteristics. It is a predator prey interaction at the larval rather than adult level which creates interesting modeling challenges. We specify the birth rate only for A. glabripennis and calculate the birth rate of the control agent D. longulus by keeping track of its consumption of larval A. glabripennis biomass and using the idea of conversion of biomass. We prove rigorous results on the stability of equilibria and on persistence of D. longulus, and we make an assessment of the kinds of characteristics that enable D. longulus, or any similar control agent, to effectively control A. glabripennis. A pest such as A. glabripennis will destroy its habitat and must continually find new host trees. Even though our model does not have explicit spatial ...