COMORE Team, INRIA, Sophia Antipolis, France.
Bull Math Biol. 2010 Nov;72(8):2113-38. doi: 10.1007/s11538-010-9531-6. Epub 2010 Mar 24.
In this paper, a model is proposed for the biological control of a pest by its natural predator. The model incorporates a qualitative description of intrapredatory interference whereby predator density decreases the per capita predation efficiency and generalises the classical Beddington-DeAngelis formulation. A pair of coupled ordinary differential equations are used, augmented by a discrete component to depict the periodic release of a fixed number of predators into the system. This number is defined in terms of the rate of predator release and the frequency at which the releases are to be carried out. This formulation allows us to compare different biological control strategies in terms of release size and frequency that involve the same overall number of predators. The stability properties of the zero-pest solution are analysed. We obtain an upper bound on the interference strength (the biological condition) and a minimal bound on the predator release rate (the managerial condition) required to eradicate a pest population. We demonstrate that increasing the frequency of releases reduces this minimal rate and also increases the rate of convergence of the system to the zero-pest solution for a given release rate. Additionally, we show that other conclusions are to be expected if the interferences between predators have weaker or stronger effects than the generalised Beddington-DeAngelis formulation proposed in this paper.
本文提出了一种通过自然捕食者控制害虫的生物防治模型。该模型包含了捕食者之间的定性干扰描述，即捕食者密度降低了每头捕食者的捕食效率，并推广了经典的 Beddington-DeAngelis 公式。采用了一对耦合的常微分方程，并增加了一个离散分量来描述固定数量的捕食者周期性地释放到系统中。这个数量是根据捕食者释放的速度和释放的频率来定义的。这种表述方式允许我们根据涉及相同总数的捕食者的释放规模和频率来比较不同的生物防治策略。分析了零害虫解决方案的稳定性特性。我们得到了消除害虫种群所需的干扰强度（生物学条件）的上限和捕食者释放率（管理条件）的下限。我们证明，增加释放的频率会降低这个最小速率，同时也会增加系统收敛到给定释放速率的零害虫解决方案的速度。此外，如果捕食者之间的干扰比本文提出的广义 Beddington-DeAngelis 公式具有更强或更弱的效果，那么还可以预期到其他结论。
