Department of Mathematics, Illinois State University Normal, IL, USA.
Front Neurosci. 2013 Aug 8;7:141. doi: 10.3389/fnins.2013.00141. eCollection 2013.
Song and Xiang (2006) developed an impulsive differential equations model for a two-prey one-predator model with stage structure for the predator. They demonstrate the conditions on the impulsive period for which a globally asymptotically stable pest-eradication periodic solution exists, as well as conditions on the impulsive period for which the prey species is permanently maintained under an economically acceptable threshold. We extend their model by including stage structure for both predator and prey as well as by adding stochastic elements in the birth rate of the prey. As in Song and Xiang (2006), we find the conditions under which a globally asymptotically stable pest eradication periodic solution exists. In addition, we numerically show the relationship between the stochastically varying birth rate of the prey and the necessary efficacy of the pesticide for which the probability of eradication of the prey species is above 90%. This is significant because the model recognizes varying environmental and climatic conditions which affect the resources needed for pest eradication.
宋和向（2006 年）为一个具有阶段结构的两食一捕食者模型开发了一个脉冲微分方程模型。他们证明了在脉冲周期上存在全局渐近稳定的害虫灭绝周期解的条件，以及在脉冲周期上存在经济上可接受的阈值下，猎物物种永久维持的条件。我们通过包括捕食者和猎物的阶段结构以及在猎物的出生率中添加随机元素来扩展他们的模型。与宋和向（2006 年）一样，我们找到了存在全局渐近稳定的害虫灭绝周期解的条件。此外，我们通过数值显示了猎物的随机变化出生率与杀虫剂的必要功效之间的关系，对于这种杀虫剂，消灭猎物物种的概率高于 90%。这是很重要的，因为该模型认识到了影响害虫灭绝所需资源的变化的环境和气候条件。
