Buzby Megan, Neckels David, Antolin Michael F, Estep Donald
Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA.
J R Soc Interface. 2008 Sep 6;5(26):1099-107. doi: 10.1098/rsif.2007.1339.
Model sensitivity is a key to evaluation of mathematical models in ecology and evolution, especially in complex models with numerous parameters. In this paper, we use some recently developed methods for sensitivity analysis to study the parameter sensitivity of a model of vector-borne bubonic plague in a rodent population proposed by Keeling & Gilligan. The new sensitivity tools are based on a variational analysis involving the adjoint equation. The new approach provides a relatively inexpensive way to obtain derivative information about model output with respect to parameters. We use this approach to determine the sensitivity of a quantity of interest (the force of infection from rats and their fleas to humans) to various model parameters, determine a region over which linearization at a specific parameter reference point is valid, develop a global picture of the output surface, and search for maxima and minima in a given region in the parameter space.
模型敏感性是评估生态学和进化领域数学模型的关键，尤其是对于具有众多参数的复杂模型。在本文中，我们使用一些最近开发的敏感性分析方法，来研究由基林和吉利根提出的啮齿动物种群中媒介传播腺鼠疫模型的参数敏感性。新的敏感性工具基于涉及伴随方程的变分分析。这种新方法提供了一种相对廉价的方式来获取关于模型输出相对于参数的导数信息。我们使用这种方法来确定感兴趣的量（从大鼠及其跳蚤到人类的感染率）对各种模型参数的敏感性，确定在特定参数参考点处线性化有效的区域，绘制输出曲面的全局图，并在参数空间的给定区域中搜索最大值和最小值。
