Forster Graeme A, Gilligan Christopher A
Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, United Kingdom.
Proc Natl Acad Sci U S A. 2007 Mar 20;104(12):4984-9. doi: 10.1073/pnas.0607900104. Epub 2007 Mar 13.
Using a contact-process model for the spread of crop disease over a regional scale, we examine the importance of the time scale for control with respect to the cost of the epidemic. The costs include the direct cost of treating infected sites as well as the indirect costs incurred through lost yield. We first use a mean-field approximation to derive analytical results for the optimal treatment regimes that minimize the total cost of the epidemic. We distinguish short- and long-term epidemics. and show that seasonal control (short time scale) requires extreme treatment, either treating all sites or none or switching between the two at some stage during the season. The optimal long-term strategy requires an intermediate level of control that results in near eradication of the disease. We also demonstrate the importance of incorporating economic constraints by deriving a critical relationship between the epidemiological and economic parameters that determine the qualitative nature of the optimal treatment strategy. The set of optimal strategies is summarized in a policy plot, which can be used to determine the nature of the optimal treatment regime given prior knowledge of the epidemiological and economic parameters. Finally, we test the robustness of the analytical results, derived from the mean-field approximation, on the spatially explicit contact process and demonstrate robustness to implementation errors and misestimation of crucial parameters.
利用作物病害在区域尺度上传播的接触过程模型，我们研究了控制时间尺度相对于疫情成本的重要性。成本包括治疗感染区域的直接成本以及因产量损失而产生的间接成本。我们首先使用平均场近似来推导使疫情总成本最小化的最优治疗方案的分析结果。我们区分短期和长期疫情，并表明季节性控制（短时间尺度）需要极端治疗，即要么治疗所有区域，要么都不治疗，或者在季节中的某个阶段在两者之间切换。最优的长期策略需要中等程度的控制，这会导致疾病几乎被根除。我们还通过推导决定最优治疗策略定性性质的流行病学和经济参数之间的关键关系，证明了纳入经济约束的重要性。最优策略集总结在一个策略图中，该图可用于在已知流行病学和经济参数的情况下确定最优治疗方案的性质。最后，我们在空间明确的接触过程上测试了从平均场近似得出的分析结果的稳健性，并证明了其对实施误差和关键参数错误估计的稳健性。
