Center for Advanced Systems Understanding (CASUS), Görlitz, Germany.
Department of Biology, University of Maryland College Park, College Park, MD, 20742, USA.
J Math Biol. 2022 May 5;84(6):48. doi: 10.1007/s00285-022-01742-2.
Throughout the vector-borne disease modeling literature, there exist two general frameworks for incorporating vector management strategies (e.g. area-wide adulticide spraying and larval source reduction campaigns) into vector population models, namely, the "implicit" and "explicit" control frameworks. The more simplistic "implicit" framework facilitates derivation of mathematically rigorous results on disease suppression and optimal control, but the biological connection of these results to real-world "explicit" control actions that could guide specific management actions is vague at best. Here, we formally define a biological and mathematical relationship between implicit and explicit control, and we provide mathematical expressions relating the strength of implicit control to management-relevant properties of explicit control for four common intervention strategies. These expressions allow the optimal control and basic reproduction number analyses typically utilized in implicit control modeling to be interpreted directly in terms of real-world actions and real-world monetary costs. Our methods reveal that only certain sub-classes of explicit control protocols are able to be represented as implicit controls, and that implicit control is a meaningful approximation of explicit control only when resonance-like synergistic effects between multiple explicit controls have negligible effects on population reduction. When non-negligible synergy exists, implicit control results, despite their mathematical tidiness, fail to provide accurate predictions regarding vector control and disease spread. Collectively, these elements build an effective bridge between analytically interesting and mathematically tractable implicit control and the challenging, action-oriented explicit control.
在虫媒传染病建模文献中，存在两种将媒介管理策略（如大面积成虫杀虫剂喷洒和幼虫源减少运动）纳入媒介种群模型的一般框架，即“隐式”和“显式”控制框架。更简单的“隐式”框架有利于推导出关于疾病抑制和最佳控制的严格数学结果，但这些结果与现实世界中可以指导具体管理行动的实际“显式”控制行动之间的生物学联系充其量是模糊的。在这里，我们正式定义了隐式和显式控制之间的生物学和数学关系，并为四种常见干预策略提供了将隐式控制的强度与显式控制的管理相关属性相关联的数学表达式。这些表达式允许在隐式控制建模中通常使用的最优控制和基本繁殖数分析直接根据实际行动和实际货币成本进行解释。我们的方法表明，只有某些特定类别的显式控制方案才能被表示为隐式控制，并且只有在多个显式控制之间的共振协同效应对种群减少的影响可以忽略不计时，隐式控制才是显式控制的有意义的近似。当存在不可忽略的协同作用时，尽管隐式控制结果在数学上很整洁，但它们无法对媒介控制和疾病传播提供准确的预测。总的来说，这些元素在有趣的分析和可处理的隐式控制与具有挑战性的、面向行动的显式控制之间建立了有效的桥梁。
