Department of Plant Sciences, University of Cambridge, Cambridge, United Kingdom.
PLoS One. 2012;7(8):e40941. doi: 10.1371/journal.pone.0040941. Epub 2012 Aug 10.
Defining appropriate policies for controlling the spread of fungal disease in agricultural landscapes requires appropriate theoretical models. Most existing models for the fungicidal control of plant diseases do not explicitly include the dynamics of the fungicide itself, nor do they consider the impact of infection occurring during the host growth phase. We introduce a modelling framework for fungicide application that allows us to consider how "explicit" modelling of fungicide dynamics affects the invasion and persistence of plant pathogens. Specifically, we show that "explicit" models exhibit bistability zones for values of the basic reproductive number (R0) less than one within which the invasion and persistence threshold depends on the initial infection levels. This is in contrast to classical models where invasion and persistence thresholds are solely dependent on R0. In addition if initial infection occurs during the growth phase then an additional "invasion zone" can exist for even smaller values of R0. Within this region the system will experience an epidemic that is not able to persist. We further show that ideal fungicides with high levels of effectiveness, low rates of application and low rates of decay lead to the existence of these bistability zones. The results are robust to the inclusion of demographic stochasticity.
定义控制农业景观中真菌病传播的适当政策需要适当的理论模型。大多数现有的植物病害杀菌剂控制模型没有明确包括杀菌剂本身的动态，也没有考虑到在宿主生长阶段发生感染的影响。我们引入了一种杀菌剂应用的建模框架，使我们能够考虑到杀菌剂动态的“显式”建模如何影响植物病原体的入侵和持续存在。具体来说，我们表明，对于基本繁殖数 (R0) 小于 1 的值，“显式”模型表现出双稳态区，其中入侵和持续存在的阈值取决于初始感染水平。这与经典模型形成对比，在经典模型中，入侵和持续存在的阈值仅取决于 R0。此外，如果初始感染发生在生长阶段，那么即使 R0 值更小，也可以存在额外的“入侵区”。在该区域内，系统将经历一场无法持续的流行病。我们进一步表明，具有高有效性、低应用率和低衰减率的理想杀菌剂会导致这些双稳态区的存在。包含人口随机性的结果是稳健的。
