In a recent paper by one of the authors and collaborators, motivated by the Olive Quick Decline Syndrome (OQDS) outbreak, which has been ongoing in Southern Italy since 2013, a simple epidemiological model describing this epidemic was presented. Beside the bacterium Xylella fastidiosa, the main players considered in the model are its insect vectors, Philaenus spumarius, and the host plants (olive trees and weeds) of the insects and of the bacterium. The model was based on a system of ordinary differential equations, the analysis of which provided interesting results about possible equilibria of the epidemic system and guidelines for its numerical simulations. Although the model presented there was mathematically rather simplified, its analysis has highlighted threshold parameters that could be the target of control strategies within an integrated pest management framework, not requiring the removal of the productive resource represented by the olive trees. Indeed, numerical simulations support the outcomes of the mathematical analysis, according to which the removal of a suitable amount of weed biomass (reservoir of Xylella fastidiosa) from olive orchards and surrounding areas resulted in the most efficient strategy to control the spread of the OQDS. In addition, as expected, the adoption of more resistant olive tree cultivars has been shown to be a good strategy, though less cost-effective, in controlling the pathogen. In this paper for a more realistic description and a clearer interpretation of the proposed control measures, a spatial structure of the epidemic system has been included, but, in order to keep mathematical technicalities to a minimum, only two players have been described in a dynamical way, trees and insects, while the weed biomass is taken to be a given quantity. The control measures have been introduced only on a subregion of the whole habitat, in order to contain costs of intervention. We show that such a practice can lead to the eradication of an epidemic outbreak. Numerical simulations confirm both the results of the previous paper and the theoretical results of the model with a spatial structure, though subject to regional control only.

在最近由一位作者和合作者撰写的一篇论文中，受到自 2013 年以来在意大利南部持续爆发的橄榄快速衰退综合症 (OQDS) 的启发，提出了一个简单的流行病学模型来描述这种流行病。除了细菌Xylella fastidiosa 之外，模型中考虑的主要参与者是其昆虫载体Philaenus spumarius，以及昆虫和细菌的寄主植物（橄榄树和杂草）。该模型基于常微分方程组，其分析提供了有关流行病系统可能平衡的有趣结果及其数值模拟的指导。尽管那里提出的模型在数学上相当简化，但其分析突出了阈值参数，这些参数可能是综合虫害管理框架内控制策略的目标，不需要移除以橄榄树为代表的生产资源。事实上，数值模拟支持数学分析的结果，根据该结果，去除适量的杂草生物量（难养木霉的水库）) 来自橄榄园和周边地区，这是控制 OQDS 传播的最有效策略。此外，正如预期的那样，采用更具抗性的橄榄树栽培品种已被证明是一种很好的策略，尽管成本效益较低，但在控制病原体方面。在本文中，为了更真实地描述和更清晰地解释所提议的控制措施，包括了流行病系统的空间结构，但是，为了将数学技术性保持在最低限度，仅在动态中描述了两个参与者方式，树木和昆虫，而杂草生物量被认为是给定的数量。控制措施仅针对整个栖息地的一个子区域实施，以控制干预成本。我们表明，这种做法可以消除流行病的爆发。数值模拟证实了前一篇论文的结果和具有空间结构的模型的理论结果，尽管仅受区域控制。