Title: Qualitative analysis of a mathematical model for Xylella fastidiosa epidemics Show Chinese title

Title: Xylella fastidiosa流行病学数学模型的定性分析

Abstract: In Southern Italy, since 2013, there has been an ongoing Olive Quick Decline Syndrome (OQDS) outbreak, due to the bacterium Xylella fastidiosa. In a couple of previous papers, the authors have proposed a mathematical approach for identifying possible control strategies for eliminating or at least reduce the economic impact of such event. The main players involved in OQDS are represented by the insect vector, Philaenus spumarius, its host plants (olive trees and weeds) and the bacterium, X. fastidiosa. A basic mathematical model has been expressed in terms of a system of ordinary differential equations; a preliminary analysis already provided interesting results about possible control strategies within an integrated pest management framework, not requiring the removal of the productive resource represented by the olive trees. The same conjectures have been later confirmed by analyzing the impact of possible spatial heterogeneities on controlling a X. fastidiosa epidemic. These encouraging facts have stimulated a more detailed and rigorous mathematical analysis of the same system, as presented in this paper. A clear picture of the possible steady states (equilibria) and their stability properties has been outlined, within a variety of different parameter scenarios, for the original spatially homogeneous ecosystem. The results obtained here confirm, in a mathematically rigorous way, what had been conjectured in the previous papers, i.e. that the removal of a suitable amount of weed biomass (reservoir of the juvenile stages of the insect vector of X. fastidiosa from olive orchards and surrounding areas is the most acceptable 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. Show Chinese abstract

Abstract: 在意大利南部，自2013年以来，由于细菌Xylella fastidiosa，持续爆发了橄榄快速衰退综合症（OQDS）。在几篇以前的论文中，作者提出了一种数学方法，用于识别可能的控制策略，以消除或至少减少此类事件的经济影响。OQDS的主要参与者包括昆虫媒介Philaenus spumarius、其寄主植物（橄榄树和杂草）以及细菌X. fastidiosa。一种基本的数学模型已用常微分方程组的形式表达；初步分析已经提供了关于在综合害虫管理框架内可能的控制策略的有趣结果，而不需要移除由橄榄树代表的生产资源。后来通过分析可能的空间异质性对控制X. fastidiosa流行病的影响，证实了这些假设。这些令人鼓舞的事实促使了对同一系统的更详细和严格的数学分析，如本文所展示的。在原始空间同质生态系统中，针对各种不同的参数情景，已经概述了可能的稳态（平衡点）及其稳定性特性。在这里获得的结果以数学上严格的方式确认了之前论文中的假设，即移除一定量的杂草生物量（X. fastidiosa昆虫媒介幼虫的储库）从橄榄园和周围地区是控制OQDS传播最可接受的策略。此外，如预期的那样，采用更抗性的橄榄树品种已被证明是一种良好的策略，尽管成本效益较低，在控制病原体方面。