The effect of heterogeniety on host-pathogen, plant-herbivore and disease-transmission systems

*研究宿主-病原体系统的动态，如传染病的传播或农业病虫害的爆发，是许多生态和社会应用的中心部分。这类系统通常显示病原体持续存在或疾病暴发的阈值。数学上类似的系统出现在研究几个物种或一个种群内特征的共存时。在结构化人群中，这种结构可能是由于影响传播的行为依赖于年龄、地点、健康或接种疫苗状态，这些阈值取决于结构的细节。如果这种结构是静态的，那么我们可以考虑病原体持久性的单一阈值。更有趣的是，结构是动态的，要么是从突然的扰动中变化的，要么是随着时间的积累而逐渐变化的。这种不断变化的种群结构可能会导致病原体入侵的机会，反过来，我们可能有兴趣通过改变种群结构来控制病原体。我建议在不断变化的种群结构中研究涉及宿主-病原体系统的各种应用，并努力建立此类系统的一般理论。*我们将针对几个具体应用开发、分析和测试模型。正在进行的研究项目包括生物入侵和传染病控制战略。被囊类在加拿大爱德华王子岛蔓延，这种扩散受到合适底物的空间格局的影响，包括贻贝租约和码头。模型和观察表明，通过仔细监测和定期清理某些关键的潜在聚居区，可以控制被囊藻的自然扩散。同样，翡翠白蜡虫的传播速度取决于寄主树木的空间排列和树龄。通过开发和验证宿主选择模型来理解这种依赖关系，将导致减缓昆虫传播的干预措施。更广泛地说，寄主种群或栖息地的空间结构将影响病原体或害虫的传播率。

***The study of the dynamics of host-pathogen systems, such as the spread of an infectious disease, or an outbreak of an agricultural pest, is a central part of many ecological and social applications. Such systems often show a threshold for pathogen persistence or disease-outbreak. Mathematically similar systems arise when studying co-existence of several species or of traits within a population. In a structured population, where the structure might be due to dependence of behaviours affecting transmission on age, location, health, or vaccination status, these thresholds depend on the details of the structure. If this structure is static, then we can consider a single threshold for pathogen persistence. Of more interest is the case where the structure is dynamic, either changing from a sudden disturbance, or by gradual changes accumulating over time. This changing population structure can lead to opportunities for pathogens to invade, and conversely, we may be interested in control of the pathogen by changing the population structure. I propose to study a variety of applications involving host-pathogen systems within a changing population structure and to work towards a general theory of such systems. ******We will develop, analyze and test models for several specific applications. Ongoing research projects include biological invasions and control strategies for infectious diseases. Tunicates are spreading throughout Prince Edward Island, Canada, and this spread is influenced by the spatial pattern of suitable substrate, including mussel leases and docks. Models and observations suggest that the natural spread of tunicates can be controlled by careful monitoring and regular cleaning of certain key potential settlement areas. Similarly, the spread rate of the Emerald Ash Borer depends on the spatial arrangement and age of host trees. Understanding this dependence by developing and validating a model for host selection will lead to interventions which slow the insect's spread. More generally, the spatial structure of a host population or habitat will influence the spread rate of a pathogen or pest.