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

* 宿主-病原体系统的动态研究，例如传染病的传播或农业害虫的爆发，是许多生态和社会应用的核心部分。 这些系统通常显示病原体持续存在或疾病爆发的阈值。 数学上相似的系统出现在研究几个物种或种群内性状的共存时。 在结构化人群中，结构可能是由于影响传播的行为依赖于年龄、地点、健康状况或疫苗接种状况，这些阈值取决于结构的细节。 如果这个结构是静态的，那么我们可以考虑病原体持续存在的单一阈值。 更令人感兴趣的是结构是动态的情况下，无论是从突然的干扰，或通过逐渐变化积累随着时间的推移。 这种不断变化的种群结构可能会导致病原体入侵的机会，相反，我们可能有兴趣通过改变种群结构来控制病原体。 我建议研究各种应用程序，涉及宿主-病原体系统内不断变化的人口结构，并努力实现这样的系统的一般理论。 ** 我们将为几个特定的应用开发、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策略。 被囊动物正在加拿大爱德华王子岛蔓延，这种蔓延受到合适基质（包括贻贝租赁地和码头）空间格局的影响。 模型和观察表明，被囊动物的自然传播可以通过仔细监测和定期清理某些关键的潜在定居区来控制。 同样地，白蜡螟的扩散速度取决于寄主树木的空间排列和年龄。 通过开发和验证宿主选择模型来理解这种依赖性，将导致减缓昆虫传播的干预措施。更一般地说，宿主种群或栖息地的空间结构将影响病原体或害虫的传播速度。

***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.