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

宿主-病原体系统的动力学研究，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。

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.