Thresholds and spread in structured host-pathogen systems

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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.