Topics in Structured Host-Antagonist Interactions.

[摘要] In many complex systems, simple parts interact to produce the large scale pat- terns we observe. The structure of these interactions can have a dramatic effect on the behavior of the system, and many systems which have simple dynamics under the assumption of well-mixed interactions display vastly different behaviors when embedded on a discrete network or a continuous space. Often, the desynchronization of local dynamics, natural delays of information transfer, and higher dimensionality of the structured system can result in extending the duration of transient dynamics, enabling the stable persistence of heterogeneous solutions, and rendering optimal control challenging. This dissertation explores these phenomena in the context of the dynamics and control infectious diseases and agricultural pests. In particular, I focus on using compartmental models to investigate the effects of age-structured social mixing in the transmission of pertussis and spatially structured mixing and resource heterogeneity in plant-herbivore-parasitoid interactions.In chapter II, I investigated the potential of age-structure in social contacts to explain the resurgence of pertussis in highly vaccinated populations. and found that strong age-assortative mixing and a past history of vaccination coverage insufficient for eradication were sufficient to generate a slow resurgence in older age-groups. In chapter III, I searched for efficient age-targeted booster vaccination strategies using a genetic algorithm, under several simulated modes of vaccine failure. and found that the type of booster schedules most successful in reducing disease strongly depended on the mechanisms of failure.With an eye to finer scale targeting of vaccination, I derived and presented a multi-way spectral graph partitioning algorithm in chapter IV.In chapter V, I investigated the effects of spatial variation in plant quality on populations of herbivore hosts and their parasitoids, finding that variation in plant quality occurring at a fine spatial scale decreased overall herbivore populations.Finally, I explored the relationship between patterns of dispersal and abundance of a population in a one-dimensional space reproduces locally according to the logistic map and disperses with a Gaussian kernel and derived the conditions under which I expect certain classes of behavior to be stable.

[发布机构] University of Michigan

[效力级别] host-pathogen

[关键词] host-parasitoid;host-pathogen;compartmental model;coupled map lattice;integrodifference equations;network theory;Mathematics;Science;Applied and Interdisciplinary Mathematics