Mixing Models and the Geometry of Epidemics
Open Access
- Author:
- Ferrari, Matthew J
- Graduate Program:
- Ecology
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 28, 2006
- Committee Members:
- Ottar N Bjornstad, Committee Chair/Co-Chair
Andrew George Stephenson, Committee Member
Peter John Hudson, Committee Member
David Russell Hunter, Committee Member - Keywords:
- epidemiology
basic reproductive ratio
plant pathogen
vector-borne disease
networks
vaccination - Abstract:
- The myriad interactions of many individuals generate broad scale patterns of mixing in populations. Here I consider, using both empirical and theoretical methods, how individual behavior generates heterogeneities in exposure to pathogens and the effect of that heterogeneity on epidemic dynamics at the population scale. The classic parameter for describing pathogen transmission at the population scale is the basic reproductive ratio, R0. Related to a number of epidemic properties R0 is a common metric for comparing transmission dynamics across populations. I develop a statistical method for estimating R0 from discretely reported incidence data. Using two insect borne plant disease systems I study the effect foraging selection by vectors pathogen exposure and the spatial dynamics of epidemic spread. I show that the transmission of the pollinator-borne smut fungus, Microbotryum violaceum, in populations of Silene latifolia is determined largely by preferential visitation by vectors to plants with many flowers. I develop a theoretical model for the spatial dynamics of Microbotryum spread by combining a spatial diffusion model for insect movement with an optimal foraging model for host selection. I also show that patterns of incidence of the bacterium, Erwinia tracheiphila, in populations of a wild gourd, Cucurbita pepo ssp. texana, with a mixed mating system are determined by selection of the beetle vectors for outcrossed rather than inbred hosts. I use explicit social network models to explore the effect of heterogeneities in transmission and exposure on population scale epidemic dynamics. I show that heterogeneities in exposure due to many network contacts predispose some individuals to infection resulting in a characteristic pattern of collapse in the active portion of the transmission network over the course of an epidemic. I provide analytical methods to calculate the expected change in network connectivity due to epidemic removal and show the effect of this structural change in the transmission network affects the potential of subsequent epidemics to invade. Finally, the scaling of transmission across populations of varying size has presented a challenge for models that assume homogenous mixing of individuals. I review the empirical evidence for the scaling of transmission and show that these patterns are in apparent conflict with the simple models of host mixing. I then show that explicit consideration of local heterogeneities due to host social organization can resolve the apparent paradox.