A greater understanding of the rate at which emerging disease advances spatially has both ecological and applied significance. Analyzing the spread of vector-borne disease can be relatively complex when the vector's acquisition of a pathogen and subsequent transmission to a host occur in different life stages. A contemporary example is Lyme disease. A long-lived tick vector acquires infection during the larval blood meal and transmits it as a nymph. We present a reaction-diffusion model for the ecological dynamics governing the velocity of the current epidemic's spread. We find that the equilibrium density of infectious tick nymphs (hence the risk of human disease) can depend on density-independent survival interacting with biotic effects on the tick's stage structure. The local risk of infection reaches a maximum at an intermediate level of adult tick mortality and at an intermediate rate of juvenile tick attacks on mammalian hosts. If the juvenile tick attack rate is low, an increase generates both a greater density of infectious nymphs and an increased spatial velocity. However, if the juvenile attack rate is relatively high, nymph density may decline while the epidemic's velocity still increases. Velocities of simulated two-dimensional epidemics correlate with the model pathogen's basic reproductive number (R0), but calculating R0 involves parameters of both host infection dynamics and the vector's stage-structured dynamics.
Abstract. Lyme disease occurs commonly in New York State, but its geographic distribution is heterogeneous. Over each of nine consecutive years, incidence rates from 57 New York State counties were subjected to spatial autocorrelation analysis. Although the epidemic advanced during the study period, the analyses reveal a consistent pattern of spatial dependence. The correlation distance, the distance over which incidence rates covary positively, remained near 120 km over the nine years. A local spatial analysis around Westchester County, a major disease focus, indicated that the global correlation distance matched the extent of the most intense local clustering; statistically weaker clustering extended to 200 km from Westchester. Analyzing the spatial character of the epidemic may reveal the epizootic processes underlying patterns in human infection, and may help identify a spatial scale for regional control of disease.
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