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Methods: Using archival death certificates from 1954 to 1961, this study quantified the age-specific seasonal patterns, excess-mortality rates, and transmissibility patterns of the 1957 pandemic in Maricopa County, Arizona. By applying cyclical Serfling linear regression models to weekly mortality rates, the excess-mortality rates due to respiratory and all-causes were estimated for each age group during the pandemic period. The reproduction number was quantified from weekly data using a simple growth rate method and generation intervals of 3 and 4 days. Local newspaper articles from The Arizona Republic were analyzed from 1957-1958.
Results: Excess-mortality rates varied between waves, age groups, and causes of death, but overall remained low. From October 1959-June 1960, the most severe wave of the pandemic, the absolute excess-mortality rate based on respiratory deaths per 10,000 population was 17.85 in the elderly (≥65 years). All other age groups had extremely low excess-mortality and the typical U-shaped age-pattern was absent. However, relative risk was greatest (3.61) among children and young adolescents (5-14 years) from October 1957-March 1958, based on incidence rates of respiratory deaths. Transmissibility was greatest during the same 1957-1958 period, when the mean reproduction number was 1.08-1.11, assuming 3 or 4 day generation intervals and exponential or fixed distributions.
Conclusions: Maricopa County largely avoided pandemic influenza from 1957-1961. Understanding this historical pandemic and the absence of high excess-mortality rates and transmissibility in Maricopa County may help public health officials prepare for and mitigate future outbreaks of influenza.
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Seroepidemiological studies before and after the epidemic wave of H1N1-2009 are useful for estimating population attack rates with a potential to validate early estimates of the reproduction number, R, in modeling studies.
Methodology/Principal Findings
Since the final epidemic size, the proportion of individuals in a population who become infected during an epidemic, is not the result of a binomial sampling process because infection events are not independent of each other, we propose the use of an asymptotic distribution of the final size to compute approximate 95% confidence intervals of the observed final size. This allows the comparison of the observed final sizes against predictions based on the modeling study (R = 1.15, 1.40 and 1.90), which also yields simple formulae for determining sample sizes for future seroepidemiological studies. We examine a total of eleven published seroepidemiological studies of H1N1-2009 that took place after observing the peak incidence in a number of countries. Observed seropositive proportions in six studies appear to be smaller than that predicted from R = 1.40; four of the six studies sampled serum less than one month after the reported peak incidence. The comparison of the observed final sizes against R = 1.15 and 1.90 reveals that all eleven studies appear not to be significantly deviating from the prediction with R = 1.15, but final sizes in nine studies indicate overestimation if the value R = 1.90 is used.
Conclusions
Sample sizes of published seroepidemiological studies were too small to assess the validity of model predictions except when R = 1.90 was used. We recommend the use of the proposed approach in determining the sample size of post-epidemic seroepidemiological studies, calculating the 95% confidence interval of observed final size, and conducting relevant hypothesis testing instead of the use of methods that rely on a binomial proportion.
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An understanding of the formation of spatial heterogeneity is important because spatial heterogeneity leads to functional consequences at the ecosystem scale; however, such an understanding is still limited. Particularly, research simultaneously considering both external variables and internal feedbacks (self-organization) is rare, partly because these two drivers are addressed under different methodological frameworks. In this dissertation, I show the prevalence of internal feedbacks and their interaction with heterogeneity in the preexisting template to form spatial pattern. I use a variety of techniques to account for both the top-down template effect and bottom-up self-organization. Spatial patterns of nutrients in stream surface water are influenced by the self-organized patch configuration originating from the internal feedbacks between nutrient concentration, biological patchiness, and the geomorphic template. Clumps of in-stream macrophyte are shaped by the spatial gradient of water permanence and local self-organization. Additionally, significant biological interactions among plant species also influence macrophyte distribution. The relative contributions of these drivers change in time, responding to the larger external environments or internal processes of ecosystem development. Hydrologic regime alters the effect of geomorphic template and self-organization on in-stream macrophyte distribution. The relative importance of niche vs. neutral processes in shaping biodiversity pattern is a function of hydrology: neutral processes are more important in either very high or very low discharge periods. For the spatial pattern of nutrients, as the ecosystem moves toward late succession and nitrogen becomes more limiting, the effect of self-organization intensifies. Changes in relative importance of different drivers directly affect ecosystem macroscopic properties, such as ecosystem resilience. Stronger internal feedbacks in average to wetter years are shown to increase ecosystem resistance to elevated external stress, and make the backward shifts (vegetation loss) much more gradual. But it causes increases in ecosystem hysteresis effect. Finally, I address the question whether functional consequences of spatial heterogeneity feed back to influence the processes from which spatial heterogeneity emerged through a conceptual review. Such feedbacks are not likely. Self-organized spatial patterning is a result of regular biological processes of organisms. Individual organisms do not benefit from such order. It is order for free, and for nothing.
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