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SARS-CoV-2 infections among vaccinated nursing home residents increased after the Omicron variant emerged. Data on booster dose effectiveness in this population are limited. During July 2021-March 2022, nursing home outbreaks in 11 US jurisdictions involving >3 infections within 14 days among residents who had received at least the primary COVID-19 vaccine(s) were monitored. Among 2,188 nursing homes, 1,247 outbreaks were reported in the periods of Delta (n = 356, 29%), mixed Delta/Omicron (n = 354, 28%), and Omicron (n = 536, 43%) predominance. During the Omicron-predominant period, the risk for infection within 14 days of an outbreak start was lower among boosted residents than among residents who had received the primary vaccine series alone (risk ratio [RR] 0.25, 95% CI 0.19-0.33). Once infected, boosted residents were at lower risk for all-cause hospitalization (RR 0.48, 95% CI 0.40-0.49) and death (RR 0.45, 95% CI 0.34-0.59) than primary vaccine-only residents.

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Previous reports of COVID-19 case, hospitalization, and death rates by vaccination status indicate that vaccine protection against infection, as well as serious COVID-19 illness for some groups, declined with the emergence of the B.1.617.2 (Delta) variant of SARS-CoV-2, the virus that causes COVID-19, and waning of vaccine-induced immunity (1-4). During August-November 2021, CDC recommended additional primary COVID-19 vaccine doses among immunocompromised persons and booster doses among persons aged ≥18 years (5). The SARS-CoV-2 B.1.1.529 (Omicron) variant emerged in the United States during December 2021 (6) and by December 25 accounted for 72% of sequenced lineages (7). To assess the impact of full vaccination with additional and booster doses (booster doses), case and death rates and incidence rate ratios (IRRs) were estimated among unvaccinated and fully vaccinated adults by receipt of booster doses during pre-Delta (April-May 2021), Delta emergence (June 2021), Delta predominance (July-November 2021), and Omicron emergence (December 2021) periods in the United States. During 2021, averaged weekly, age-standardized case IRRs among unvaccinated persons compared with fully vaccinated persons decreased from 13.9 pre-Delta to 8.7 as Delta emerged, and to 5.1 during the period of Delta predominance. During October-November, unvaccinated persons had 13.9 and 53.2 times the risks for infection and COVID-19-associated death, respectively, compared with fully vaccinated persons who received booster doses, and 4.0 and 12.7 times the risks compared with fully vaccinated persons without booster doses. When the Omicron variant emerged during December 2021, case IRRs decreased to 4.9 for fully vaccinated persons with booster doses and 2.8 for those without booster doses, relative to October-November 2021. The highest impact of booster doses against infection and death compared with full vaccination without booster doses was recorded among persons aged 50-64 and ≥65 years. Eligible persons should stay up to date with COVID-19 vaccinations.

In the field of computational fluid dynamics, lattice gas and lattice Boltzmann methods are powerful simulation methods derived from kinetic theory. These methods are renowned for their simplicity of implementation and computational speed. In recent years, lattice Boltzmann has risen in popularity for modeling hydrodynamic flows, diffusion, and more. However, a limitation of these methods is the lack of fluctuations due to the continuous nature of the model. Fluctuations arise from the discreteness found in nature, so including fluctuations presents difficulties. This dissertation explores new and novel ways of improving lattice Boltzmann and lattice gas methods.First, we present a new derivation for a fluctuating lattice Boltzmann method in a diffusive system. Fluctuations are absent lattice Boltzmann since they were derived as a Boltzmann average of discrete lattice gases. This lattice Boltzmann method is exact and includes density dependent noise which models fluctuations to high accuracy.Second, we extend diffusive lattice Boltzmann methods to apply to physical systems for diffusion through barrier coatings. We found that these models were able to reproduce the behavior from previous experiments and provided a simple tool for analyzing such systems. Higher order corrections to lattice Boltzmann methods are explored for extending the range for successful lattice Boltzmann implementations.Recently, the implementation of an integer lattice gas with a Monte Carlo collision operator by Blommel et al. provided a template for incorporating fluctuations through the discrete nature of lattice gases. A sampling collision operator for integer lattice gases by Seekins et al. was able to reproduce the fluctuating diffusion equation in the Boltzmann limit similar to the diffusive fluctuating lattice Boltzmann. However, lattice gases have a more limited range of transport coefficients than lattice Boltzmann methods, since lattice Boltzmann collisions are deterministic and allow for the implementation of over-relaxation and lattice gas collisions are probabilistic and overrelaxation in a lattice gas requires a probability greater than 1.The final section of this dissertation presents a simple method for including overrelaxation into an integer lattice gas using the sampling collision operator. It will be shown that this is possible through a permutation of occupation numbers.

Background SARS-CoV-2 Omicron variants have the potential to impact vaccine effectiveness and duration of vaccine-derived immunity. We analyzed U.S. multi-jurisdictional COVID-19 vaccine breakthrough surveillance data to examine potential waning of protection against SARS-CoV-2 infection for the Pfizer-BioNTech (BNT162b) primary vaccination series by age. Methods Weekly numbers of SARS-CoV-2 infections during January 16, 2022–May 28, 2022 were analyzed by age group from 22 U.S. jurisdictions that routinely linked COVID-19 case surveillance and immunization data. A life table approach incorporating line-listed and aggregated COVID-19 case datasets with vaccine administration and U.S. Census data was used to estimate hazard rates of SARS-CoV-2 infections, hazard rate ratios (HRR) and percent reductions in hazard rate comparing unvaccinated people to people vaccinated with a Pfizer-BioNTech primary series only, by age group and time since vaccination. Results The percent reduction in hazard rates for persons 2 weeks after vaccination with a Pfizer-BioNTech primary series compared with unvaccinated persons was lowest among children aged 5–11 years at 35.5% (95% CI: 33.3%, 37.6%) compared to the older age groups, which ranged from 68.7%–89.6%. By 19 weeks after vaccination, all age groups showed decreases in the percent reduction in the hazard rates compared with unvaccinated people; with the largest declines observed among those aged 5–11 and 12–17 years and more modest declines observed among those 18 years and older. Conclusions The decline in vaccine protection against SARS-CoV-2 infection observed in this study is consistent with other studies and demonstrates that national case surveillance data were useful for assessing early signals in age-specific waning of vaccine protection during the initial period of SARS-CoV-2 Omicron variant predominance. The potential for waning immunity during the Omicron period emphasizes the importance of continued monitoring and consideration of optimal timing and provision of booster doses in the future.

Among nursing home outbreaks of coronavirus disease 2019 (COVID-19) with ≥3 breakthrough infections when the predominant severe acute respiratory coronavirus virus 2 (SARS-CoV-2) variant circulating was the SARS-CoV-2 δ (delta) variant, fully vaccinated residents were 28% less likely to be infected than were unvaccinated residents. Once infected, they had approximately half the risk for all-cause hospitalization and all-cause death compared with unvaccinated infected residents.

One of the most striking draw-backs of standard lattice gas methods over lattice Boltzmann methods is a much more limited range of transport parameters that can be achieved. It is common for lattice Boltzmann methods to use over-relaxation to achieve arbitrarily small transport parameters in the hydrodynamic equations. Here, we show that it is possible to implement over-relaxation for integer lattice gases. For simplicity we focus here on lattice gases for the diffusion equation. We demonstrate that adding a flipping operation to lattice gases results in a multi-relaxation time lattice Boltzmann scheme with over-relaxation in the Boltzmann limit.

A expansion to fourth-order for lattice Boltzmann methods is presented. This expansion provides an easy model for finding fourth-order corrections to lattice Boltzmann methods for various physical systems. The fourth-order terms can give rise to improved results over traditional second-order lattice Boltzmann implementations. Although, this manuscript solely deals with fourth-order expansions, this expansion is easily extended to arbitrary order. We present examples of how this expansion is utilized and provide basic analysis to show how the fourth-order methods differ from lower order models for both diffusive systems and phase separating systems.