Background The duration of protection afforded by coronavirus disease 2019 (Covid-19) vaccines in the United States is unclear. Whether the increase in postvaccination infections during the summer of 2021 was caused by declining immunity over time, the emergence of the B.1.617.2 (delta) variant, or both is unknown. Methods We extracted data regarding Covid-19–related vaccination and outcomes during a 9-month period (December 11, 2020, to September 8, 2021) for approximately 10.6 million North Carolina residents by linking data from the North Carolina Covid-19 Surveillance System and the Covid-19 Vaccine Management System. We used a Cox regression model to estimate the effectiveness of the BNT162b2 (Pfizer–BioNTech), mRNA-1273 (Moderna), and Ad26.COV2.S (Johnson & Johnson–Janssen) vaccines in reducing the current risks of Covid-19, hospitalization, and death, as a function of time elapsed since vaccination. Results For the two-dose regimens of messenger RNA (mRNA) vaccines BNT162b2 (30 μg per dose) and mRNA-1273 (100 μg per dose), vaccine effectiveness against Covid-19 was 94.5% (95% confidence interval [CI], 94.1 to 94.9) and 95.9% (95% CI, 95.5 to 96.2), respectively, at 2 months after the first dose and decreased to 66.6% (95% CI, 65.2 to 67.8) and 80.3% (95% CI, 79.3 to 81.2), respectively, at 7 months. Among early recipients of BNT162b2 and mRNA-1273, effectiveness decreased by approximately 15 and 10 percentage points, respectively, from mid-June to mid-July, when the delta variant became dominant. For the one-dose regimen of Ad26.COV2.S (5×10 10 viral particles), effectiveness against Covid-19 was 74.8% (95% CI, 72.5 to 76.9) at 1 month and decreased to 59.4% (95% CI, 57.2 to 61.5) at 5 months. All three vaccines maintained better effectiveness in preventing hospitalization and death than in preventing infection over time, although the two mRNA vaccines provided higher levels of protection than Ad26.COV2.S. Conclusions All three Covid-19 vaccines had durable effectiveness in reducing the risks of hospitalization and death. Waning protection against infection over time was due to both declining immunity and the emergence of the delta variant. (Funded by a Dennis Gillings Distinguished Professorship and the National Institutes of Health.)

We develop a behavior-based anomaly detection method that detects network anomalies by comparing the current network traffic against a baseline distribution. The Maximum Entropy technique provides a flexible and fast approach to estimate the baseline distribution, which also gives the network administrator a multi-dimensional view of the network traffic. By computing a measure related to the relative entropy of the network traffic under observation with respect to the baseline distribution, we are able to distinguish anomalies that change the traffic either abruptly or slowly. In addition, our method provides information revealing the type of the anomaly detected. It requires a constant memory and a computation time proportional to the traffic rate.

No abstract

No abstract

ImportanceData about the association of COVID-19 vaccination and prior SARS-CoV-2 infection with risk of SARS-CoV-2 infection and severe COVID-19 outcomes may guide prevention strategies.ObjectiveTo estimate the time-varying association of primary and booster COVID-19 vaccination and prior SARS-CoV-2 infection with subsequent SARS-CoV-2 infection, hospitalization, and death.Design, Setting, and ParticipantsCohort study of 10.6 million residents in North Carolina from March 2, 2020, through June 3, 2022.ExposuresCOVID-19 primary vaccine series and boosters and prior SARS-CoV-2 infection.Main Outcomes and MeasuresRate ratio (RR) of SARS-CoV-2 infection and hazard ratio (HR) of COVID-19–related hospitalization and death.ResultsThe median age among the 10.6 million participants was 39 years; 51.3% were female, 71.5% were White, and 9.9% were Hispanic. As of June 3, 2022, 67% of participants had been vaccinated. There were 2 771 364 SARS-CoV-2 infections, with a hospitalization rate of 6.3% and mortality rate of 1.4%. The adjusted RR of the primary vaccine series compared with being unvaccinated against infection became 0.53 (95% CI, 0.52-0.53) for BNT162b2, 0.52 (95% CI, 0.51-0.53) for mRNA-1273, and 0.51 (95% CI, 0.50-0.53) for Ad26.COV2.S 10 months after the first dose, but the adjusted HR for hospitalization remained at 0.29 (95% CI, 0.24-0.35) for BNT162b2, 0.27 (95% CI, 0.23-0.32) for mRNA-1273, and 0.35 (95% CI, 0.29-0.42) for Ad26.COV2.S and the adjusted HR of death remained at 0.23 (95% CI, 0.17-0.29) for BNT162b2, 0.15 (95% CI, 0.11-0.20) for mRNA-1273, and 0.24 (95% CI, 0.19-0.31) for Ad26.COV2.S. For the BNT162b2 primary series, boosting in December 2021 with BNT162b2 had the adjusted RR relative to primary series of 0.39 (95% CI, 0.38-0.40) and boosting with mRNA-1273 had the adjusted RR of 0.32 (95% CI, 0.30-0.34) against infection after 1 month and boosting with BNT162b2 had the adjusted RR of 0.84 (95% CI, 0.82-0.86) and boosting with mRNA-1273 had the adjusted RR of 0.60 (95% CI, 0.57-0.62) after 3 months. Among all participants, the adjusted RR of Omicron infection compared with no prior infection was estimated at 0.23 (95% CI, 0.22-0.24) against infection, and the adjusted HRs were 0.10 (95% CI, 0.07-0.14) against hospitalization and 0.11 (95% CI, 0.08-0.15) against death after 4 months.Conclusions and RelevanceReceipt of primary COVID-19 vaccine series compared with being unvaccinated, receipt of boosters compared with primary vaccination, and prior infection compared with no prior infection were all significantly associated with lower risk of SARS-CoV-2 infection (including Omicron) and resulting hospitalization and death. The associated protection waned over time, especially against infection.