The Number Systems Tower

For high school and college instructors and students, this paper connects number systems, field axioms, and polynomials. It also considers other properties such as cardinality, density, subset, and superset relationships. Additional aspects of this paper include gains and losses through sequences of number systems. The paper ends with a great number of activities for classroom use

Community-Based Population Health Research: A Report from the Field

This Forum, “Community-Based Population Health Research: A Report from the Field” highlights the work of 1889 Jefferson Center for Population Health and Mainline Center for Population Health Research. Leaders from both research centers provide an overview of the history and purpose of the centers and describe accomplishments and current initiatives. Objectives: Describe two innovative models for population health research centers List three benefits of partnering with a University when establishing a population health center Characterize challenges associated with the development of community-engaged and health system embedded, population health research centers Presentation: 49:1

Working together to make information accessible: Principles of university-community engagement through the Detroit Housing Counseling and Homeownership Project

The Center for Equitable Family and Community Well-Being is committed to community-engaged research. In this paper, we explain what that means in practice through our work on the Detroit Housing Counseling and Homeownership Project. Together with community partners, our project team made important information about the state of mortgage financing and homeownership accessible to stakeholders and residents. The project was successful, in particular, for observing four key principles of community-engaged research: (1) equity in the design and distribution of power in the partnership; (2) leverage partners’ strengths; (3) transparency and regular communication; and (4) focus on sustainability and accessibility.http://deepblue.lib.umich.edu/bitstream/2027.42/176357/1/detroit-housing-practice-paper.pdfSEL

Risk of COVID-19 after natural infection or vaccinationResearch in context

Background: While vaccines have established utility against COVID-19, phase 3 efficacy studies have generally not comprehensively evaluated protection provided by previous infection or hybrid immunity (previous infection plus vaccination). Individual patient data from US government-supported harmonized vaccine trials provide an unprecedented sample population to address this issue. We characterized the protective efficacy of previous SARS-CoV-2 infection and hybrid immunity against COVID-19 early in the pandemic over three-to six-month follow-up and compared with vaccine-associated protection. Methods: In this post-hoc cross-protocol analysis of the Moderna, AstraZeneca, Janssen, and Novavax COVID-19 vaccine clinical trials, we allocated participants into four groups based on previous-infection status at enrolment and treatment: no previous infection/placebo; previous infection/placebo; no previous infection/vaccine; and previous infection/vaccine. The main outcome was RT-PCR-confirmed COVID-19 >7–15 days (per original protocols) after final study injection. We calculated crude and adjusted efficacy measures. Findings: Previous infection/placebo participants had a 92% decreased risk of future COVID-19 compared to no previous infection/placebo participants (overall hazard ratio [HR] ratio: 0.08; 95% CI: 0.05–0.13). Among single-dose Janssen participants, hybrid immunity conferred greater protection than vaccine alone (HR: 0.03; 95% CI: 0.01–0.10). Too few infections were observed to draw statistical inferences comparing hybrid immunity to vaccine alone for other trials. Vaccination, previous infection, and hybrid immunity all provided near-complete protection against severe disease. Interpretation: Previous infection, any hybrid immunity, and two-dose vaccination all provided substantial protection against symptomatic and severe COVID-19 through the early Delta period. Thus, as a surrogate for natural infection, vaccination remains the safest approach to protection. Funding: National Institutes of Health

Risk of COVID-19 after natural infection or vaccinationResearch in context

Summary: Background: While vaccines have established utility against COVID-19, phase 3 efficacy studies have generally not comprehensively evaluated protection provided by previous infection or hybrid immunity (previous infection plus vaccination). Individual patient data from US government-supported harmonized vaccine trials provide an unprecedented sample population to address this issue. We characterized the protective efficacy of previous SARS-CoV-2 infection and hybrid immunity against COVID-19 early in the pandemic over three-to six-month follow-up and compared with vaccine-associated protection. Methods: In this post-hoc cross-protocol analysis of the Moderna, AstraZeneca, Janssen, and Novavax COVID-19 vaccine clinical trials, we allocated participants into four groups based on previous-infection status at enrolment and treatment: no previous infection/placebo; previous infection/placebo; no previous infection/vaccine; and previous infection/vaccine. The main outcome was RT-PCR-confirmed COVID-19 >7–15 days (per original protocols) after final study injection. We calculated crude and adjusted efficacy measures. Findings: Previous infection/placebo participants had a 92% decreased risk of future COVID-19 compared to no previous infection/placebo participants (overall hazard ratio [HR] ratio: 0.08; 95% CI: 0.05–0.13). Among single-dose Janssen participants, hybrid immunity conferred greater protection than vaccine alone (HR: 0.03; 95% CI: 0.01–0.10). Too few infections were observed to draw statistical inferences comparing hybrid immunity to vaccine alone for other trials. Vaccination, previous infection, and hybrid immunity all provided near-complete protection against severe disease. Interpretation: Previous infection, any hybrid immunity, and two-dose vaccination all provided substantial protection against symptomatic and severe COVID-19 through the early Delta period. Thus, as a surrogate for natural infection, vaccination remains the safest approach to protection. Funding: National Institutes of Health