Optimizing vaccine distribution via mobile clinics: a case study on COVID-19 vaccine distribution to long-term care facilities.

BACKGROUND: People living in clustered communities with health comorbidities are highly vulnerable to COVID-19 infection. Rapid vaccination of vulnerable populations is critical to reducing fatalities and mitigating strain on healthcare systems. We present a case study on COVID-19 vaccine distribution via mobile vans to residents/staff of 47,907 long-term care facilities (LTCFs) across the United States that relied on algorithms to optimize vaccine distribution. METHODS: We developed a modeling framework for vaccine distribution to high-risk populations in a supply-constrained environment. Our framework decomposed this challenge as two separate problems: an assignment problem where we optimally mapped each LTCF to select CVS stores responsible for distributing vaccines; and a scheduling problem where we developed an algorithm to assign available resources efficiently. RESULTS: We assigned 1,214 retail stores as depots for vaccine distribution to LTCFs throughout the United States. Forty-one percent of matched depot-LTCF pairs were within 5 miles of a depot, 74% were within 20 miles, and only 8% mapped to depots farther than 50 miles away. Our two-step approach ensured that the first LTCF vaccination dose was distributed within 9 days after the program start date in 76% of states, and greater than 90% of doses were administered in the minimum amount of time. CONCLUSIONS: We demonstrate that algorithmic approaches are instrumental in maximizing vaccine distribution efficiency. Our learning and framework may be of use to other organizations, including communities where mobile clinics can be established to efficiently distribute vaccines and other healthcare resources in a variety of scenarios.

The same frequency of planets inside and outside open clusters of stars.

Most stars and their planets form in open clusters. Over 95 per cent of such clusters have stellar densities too low (less than a hundred stars per cubic parsec) to withstand internal and external dynamical stresses and fall apart within a few hundred million years. Older open clusters have survived by virtue of being richer and denser in stars (1,000 to 10,000 per cubic parsec) when they formed. Such clusters represent a stellar environment very different from the birthplace of the Sun and other planet-hosting field stars. So far more than 800 planets have been found around Sun-like stars in the field. The field planets are usually the size of Neptune or smaller. In contrast, only four planets have been found orbiting stars in open clusters, all with masses similar to or greater than that of Jupiter. Here we report observations of the transits of two Sun-like stars by planets smaller than Neptune in the billion-year-old open cluster NGC6811. This demonstrates that small planets can form and survive in a dense cluster environment, and implies that the frequency and properties of planets in open clusters are consistent with those of planets around field stars in the Galaxy.

Kepler-62: a five-planet system with planets of 1.4 and 1.6 Earth radii in the habitable zone.

We present the detection of five planets--Kepler-62b, c, d, e, and f--of size 1.31, 0.54, 1.95, 1.61 and 1.41 Earth radii (R⊕), orbiting a K2V star at periods of 5.7, 12.4, 18.2, 122.4, and 267.3 days, respectively. The outermost planets, Kepler-62e and -62f, are super-Earth-size (1.25 R⊕ < planet radius ≤ 2.0 R⊕) planets in the habitable zone of their host star, respectively receiving 1.2 ± 0.2 times and 0.41 ± 0.05 times the solar flux at Earth's orbit. Theoretical models of Kepler-62e and -62f for a stellar age of ~7 billion years suggest that both planets could be solid, either with a rocky composition or composed of mostly solid water in their bulk.

A sub-Mercury-sized exoplanet.

Since the discovery of the first exoplanets, it has been known that other planetary systems can look quite unlike our own. Until fairly recently, we have been able to probe only the upper range of the planet size distribution, and, since last year, to detect planets that are the size of Earth or somewhat smaller. Hitherto, no planets have been found that are smaller than those we see in the Solar System. Here we report a planet significantly smaller than Mercury. This tiny planet is the innermost of three that orbit the Sun-like host star, which we have designated Kepler-37. Owing to its extremely small size, similar to that of the Moon, and highly irradiated surface, the planet, Kepler-37b, is probably rocky with no atmosphere or water, similar to Mercury.

Two Earth-sized planets orbiting Kepler-20.

Since the discovery of the first extrasolar giant planets around Sun-like stars, evolving observational capabilities have brought us closer to the detection of true Earth analogues. The size of an exoplanet can be determined when it periodically passes in front of (transits) its parent star, causing a decrease in starlight proportional to its radius. The smallest exoplanet hitherto discovered has a radius 1.42 times that of the Earth's radius (R(⊕)), and hence has 2.9 times its volume. Here we report the discovery of two planets, one Earth-sized (1.03R(⊕)) and the other smaller than the Earth (0.87R(⊕)), orbiting the star Kepler-20, which is already known to host three other, larger, transiting planets. The gravitational pull of the new planets on the parent star is too small to measure with current instrumentation. We apply a statistical method to show that the likelihood of the planetary interpretation of the transit signals is more than three orders of magnitude larger than that of the alternative hypothesis that the signals result from an eclipsing binary star. Theoretical considerations imply that these planets are rocky, with a composition of iron and silicate. The outer planet could have developed a thick water vapour atmosphere.

A closely packed system of low-mass, low-density planets transiting Kepler-11.

When an extrasolar planet passes in front of (transits) its star, its radius can be measured from the decrease in starlight and its orbital period from the time between transits. Multiple planets transiting the same star reveal much more: period ratios determine stability and dynamics, mutual gravitational interactions reflect planet masses and orbital shapes, and the fraction of transiting planets observed as multiples has implications for the planarity of planetary systems. But few stars have more than one known transiting planet, and none has more than three. Here we report Kepler spacecraft observations of a single Sun-like star, which we call Kepler-11, that reveal six transiting planets, five with orbital periods between 10 and 47 days and a sixth planet with a longer period. The five inner planets are among the smallest for which mass and size have both been measured, and these measurements imply substantial envelopes of light gases. The degree of coplanarity and proximity of the planetary orbits imply energy dissipation near the end of planet formation.

Kepler-9: a system of multiple planets transiting a Sun-like star, confirmed by timing variations.

The Kepler spacecraft is monitoring more than 150,000 stars for evidence of planets transiting those stars. We report the detection of two Saturn-size planets that transit the same Sun-like star, based on 7 months of Kepler observations. Their 19.2- and 38.9-day periods are presently increasing and decreasing at respective average rates of 4 and 39 minutes per orbit; in addition, the transit times of the inner body display an alternating variation of smaller amplitude. These signatures are characteristic of gravitational interaction of two planets near a 2:1 orbital resonance. Six radial-velocity observations show that these two planets are the most massive objects orbiting close to the star and substantially improve the estimates of their masses. After removing the signal of the two confirmed giant planets, we identified an additional transiting super-Earth-size planet candidate with a period of 1.6 days.