The approximately universal shapes of epidemic curves in the Susceptible-Exposed-Infectious-Recovered (SEIR) model.

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the approach of Harko et al. (Appl. Math. Comput. 236:184-194, 2014) is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The SEIR model curves have nearly the same shapes as the SIR ones, but with a stretch factor applied to them across time that is related to the ratio of the incubation to infectious periods. This finding implies an approximate characteristic timescale, scaled by this stretch factor, that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious.

Dynamic interventions to control COVID-19 pandemic: a multivariate prediction modelling study comparing 16 worldwide countries.

To date, non-pharmacological interventions (NPI) have been the mainstay for controlling the coronavirus disease-2019 (COVID-19) pandemic. While NPIs are effective in preventing health systems overload, these long-term measures are likely to have significant adverse economic consequences. Therefore, many countries are currently considering to lift the NPIs-increasing the likelihood of disease resurgence. In this regard, dynamic NPIs, with intervals of relaxed social distancing, may provide a more suitable alternative. However, the ideal frequency and duration of intermittent NPIs, and the ideal "break" when interventions can be temporarily relaxed, remain uncertain, especially in resource-poor settings. We employed a multivariate prediction model, based on up-to-date transmission and clinical parameters, to simulate outbreak trajectories in 16 countries, from diverse regions and economic categories. In each country, we then modelled the impacts on intensive care unit (ICU) admissions and deaths over an 18-month period for following scenarios: (1) no intervention, (2) consecutive cycles of mitigation measures followed by a relaxation period, and (3) consecutive cycles of suppression measures followed by a relaxation period. We defined these dynamic interventions based on reduction of the mean reproduction number during each cycle, assuming a basic reproduction number (R0) of 2.2 for no intervention, and subsequent effective reproduction numbers (R) of 0.8 and 0.5 for illustrative dynamic mitigation and suppression interventions, respectively. We found that dynamic cycles of 50-day mitigation followed by a 30-day relaxation reduced transmission, however, were unsuccessful in lowering ICU hospitalizations below manageable limits. By contrast, dynamic cycles of 50-day suppression followed by a 30-day relaxation kept the ICU demands below the national capacities. Additionally, we estimated that a significant number of new infections and deaths, especially in resource-poor countries, would be averted if these dynamic suppression measures were kept in place over an 18-month period. This multi-country analysis demonstrates that intermittent reductions of R below 1 through a potential combination of suppression interventions and relaxation can be an effective strategy for COVID-19 pandemic control. Such a "schedule" of social distancing might be particularly relevant to low-income countries, where a single, prolonged suppression intervention is unsustainable. Efficient implementation of dynamic suppression interventions, therefore, confers a pragmatic option to: (1) prevent critical care overload and deaths, (2) gain time to develop preventive and clinical measures, and (3) reduce economic hardship globally.

Atomic iron and titanium in the atmosphere of the exoplanet KELT-9b.

To constrain the formation history of an exoplanet, we need to know its chemical composition1-3. With an equilibrium temperature of about 4,050 kelvin4, the exoplanet KELT-9b (also known as HD 195689b) is an archetype of the class of ultrahot Jupiters that straddle the transition between stars and gas-giant exoplanets and are therefore useful for studying atmospheric chemistry. At these high temperatures, iron and several other transition metals are not sequestered in molecules or cloud particles and exist solely in their atomic forms5. However, despite being the most abundant transition metal in nature, iron has not hitherto been detected directly in an exoplanet because it is highly refractory. The high temperatures of KELT-9b imply that its atmosphere is a tightly constrained chemical system that is expected to be nearly in chemical equilibrium5 and cloud-free6,7, and it has been predicted that spectral lines of iron should be detectable in the visible range of wavelengths5. Here we report observations of neutral and singly ionized atomic iron (Fe and Fe+) and singly ionized atomic titanium (Ti+) in the atmosphere of KELT-9b. We identify these species using cross-correlation analysis8 of high-resolution spectra obtained as the exoplanet passed in front of its host star. Similar detections of metals in other ultrahot Jupiters will provide constraints for planetary formation theories.

Orbital misalignment of the Neptune-mass exoplanet GJ 436b with the spin of its cool star.

The angle between the spin of a star and the orbital planes of its planets traces the history of the planetary system. Exoplanets orbiting close to cool stars are expected to be on circular, aligned orbits because of strong tidal interactions with the stellar convective envelope. Spin-orbit alignment can be measured when the planet transits its star, but such ground-based spectroscopic measurements are challenging for cool, slowly rotating stars. Here we report the three-dimensional characterization of the trajectory of an exoplanet around an M dwarf star, derived by mapping the spectrum of the stellar photosphere along the chord transited by the planet. We find that the eccentric orbit of the Neptune-mass exoplanet GJ 436b is nearly perpendicular to the stellar equator. Both eccentricity and misalignment, surprising around a cool star, can result from dynamical interactions (via Kozai migration) with a yet-undetected outer companion. This inward migration of GJ 436b could have triggered the atmospheric escape that now sustains its giant exosphere.

A map of the large day-night temperature gradient of a super-Earth exoplanet.

Over the past decade, observations of giant exoplanets (Jupiter-size) have provided key insights into their atmospheres, but the properties of lower-mass exoplanets (sub-Neptune) remain largely unconstrained because of the challenges of observing small planets. Numerous efforts to observe the spectra of super-Earths--exoplanets with masses of one to ten times that of Earth--have so far revealed only featureless spectra. Here we report a longitudinal thermal brightness map of the nearby transiting super-Earth 55 Cancri e (refs 4, 5) revealing highly asymmetric dayside thermal emission and a strong day-night temperature contrast. Dedicated space-based monitoring of the planet in the infrared revealed a modulation of the thermal flux as 55 Cancri e revolves around its star in a tidally locked configuration. These observations reveal a hot spot that is located 41 ± 12 degrees east of the substellar point (the point at which incident light from the star is perpendicular to the surface of the planet). From the orbital phase curve, we also constrain the nightside brightness temperature of the planet to 1,380 ± 400 kelvin and the temperature of the warmest hemisphere (centred on the hot spot) to be about 1,300 kelvin hotter (2,700 ± 270 kelvin) at a wavelength of 4.5 micrometres, which indicates inefficient heat redistribution from the dayside to the nightside. Our observations are consistent with either an optically thick atmosphere with heat recirculation confined to the planetary dayside, or a planet devoid of atmosphere with low-viscosity magma flows at the surface.

An integral view of fast shocks around supernova 1006.

Supernova remnants are among the most spectacular examples of astrophysical pistons in our cosmic neighborhood. The gas expelled by the supernova explosion is launched with velocities ~1000 kilometers per second into the ambient, tenuous interstellar medium, producing shocks that excite hydrogen lines. We have used an optical integral-field spectrograph to obtain high-resolution spatial-spectral maps that allow us to study in detail the shocks in the northwestern rim of supernova 1006. The two-component Hα line is detected at 133 sky locations. Variations in the broad line widths and the broad-to-narrow line intensity ratios across tens of atomic mean free paths suggest the presence of suprathermal protons, the potential seed particles for generating high-energy cosmic rays.

Observing supernova 1987A with the refurbished Hubble Space Telescope.

Observations with the Hubble Space Telescope (HST), conducted since 1990, now offer an unprecedented glimpse into fast astrophysical shocks in the young remnant of supernova 1987A. Comparing observations taken in 2010 with the use of the refurbished instruments on HST with data taken in 2004, just before the Space Telescope Imaging Spectrograph failed, we find that the Lyα and Hα lines from shock emission continue to brighten, whereas their maximum velocities continue to decrease. We observe broad, blueshifted Lyα, which we attribute to resonant scattering of photons emitted from hot spots on the equatorial ring. We also detect N v λλ1239, 1243 angstrom line emission, but only to the red of Lyα. The profiles of the N v lines differ markedly from that of Hα, suggesting that the N4+ ions are scattered and accelerated by turbulent electromagnetic fields that isotropize the ions in the collisionless shock.