Although the SARS-CoV-19 virus spread rapidly around in world in early 2020, disease epidemics in different places evolved differently as the year progressed - and the state of the COVID-19 pandemic now varies significantly across different countries and territories. We have created a taxonomy of possible categories of disease dynamics, and used the evolution of reported COVID-19 cases relative to changes in disease control measures, together with total reported cases and deaths, to allocate most countries and territories among the possible categories. As of 31 January 2021, we find that the disease was (1) kept out or suppressed quickly through quarantines and testing & tracing in 39 countries with 29 million people, (2) suppressed on one or more occasions through control measures in 74 countries with 2.49 billion people, (3) spread slowly but not suppressed, with cases still increasing or just past a peak, in 31 countries with 1.45 billion people, (4) spread through the population, but slowed a result of control measures, leading to a "flattened curve" and fewer infections than if the epidemic were unmitigated, in 32 countries with 2.24 billion people, and (5) spread through the population with some but limited mitigation in 5 countries with 168 million people. In addition, several countries have experienced increases in cases after disease appeared to have finished spreading due to declining numbers of susceptible people. For some of these countries - for example Kenya, Pakistan and Afghanistan - the resurgences can be explained by the relaxation of control measures (and may have been enhanced by disease spread in population segments that experienced lower infection levels during the first waves). For other countries, the resurgences point to the effects of new virus variants with higher-transmissibility or immunity resistance - including most countries in Southern Africa (where the B.1.351 variant has been identified) and several countries in West Africa (maybe due to the B.1.351 or a different variant). These findings are consistent with mounting evidence of high infection rates in several low- and middle-income countries, both from seroprevalence studies and estimates of actual deaths from COVID-19 combined with estimates of expected mortality rates. We estimate that 1.3-3.0 billion people, or 17-39% of the global population, have been infected by SARS-CoV-2 to date, and that at least 5 million people have died from COVID-19 - much higher than reported cases and deaths. Disease control policies and vaccination strategies should be designed based on the state of the COVID-19 epidemic in the population - and consequently may need to be different in different countries.

The pinch-off of liquid drops from the end of a flat plate has been studied. Gas flows parallel to the plate with mean velocity v, and creates a wake at the plate end. The break-up process is found to be reproducible, with the number of satellites increasing with both increasing velocity and increasing mass density. The diameter of the main drop after detachment, d, at Weber numbers exceeding 5 is found to be given bywith C = (5.6 ± 0.3).10 -5 for ethanol and C = (2.9 ± 0.4).10 -5 for water. The diameter in quiescent gas, d v=0 , is easily predicted, and Re pl is the Reynolds number based on v and the thickness of the plate. Diameters at smaller Weber numbers are better predicted by a similar correlation in terms of the Weber number.Instantaneous acceleration and forces on a drop have been measured and analyzed. Hydrodynamic interaction between liquid and gas at high gas velocities at moments of strong interaction could be quantified with the usual expression for the drag force and a drag coefficient of about 1.3.

We have studied the evolution of COVID-19 in 12 low and middle income countries in which reported cases have peaked and declined rapidly in the past 2-3 months. In most of these countries the declines happened while control measures were consistent or even relaxing, and without signs of significant increases in cases that might indicate second waves. For the 12 countries we studied, the hypothesis that these countries have reached herd immunity warrants serious consideration. The Reed-Frost model, perhaps the simplest description for the evolution of cases in an epidemic, with only a few constant parameters, fits the observed case data remarkably well, and yields parameter values that are reasonable. The best-fitting curves suggest that the effective basic reproduction number in these countries ranged between 1.5 and 2.0, indicating that the curve was flattened in some countries but not suppressed by pushing the reproduction number below 1. The results suggest that between 51 and 80% of the population in these countries have been infected, and that between 0.05% and 2.50% of cases have been detected; values which are consistent with findings from serological and T-cell immunity studies. The infection rates, combined with data and estimates for deaths from COVID-19, allow us to estimate overall infection fatality rates for three of the countries. The values are lower than expected from reported infection fatality rates by age, based on data from several high-income countries, and the country population by age. COVID-19 may have a lower mortality risk in these three countries (to differing degrees in each country) than in high-income countries, due to differences in immune response, prior exposure to coronaviruses, disease characteristics or other factors. We find that the herd immunity hypothesis would not have fit the evolution of reported cases in several European countries, even just after the initial peaks; and subsequent resurgences of cases obviously prove that those countries have infection rates well below herd immunity levels. Our hypothesis that the 12 countries we studied have reached herd immunity should now be tested further, through serological and T cell immunity studies.

The pinch-off of drops from the downstream end of plates is an important re-entrainment mechanism of condensate in compact condensers. The present experimental study complements a previous one [1], in which ethanol and water drops were created for various mass densities and gas velocities at the downstream end of a plate that was fully wetted. In the present study, the effects of plate thickness and surface tension are studied with ethane drops detaching in ethane vapor flow at nearcritical conditions.If the thickness of the plate, D, is introduced as a governing length scale, the Bond number ∆ρ g D 2 / σ is found to indicate whether or not the plate thickness affects drop detachment. A theoretical prediction for the drop size after pinch-off in otherwise quiescent vapor is compared with experiments, which results in a correlation valid for high Bond numbers that are based on the drop diameter. The predictive method presented in the previous study took account of the effect of flow on detaching drop size. It has now been extended and generalized.The combined effect of plate thickness and high vapor velocity is found to lead to a bifurcation in the main drop size after detachment. This phenomenon is due to the facts that the position of the drop foot underneath the plate is unstable, and that detachment near the rim of a plate is essentially different from that from the center of the plate.