Trajectories of COVID-19: A longitudinal analysis of many nations and subnational regions.

The COVID-19 pandemic is the first to be rapidly and sequentially measured by nation-wide PCR community testing for the presence of the viral RNA at a global scale. We take advantage of the novel "natural experiment" where diverse nations and major subnational regions implemented various policies including social distancing and vaccination at different times with different levels of stringency and adherence. Initially, case numbers expand exponentially with doubling times of ~1-2 weeks. In the nations where interventions were not implemented or perhaps lees effectual, case numbers increased exponentially but then stabilized around 102-to-103 new infections (per km2 built-up area per day). Dynamics under effective interventions were perturbed and infections decayed to low levels. They rebounded concomitantly with the lifting of social distancing policies or pharmaceutical efficacy decline, converging on a stable equilibrium setpoint. Here we deploy a mathematical model which captures this V-shape behavior, incorporating a direct measure of intervention efficacy. Importantly, it allows the derivation of a maximal estimate for the basic reproductive number Ro (mean 1.6-1.8). We were able to test this approach by comparing the approximated "herd immunity" to the vaccination coverage observed that corresponded to rapid declines in community infections during 2021. The estimates reported here agree with the observed phenomena. Moreover, the decay (0.4-0.5) and rebound rates (0.2-0.3) were similar throughout the pandemic and among all the nations and regions studied. Finally, a longitudinal analysis comparing multiple national and regional results provides insights on the underlying epidemiology of SARS-CoV-2 and intervention efficacy, as well as evidence for the existence of an endemic steady state of COVID-19.

Moore's Law revisited through Intel chip density.

Gordon Moore famously observed that the number of transistors in state-of-the-art integrated circuits (units per chip) increases exponentially, doubling every 12-24 months. Analysts have debated whether simple exponential growth describes the dynamics of computer processor evolution. We note that the increase encompasses two related phenomena, integration of larger numbers of transistors and transistor miniaturization. Growth in the number of transistors per unit area, or chip density, allows examination of the evolution with a single measure. Density of Intel processors between 1959 and 2013 are consistent with a biphasic sigmoidal curve with characteristic times of 9.5 years. During each stage, transistor density increased at least tenfold within approximately six years, followed by at least three years with negligible growth rates. The six waves of transistor density increase account for and give insight into the underlying processes driving advances in processor manufacturing and point to future limits that might be overcome.

A national and international analysis of changing forest density.

Like cities, forests grow by spreading out or by growing denser. Both inventories taken steadily by a single nation and other inventories gathered recently from many nations by the United Nations confirm the asynchronous effects of changing area and of density or volume per hectare. United States forests spread little after 1953, while growing density per hectare increased national volume and thus sequestered carbon. The 2010 United Nations appraisal of global forests during the briefer span of two decades after 1990 reveals a similar pattern: A slowing decline of area with growing volume means growing density in 68 nations encompassing 72% of reported global forest land and 68% of reported global carbon mass. To summarize, the nations were placed in 5 regions named for continents. During 1990-2010 national density grew unevenly, but nevertheless grew in all regions. Growing density was responsible for substantially increasing sequestered carbon in the European and North American regions, despite smaller changes in area. Density nudged upward in the African and South American regions as area loss outstripped the loss of carbon. For the Asian region, density grew in the first decade and fell slightly in the second as forest area expanded. The different courses of area and density disqualify area as a proxy for volume and carbon. Applying forestry methods traditionally used to measure timber volumes still offers a necessary route to measuring carbon stocks. With little expansion of forest area, managing for timber growth and density offered a way to increase carbon stocks.

Dematerialization: Variety, caution, and persistence.

Dematerialization, represented by declining consumption per GDP of energy or of goods, offers some hope for rising environmental quality with development. The declining proportion of income spent on staples as affluence grows, which income elasticity <1.0 measures, makes dematerialization widespread. Further, as learning improves efficiency of resource use, the intensity of environmental impact per production of staples often declines. We observe that combinations of low income elasticity for staples and of learning by producers cause a variety of dematerializations and declining intensities of impact, from energy use and carbon emission to food consumption and fertilizer use, globally and in countries ranging from the United States and France to China, India, Brazil, and Indonesia. Because dematerialization and intensity of impact are ratios of parameters that may be variously defined and are sometimes difficult to estimate, their fluctuations must be interpreted cautiously. Nevertheless, substantial declining intensity of impact, and especially, dematerialization persisted between 1980 and 2006.

Returning forests analyzed with the forest identity.

Amid widespread reports of deforestation, some nations have nevertheless experienced transitions from deforestation to reforestation. In a causal relationship, the Forest Identity relates the carbon sequestered in forests to the changing variables of national or regional forest area, growing stock density per area, biomass per growing stock volume, and carbon concentration in the biomass. It quantifies the sources of change of a nation's forests. The Identity also logically relates the quantitative impact on forest expanse of shifting timber harvest to regions and plantations where density grows faster. Among 50 nations with extensive forests reported in the Food and Agriculture Organization's comprehensive Global Forest Resources Assessment 2005, no nation where annual per capita gross domestic product exceeded 4,600 dollars had a negative rate of growing stock change. Using the Forest Identity and national data from the Assessment report, a single synoptic chart arrays the 50 nations with coordinates of the rates of change of basic variables, reveals both clusters of nations and outliers, and suggests trends in returning forests and their attributes. The Forest Identity also could serve as a tool for setting forest goals and illuminating how national policies accelerate or retard the forest transitions that are diffusing among nations.