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The presence and action of humans on Earth has exerted a strong influence on the evolution of the planet over the past $\approx$ 10,000 years, the consequences of which are now becoming broadly evident. Despite a deluge of tightly-focused and necessarily technical studies exploring each facet of "human impacts" on the planet, their integration into a complete picture of the human-Earth system lags far behind. Here, we quantify twelve dimensionless ratios which put the magnitude of human impacts in context, comparing the magnitude of anthropogenic processes to their natural analogues. These ratios capture the extent to which humans alter the terrestrial surface, hydrosphere, biosphere, atmosphere, and biogeochemistry of Earth. In almost all twelve cases, the impact of human processes rivals or exceeds their natural counterparts. The values and corresponding uncertainties for these impacts at global and regional resolution are drawn from the primary scientific literature, governmental and international databases, and industry reports. We present this synthesis of the current "state of affairs" as a graphical snapshot designed to be used as a reference. Furthermore, we establish a searchable database termed the Human Impacts Database (www.anthroponumbers.org) which houses all quantities reported here and many others with extensive curation and annotation. While necessarily incomplete, this work collates and contextualizes a set of essential numbers summarizing the broad impacts of human activities on Earth's atmosphere, land, water, and biota.

Modeling the spread of COVID-19 is crucial for informing public health policy. All models for COVID-19 epidemiology rely on parameters describing the dynamics of the infection process. The meanings of epidemiological parameters like R_0, R_t, the "serial interval" and "generation interval" can be challenging to understand, especially as these and other parameters are conceptually overlapping and sometimes confusingly named. Moreover, the procedures used to estimate these parameters make various assumptions and use different mathematical approaches that should be understood and accounted for when relying on parameter values and reporting them to the public. Here, we offer several insights regarding the derivation of commonly-reported epidemiological parameters, and describe how mitigation measures like lockdown are expected to affect their values. We aim to present these quantitative relationships in a manner that is accessible to the widest audience possible. We hope that better communicating the intricacies of epidemiological models will improve our collective understanding of their strengths and weaknesses, and will help avoid possible pitfalls when using them., Comment: arXiv admin note: substantial text overlap with arXiv:2006.01283

Accurate numbers are needed to understand and predict viral dynamics. Curation of high-quality literature values for the infectious period duration or household secondary attack rate, for example, is especially pressing currently because these numbers inform decisions about how and when to lockdown or reopen societies. We aim to provide a curated source for the key numbers that help us understand the virus driving our current global crisis. This compendium focuses solely on COVID-19 epidemiology. The numbers reported in summary format are substantiated by annotated references. For each property, we provide a concise definition, description of measurement and inference methods, and associated caveats. We hope this compendium will make essential numbers more accessible and avoid common sources of confusion for the many newcomers to the field such as using the incubation period to denote and quantify the latent period or using the hospitalization duration for the infectiousness period duration. This document will be repeatedly updated and the community is invited to participate in improving it.

The current SARS-CoV-2 pandemic is a harsh reminder of the fact that, whether in a single human host or a wave of infection across continents, viral dynamics is often a story about the numbers. In this snapshot, our aim is to provide a one-stop, curated graphical source for the key numbers that help us understand the virus driving our current global crisis. The discussion is framed around two broad themes: 1) the biology of the virus itself and 2) the characteristics of the infection of a single human host. Our one-page summary provides the key numbers pertaining to SARS-CoV-2, based mostly on peer-reviewed literature. The numbers reported in summary format are substantiated by the annotated references below. Readers are urged to remember that much uncertainty remains and knowledge of this pandemic and the virus driving it is rapidly evolving. In the paragraphs below we provide "back of the envelope" calculations that exemplify the insights that can be gained from knowing some key numbers and using quantitative logic. These calculations serve to improve our intuition through sanity checks, but do not replace detailed epidemiological analysis.

In permissive environments, E. coli can double its dry mass every 21 minutes. During this time, ribosomes, RNA polymerases, and the proteome are all doubled. Yet, the question of how to relate bacterial doubling time to other biologically relevant time scales in the growth process remains illusive, due to the complex temporal nesting pattern of these processes. In particular, the relation between the cell's doubling time and the ribosome assembly time is not known. Here we develop a model that connects growth rate to ribosome assembly time and show that the existence of a self-assembly step increases the overall growth rate, because during ribosome self-assembly existing ribosomes can start a new round of reproduction, by making a new batch of ribosomal proteins prior to the completion of the previous round. This overlapping of ribosome reproduction cycles increases growth rate beyond the serial-limit that is typically assumed to hold. Using recent data from ribosome profiling and well known measurements of the average translation rate, rigid bounds on the in-vivo ribosome self-assembly time are set, which are robust to the assumptions regarding the biological noises involved. At 21 minutes doubling time, the ribosome assembly time is found to be approximately 6 minutes --- three fold larger than the common estimate. We further use our model to explain the detrimental effect of a recently discovered ribosome assembly inhibitor drug, and predict the effect of limiting the expression of ribosome assembly chaperons on the overall growth rate., Comment: 7 pages, 4 figures