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We report key epidemiologic parameter estimates for coronavirus disease identified in peer-reviewed publications, preprint articles, and online reports. Range estimates for incubation period were 1.8-6.9 days, serial interval 4.0-7.5 days, and doubling time 2.3-7.4 days. The effective reproductive number varied widely, with reductions attributable to interventions. Case burden and infection fatality ratios increased with patient age. Implementation of combined interventions could reduce cases and delay epidemic peak up to 1 month. These parameters for transmission, disease severity, and intervention effectiveness are critical for guiding policy decisions. Estimates will likely change as new information becomes available.

In their natural environment, plants are part of a rich ecosystem including numerous and diverse microorganisms in the soil. It has been long recognized that some of these microbes, such as mycorrhizal fungi or nitrogen fixing symbiotic bacteria, play important roles in plant performance by improving mineral nutrition. However, the full range of microbes associated with plants and their potential to replace synthetic agricultural inputs has only recently started to be uncovered. In the last few years, a great progress has been made in the knowledge on composition of rhizospheric microbiomes and their dynamics. There is clear evidence that plants shape microbiome structures, most probably by root exudates, and also that bacteria have developed various adaptations to thrive in the rhizospheric niche. The mechanisms of these interactions and the processes driving the alterations in microbiomes are, however, largely unknown. In this review, we focus on the interaction of plants and root associated bacteria enhancing plant mineral nutrition, summarizing the current knowledge in several research fields that can converge to improve our understanding of the molecular mechanisms underpinning this phenomenon.

\"The Final Volume of the Groundbreaking Trilogy on Agent-Based ModelingIn this pioneering synthesis, Joshua Epstein introduces a new theoretical entity: Agent Zero. This software individual, or \"agent,\" is endowed with distinct emotional/affective, cognitive/deliberative, and social modules. Grounded in contemporary neuroscience, these internal components interact to generate observed, often far-from-rational, individual behavior. When multiple agents of this new type move and interact spatially, they collectively generate an astonishing range of dynamics spanning the fields of social conflict, psychology, public health, law, network science, and economics.Epstein weaves a computational tapestry with threads from Plato, Hume, Darwin, Pavlov, Smith, Tolstoy, Marx, James, and Dostoevsky, among others. This transformative synthesis of social philosophy, cognitive neuroscience, and agent-based modeling will fascinate scholars and students of every stripe. Epstein's computer programs are provided in the book or on its Princeton University Press website, along with movies of his \"computational parables.\" Agent Zero is a signal departure in what it includes (e.g., a new synthesis of neurally grounded internal modules), what it eschews (e.g., standard behavioral imitation), the phenomena it generates (from genocide to financial panic), and the modeling arsenal it offers the scientific community. For generative social science, Agent Zero presents a groundbreaking vision and the tools to realize it\"-- Provided by publisher.

Spontaneous filling and voiding cycles represent a key dynamical feature of the healthy lower urinary tract. Some urinary tract dysfunctions, such as over-flow incontinence, may alter the natural occurrence of these cycles. As the function of the lower urinary tract arises from the interplay of a multitude of factors, it is difficult to determine which of them can be modulated to regain spontaneous cycles. In this study, we develop a mathematical model of the lower urinary tract that can capture filling and voiding cycles in the form of periodic solutions of a system of ordinary differential equations. After experimental validation, we utilize this model to study the effect that several physiological quantities have on the onset of cycles. We find that some parameters have an associated numerical threshold that determines whether the system exhibits healthy cycles or settles in a state of constant overflow.

Circadian clocks are endogenous oscillators driving daily rhythms in physiology and behavior. Synchronization of these timers to environmental light–dark cycles (‘entrainment’) is crucial for an organism's fitness. Little is known about which oscillator qualities determine entrainment, i.e., entrainment range, phase and amplitude. In a systematic theoretical and experimental study, we uncovered these qualities for circadian oscillators in the suprachiasmatic nucleus (SCN—the master clock in mammals) and the lung (a peripheral clock): (i) the ratio between stimulus (zeitgeber) strength and oscillator amplitude and (ii) the rigidity of the oscillatory system (relaxation rate upon perturbation) determine entrainment properties. Coupling among oscillators affects both qualities resulting in increased amplitude and rigidity. These principles explain our experimental findings that lung clocks entrain to extreme zeitgeber cycles, whereas SCN clocks do not. We confirmed our theoretical predictions by showing that pharmacological inhibition of coupling in the SCN leads to larger ranges of entrainment. These differences between master and the peripheral clocks suggest that coupling‐induced rigidity in the SCN filters environmental noise to create a robust circadian system. Synopsis Daily rhythms in physiology, metabolism and behavior are controlled by an endogenous circadian timing system, which has evolved to synchronize an organism to periodically recurring environmental conditions, such as light–dark or temperature cycles. In mammals, the circadian system relies on cell‐autonomous oscillators residing in almost every cell of the body. Cells of the SCN in the anterior hypothalamus are able to generate precise, long‐lasting self‐sustained circadian oscillations, which drive most rhythmic behavioral and physiological outputs, and which are believed to originate from the fact that the SCN tissue consists of tightly coupled cells (Aton and Herzog, 2005 ). In contrast, peripheral oscillators, such as lung tissue, exhibit seemingly damped and usually less precise oscillations, which are thought to be brought about by the lack of intercellular coupling. Precise synchronization of these rhythms within the organism, but also with the environment (so‐called entrainment), is an essential part of circadian organization. Entrainment is one of the cornerstones of circadian biology (Roenneberg et al , 2003 ). In evolution, the phase of a rhythmic variable is selective rather than its endogenous period. Thus, the synchronization of endogenous rhythms to zeitgeber cycles of the environment (resulting in a specific phase of entrainment) is fundamental for the adaptive value of circadian clocks. In this study, we systematically investigated the properties of circadian oscillators that are essential for entrainment behavior and describe coupling as a primary determinant. As an experimental starting point of this study, we found that the circadian oscillators of lung tissue have a larger range of entrainment than SCN tissue—they readily entrained to extreme experimental temperature cycle of 20 or 28 h, whereas SCN tissue did not (Figure 4 ). For this purpose, we cultured SCN and lung slices derived from mice that express luciferase as fusion protein together with the clock protein PERIOD2 (Yoo et al , 2004 ). The detection of luciferase‐driven bioluminescence allowed us to follow molecular clock gene activity in real‐time over the course of several days. In theoretical analyses, we show that both the ratio of amplitude and zeitgeber strength and, importantly, inter‐oscillator coupling are major determinants for entrainment. The reason for coupling being critical is twofold: (i) Coupling makes an oscillatory system more rigid, i.e., it relaxes faster in response to a perturbation, and (ii) coupling increases the amplitude of the oscillatory system. Both of these consequences of coupling lead to a smaller entrainment range, because zeitgeber stimuli affect the oscillatory system less if the relaxation is fast and the amplitude is high (Figure 1 ). From these theoretical considerations, we conclude that the lung clock probably constitutes a weak oscillatory system, likely because a lack in coupling leads to a slow amplitude relaxation. (Circadian amplitude is not particularly low in lung (Figure 4 ).) In contrast, the SCN constitutes a rigid oscillator, whereby coupling and its described consequences probably are the primary causes for this rigidity. We then tested these theoretical predictions by experimentally perturbing coupling in the SCN (with MDL and TTX; O'Neill et al , 2008 ; Yamaguchi et al , 2003 ) and find that, indeed, reducing the coupling weakens the circadian oscillatory system in the SCN, which results in an enlargement of the entrainment range (Figure 6 ). Why is the SCN designed to be a stronger circadian oscillator than peripheral organs? We speculate that the position of the SCN—as the tissue that conveys environmental timing information (i.e., light) to the rest of the body—makes it necessary to create a circadian clock that is robust against noisy environmental stimuli. The SCN oscillator needs to be robust enough to be protected from environmental noise, but flexible enough to fulfill its function as an entrainable clock even in extreme photoperiods (i.e., seasons). By the same token, peripheral clocks are more protected from the environmental zeitgebers due to intrinsic homeostatic mechanisms. Thus, they do not necessarily need to develop a strong oscillatory system (e.g., by strengthening the coupling), rather they need to stay flexible enough to respond to direct or indirect signals from the SCN, such as hormonal, neural, temperature or metabolic signals. Such a design ensures that only robust and persistent environmental signals trigger an SCN resetting response, while SCN signals can relatively easily be conveyed to the rest of the body. Thus, the robustness in the SCN clock likely serves as a filter for environmental noise. In summary, using a combination of simulation studies, analytical calculations and experiments, we uncovered critical features for entrainment, such as zeitgeber‐to‐amplitude ratio and amplitude relaxation rate. Coupling is a primary factor that governs these features explaining important differences in the design of SCN and peripheral oscillators that ensure a robust, but also flexible circadian system. Circadian clock oscillator properties that are crucial for synchronization with the environment (entrainment) are studied in experiment and theory. The ratio between stimulus (zeitgeber) strength and oscillator amplitude, and the rigidity of the oscillatory system (relaxation rate upon perturbation) determine entrainment properties. Coupling among oscillators affects both qualities resulting in increased amplitude and rigidity. Uncoupled lung clocks entrain to extreme zeitgeber cycles, whereas the coupled oscillator system in the suprachiasmatic nucleus (SCN) does not; however, when coupling in the SCN is inhibited, larger ranges of entrainment can be achieved.

The Pacific Island country of Vanuatu is considering strategies to remove border restrictions implemented during 2020 to prevent imported coronavirus disease. We performed mathematical modeling to estimate the number of infectious travelers who had different entry scenarios and testing strategies. Travel bubbles and testing on entry have the greatest importation risk reduction.

Multilayered membrane filters, which consist of a stack of thin porous membranes with different properties (such as pore size and void fraction), are widely used in industrial applications to remove contaminants and undesired impurities (particles) from a solvent. It has been experimentally observed that the performance of well-designed multilayer structured membranes is markedly better than that of equivalent homogeneous membranes. Mathematical characterization and modeling of multilayered membranes can help our understanding of how the properties of each layer affect the performance of the overall membrane stack. In this paper, we present a simplified mathematical model to describe how the pore-scale properties of a multilayered membrane affect the overall filter performance. Our results show that, for membrane stacks where the initial layer porosity decreases with depth, larger (negative) porosity gradients within a filter membrane are favorable for increasing throughput and filter lifetime, but at the expense of moderately poorer initial particle retention. We also found that the optimal layer thickness distribution that maximizes total throughput corresponds to a membrane stack with larger (negative) porosity gradients in which layer thickness increases slightly between successive layers in the depth of the membrane.

Drug delivery carriers are considered an encouraging approach for the localized treatment of disease with minimum effect on the surrounding tissue. Particularly, layer-by-layer releasing particles have gained increasing interest for their ability to develop multifunctional systems able to control the release of one or more therapeutical drugs and biomolecules. Although experimental methods can offer the opportunity to establish cause and effect relationships, the data collection can be excessively expensive or/and time-consuming. For a better understanding of the impact of different design conditions on the drug-kinetics and release profile, properly designed mathematical models can be greatly beneficial. In this work, we develop a continuum-scale mathematical model to evaluate the transport and release of a drug from a microparticle based on an inner core covered by a polymeric shell. The present mathematical model includes the dissolution and diffusion of the drug and accounts for a mechanism that takes into consideration the drug biomolecules entrapped into the polymeric shell. We test a sensitivity analysis to evaluate the influence of changing the model conditions on the total system behavior. To prove the effectiveness of this proposed model, we consider the specific application of antibacterial treatment and calibrate the model against the data of the release profile for an antibiotic drug, metronidazole. The results of the numerical simulation show that ∼85% of the drug is released in 230 h, and its release is characterized by two regimes where the drug dissolves, diffuses, and travels the external shell layer at a shorter time, while the drug is released from the shell to the surrounding medium at a longer time. Within the sensitivity analysis, the outer layer diffusivity is more significant than the value of diffusivity in the core, and the increase of the dissolution parameters causes an initial burst release of the drug. Finally, changing the shape of the particle to an ellipse produces an increased percentage of drugs released with an unchanged release time.