Plant xylem response to drought is routinely represented by a vulnerability curve (VC). Despite the significance of VCs, the connection between anatomy and tissue-level hydraulic response to drought remains a subject of inquiry. We present a numerical model of water flow in flowering plant xylem that combines current knowledge on diffuse-porous anatomy and embolism spread to explore this connection. The model produces xylem networks and uses different parameterizations of intervessel connection vulnerability to embolism spread: the Young-Laplace equation and pit membrane stretching. Its purpose is upscaling processes occurring on the microscopic length scales, such as embolism propagation through pit membranes, to obtain tissue-scale hydraulics. The terminal branch VC of Acer glabrum was successfully reproduced relying only on real observations of xylem tissue anatomy. A sensitivity analysis shows that hydraulic performance and VC shape and location along the water tension axis are heavily dependent on anatomy. The main result is that the linkage between pit-scale and vessel-scale anatomical characters, along with xylem network topology, affects VCs significantly. This work underscores the importance of stepping up research related to the three-dimensional network structure of xylem tissues. The proposed model's versatility makes it an important tool to explore similar future questions.
The SIR ('susceptible-infectious-recovered') formulation is used to uncover the generic spread mechanisms observed by COVID-19 dynamics globally, especially in the early phases of infectious spread. During this early period, potential controls were not effectively put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of COVID-19 basic reproduction number R o inferred from SIR formulation. The work here shows that there is global convergence (i.e., across many nations) to an uncontrolled R o = 4.5 that describes the early time spread of COVID-19. This value is in agreement with independent estimates from other sources reviewed here and adds to the growing consensus that the early estimate of R o = 2.2 adopted by the World Health Organization is low. A reconciliation between power-law and exponential growth predictions is also featured within the confines of the SIR formulation. The effects of testing ramp-up and the role of 'super-spreaders' on the inference of R o are analyzed using idealized scenarios. Implications for evaluating potential control strategies from this uncontrolled R o are briefly discussed in the context of the maximum possible infected fraction of the population (needed to assess health care capacity) and mortality (especially in the USA given diverging projections). Model results indicate that if intervention measures still result in R o > 2.7 within 44 days after first infection, intervention is unlikely to be effective in general for COVID-19.
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The SIR ('susceptible-infectious-recovered') formulation is used to uncover the generic spread mechanisms observed by COVID-19 dynamics globally, especially in the early phases of infectious spread. During this early period, potential controls were not effectively put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of COVID-19 basic reproduction number R o . The work here shows that there is global convergence (i.e. across many nations) to an uncontrolled R o = 4.5 that describes the early time spread of COVID-19. This value is in agreement with independent estimates from other sources reviewed here and adds to the growing consensus that the early estimate of R o = 2.2 adopted by the World Health Organization is low. A reconciliation between power-law and exponential growth predictions is also featured within the confines of the SIR formulation. Implications for evaluating potential control strategies from this uncontrolled R o are briefly discussed in the context of the maximum possible infected fraction of the population (needed for assessing health care capacity) and mortality (especially in the USA given diverging projections). Model results indicate that if intervention measures still result in R o > 2.7 within 49 days after first infection, intervention is unlikely to be effective in general for COVID-19. Current optimistic projections place mortality figures in the USA in the range of 100,000 fatalities. For fatalities to be confined to 100,000 requires a reduction in R o from 4.5 to 2.7 within 17 days of first infection assuming a mortality rate of 3.4%. : medRxiv preprint in epidemiology. This dispute moved inoculation from the domain of philosophy, 4 religion, and disjointed trials plagued by high uncertainty into a debate about 5 mathematical models -put forth by Daniel Bernoulli (in 1766) and Jean-Baptiste le 6 Rond D'Alembert (in 1761), both dealing with competing risks of death and 7 interpretation of trials [1]. Since then, the mathematical description of infectious 8 diseases continues to draw significant attention from researchers and practitioners in 9 governments and health agencies alike. Even news agencies are now seeking out 10 explanations to models so as to offer advice and clarity to their audiences during the 11 (near-continuous) coverage of the spread of COVID-19 [2]. The prospect of using 12 mathematical models in conjunction with data is succinctly summarized by the Nobel 13 laureate Ronald Ross, whose 1916 abstract [3] enlightens the role of mathematics in 14 epidemiology today. A quotation from this abstract below, which foreshadows the 15 requirements and challenges for mathematical models to describe emerging epidemics 16 such as 5], needs no further elaboration: 17
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