What does simple power law kinetics tell about our response to coronavirus pandemic?

Coronavirus pandemic of 2019-2020 has already affected over a million people and caused over 50,000 deaths worldwide (as on April 3, 2020). Roughly half of the world population has been asked to work from home and practice social distancing as the search for a vaccine continues. Though government interventions such as lockdown and social distancing are theoretically useful, its debatable whether such interventions are effective in flattening the curve, which is ceasing or reducing the growth of infection in control populations. In this article, I present a simple power law model that enables a comparison of countries in time windows of 14 days since first coronavirus related death is reported in that country. It therefore provides means to access the efficacy of above interventions.

Fractal kinetics of COVID-19 pandemic (with update 3/1/20)

We give an update to the original paper posted on 2/17/20 – now (as of 3/1/20) the China deaths are rapidly decreasing, and we find an exponential decline to the power law similar to the that predicted by the network model of Vazquez [2006]. At the same time, we see non-China deaths increasing rapidly, and similar to the early behavior of the China statistics. Thus, we see three stages of the spread of the disease in terms of number of deaths: exponential growth, power-law behavior, and then exponential decline in the daily rate.(Original abstract) The novel coronavirus (COVID-19) continues to grow rapidly in China and is spreading in other parts of the world. The classic epidemiological approach in studying this growth is to quantify a reproduction number and infection time, and this is the approach followed by many studies on the epidemiology of this disease. However, this assumption leads to exponential growth, and while the growth rate is high, it is not following exponential behavior. One approach that is being used is to simply keep adjusting the reproduction number to match the dynamics. Other approaches use rate equations such as the SEIR and logistical models. Here we show that the current growth closely follows power-law kinetics, indicative of an underlying fractal or small-world network of connections between susceptible and infected individuals. Positive deviations from this growth law might indicate either a failure of the current containment efforts while negative deviations might indicate the beginnings of the end of the pandemic. We cannot predict the ultimate extent of the pandemic but can get an estimate of the growth of the disease.

Slow domain reconfiguration causes power-law kinetics in a two-state enzyme

Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.

Overall Effectiveness Factor for Slab Geometry in a Three-Phase Reaction System

The overall effectiveness factor for slab geometry applicable to uniform washcoats on a monolith surface for three-phase reaction systems was studied in the present work. Analytical solutions for zero-order reactions and Langmuir–Hinshelwood and power law kinetics were reported. The analysis of the theoretical results showed that not considering the geometry of the monolithic system in a proper way lead to 14% errors in reactions parameters when operating under mixed control (kinetic-internal diffusion) and negligible external mass-transfer resistances.

High-Temperature Steam Oxidation Kinetics and Mechanism of SCWR Fuel Cladding Candidate Materials

Effects of temperature, dissolved oxygen (DO), and degree of cold work (CW) on the oxidation kinetics of supercritical-water-cooled reactor (SCWR) fuel cladding candidate materials, including three types of 15Cr-20Ni austenitic stainless steels (1520 SSs), in superheated steam have been investigated assuming power-law kinetics. Characteristics of oxide layers and its relation to oxidation behaviors are also discussed. The effect of DO on the weight gain behavior in superheated steam at 700 °C was minor for all specimens at least up to 200 ppb DO. The tube-shaped specimens of 1520 SSs showed very good oxidation resistance at 700–780 °C. There was no clear difference in the oxidation kinetics among the three investigated types of 1520 SSs. The degree of CW is a significant parameter to mitigate oxidation in superheated steam. It has been suggested that the tube specimens showed a very slow oxidation kinetics since Cr diffusion in the outside surface of the tubes is accelerated as a result of an increase of dislocation density and/or grain refinement by a high degree of CW.

Reaction Laws and Macro-Kinetics of 4-Carboxybenzaldehyde Hydrogenation over Pd/TiO2 Catalyst

The effects of temperature and hydrogen partial pressure on 4-Carboxybenzaldehyde (4-CBA) hydrogenation over Pd/TiO2 catalyst were investigated in a batch reactor. The results show that 4-CBA hydrogenation is a consecutive reaction. And 4-CBA hydrogenation to 4-hydroxymethylbenzoic (4-HMBA) is a reversible exothermic reaction. Meanwhile, a parallel reaction of 4-CBA decarbonylation occurs during the process. The hydrogenation rate of 4-HMBA is more sensitive to temperature and hydrogen partial pressure than that of 4-CBA. Macro-kinetics of 4-CBA reaction over Pd/TiO2 was obtained from the experimental data using the power-law kinetics model. The apparent activation energies of 4-CBA hydrogenation, 4-HMBA hydrogenation, 4-CBA decarbonylation and 4-HMBA dehydrogenation are 29.65 kJ/mol, 42.55 kJ/mol, 74.32 kJ/mol and 69.34 kJ/mol, respectively. The reaction orders with respect to 4-CBA and 4-HMBA are both first-order.