Rational Design Strategy for High-Valence Metal-Driven Electronically Modulated High-Entropy Co-Ni-Fe-Cu-Mo (Oxy)Hydroxide as Superior Multifunctional Electrocatalysts.

Creating durable and efficient multifunctional electrocatalysts capable of high current densities at low applied potentials is crucial for widespread industrial use in hydrogen production. Herein, a Co-Ni-Fe-Cu-Mo (oxy)hydroxide electrocatalyst with abundant grain boundaries on nickel foam using a scalable coating method followed by chemical precipitation is synthesized. This technique efficiently organizes hierarchical Co-Ni-Fe-Cu-Mo (oxy)hydroxide nanoparticles within ultrafine crystalline regions (<4 nm), enriched with numerous grain boundaries, enhancing catalytic site density and facilitating charge and mass transfer. The resulting catalyst, structured into nanosheets enriched with grain boundaries, exhibits superior electrocatalytic activity. It achieves a reduced overpotential of 199 mV at 10 mA cm2 current density with a Tafel slope of 48.8 mV dec1 in a 1 m KOH solution, maintaining stability over 72 h. Advanced analytical techniques reveal that incorporating high-valency copper and molybdenum elements significantly enhances lattice oxygen activation, attributed to weakened metal-oxygen bonds facilitating the lattice oxygen mechanism (LOM). Synchrotron radiation studies confirm a synergistic interaction among constituent elements. Furthermore, the developed high-entropy electrode demonstrates exceptional long-term stability under high current density in alkaline environments, showcasing the effectiveness of high-entropy strategies in advancing electrocatalytic materials for energy-related applications.

Correlated stochastic epidemic model for the dynamics of SARS-CoV-2 with vaccination.

In this paper, we propose a mathematical model to describe the influence of the SARS-CoV-2 virus with correlated sources of randomness and with vaccination. The total human population is divided into three groups susceptible, infected, and recovered. Each population group of the model is assumed to be subject to various types of randomness. We develop the correlated stochastic model by considering correlated Brownian motions for the population groups. As the environmental reservoir plays a weighty role in the transmission of the SARS-CoV-2 virus, our model encompasses a fourth stochastic differential equation representing the reservoir. Moreover, the vaccination of susceptible is also considered. Once the correlated stochastic model, the existence and uniqueness of a positive solution are discussed to show the problem's feasibility. The SARS-CoV-2 extinction, as well as persistency, are also examined, and sufficient conditions resulted from our investigation. The theoretical results are supported through numerical/graphical findings.

Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach.

Super-spreaders of the novel coronavirus disease (or COVID-19) are those with greater potential for disease transmission to infect other people. Understanding and isolating the super-spreaders are important for controlling the COVID-19 incidence as well as future infectious disease outbreaks. Many scientific evidences can be found in the literature on reporting and impact of super-spreaders and super-spreading events on the COVID-19 dynamics. This paper deals with the formulation and simulation of a new epidemic model addressing the dynamics of COVID-19 with the presence of super-spreader individuals. In the first step, we formulate the model using classical integer order nonlinear differential system composed of six equations. The individuals responsible for the disease transmission are further categorized into three sub-classes, i.e., the symptomatic, super-spreader and asymptomatic. The model is parameterized using the actual infected cases reported in the kingdom of Saudi Arabia in order to enhance the biological suitability of the study. Moreover, to analyze the impact of memory index, we extend the model to fractional case using the well-known Caputo-Fabrizio derivative. By making use of the Picard-Lindelöf theorem and fixed point approach, we establish the existence and uniqueness criteria for the fractional-order model. Furthermore, we applied the novel fractal-fractional operator in Caputo-Fabrizio sense to obtain a more generalized model. Finally, to simulate the models in both fractional and fractal-fractional cases, efficient iterative schemes are utilized in order to present the impact of the fractional and fractal orders coupled with the key parameters (including transmission rate due to super-spreaders) on the pandemic peaks.

Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory.

The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this paper, we studied the impact of various constant and time-dependent variable control measures coupled with vaccination on the dynamics of COVID-19. The optimal control theory is used to optimize the model and set an effective control intervention for the infection. Initially, we formulate the mathematical epidemic model for the COVID-19 without variable controls. The model basic mathematical assessment is presented. The nonlinear least-square procedure is utilized to parameterize the model from actual cases reported in Pakistan. A well-known technique based on statistical tools known as the Latin-hypercube sampling approach (LHS) coupled with the partial rank correlation coefficient (PRCC) is applied to present the model global sensitivity analysis. Based on global sensitivity analysis, the COVID-19 vaccine model is reformulated to obtain a control problem by introducing three time dependent control variables for isolation, vaccine efficacy and treatment enhancement represented by u 1 ( t ) , u 2 ( t ) and u 3 ( t ) , respectively. The necessary optimality conditions of the control problem are derived via the optimal control theory. Finally, the simulation results are depicted with and without variable controls using the well-known Runge-Kutta numerical scheme. The simulation results revealed that time-dependent control measures play a vital role in disease eradication.