Mathematical model explains differences in Omicron and Delta SARS-CoV-2 dynamics in Caco-2 and Calu-3 cells.

Within-host infection dynamics of Omicron dramatically differs from previous variants of SARS-CoV-2. However, little is still known about which parameters of virus-cell interplay contribute to the observed attenuated replication and pathogenicity of Omicron. Mathematical models, often expressed as systems of differential equations, are frequently employed to study the infection dynamics of various viruses. Adopting such models for results of in vitro experiments can be beneficial in a number of aspects, such as model simplification (e.g., the absence of adaptive immune response and innate immunity cells), better measurement accuracy, and the possibility to measure additional data types in comparison with in vivo case. In this study, we consider a refinement of our previously developed and validated model based on a system of integro-differential equations. We fit the model to the experimental data of Omicron and Delta infections in Caco-2 (human intestinal epithelium model) and Calu-3 (lung epithelium model) cell lines. The data include known information on initial conditions, infectious virus titers, and intracellular viral RNA measurements at several time points post-infection. The model accurately explains the experimental data for both variants in both cell lines using only three variant- and cell-line-specific parameters. Namely, the cell entry rate is significantly lower for Omicron, and Omicron triggers a stronger cytokine production rate (i.e., innate immune response) in infected cells, ultimately making uninfected cells resistant to the virus. Notably, differences in only a single parameter (e.g., cell entry rate) are insufficient to obtain a reliable model fit for the experimental data.

Analysis and dynamical structure of glucose insulin glucagon system with Mittage-Leffler kernel for type I diabetes mellitus.

In this paper, we propose a fractional-order mathematical model to explain the role of glucagon in maintaining the glucose level in the human body by using a generalised form of a fractal fractional operator. The existence, boundedness, and positivity of the results are constructed by fixed point theory and the Lipschitz condition for the biological feasibility of the system. Also, global stability analysis with Lyapunov's first derivative functions is treated. Numerical simulations for fractional-order systems are derived with the help of Lagrange interpolation under the Mittage-Leffler kernel. Results are derived for normal and type 1 diabetes at different initial conditions, which support the theoretical observations. These results play an important role in the glucose-insulin-glucagon system in the sense of a closed-loop design, which is helpful for the development of artificial pancreas to control diabetes in society.

Contributions of representing the elements of nursing practice in the ISO 18.104:2023 standard: a theoretical study.

OBJECTIVE: To reflect on the contributions of representing nursing practice elements in the ISO 18.104:2023 standard. METHOD: This is a theoretical study with standard analysis. Categorical structures were described to represent nursing practice in terminological systems and contributions identified in the parts of the version were analyzed. RESULTS: There is innovation in the inclusion of nurse sensitive outcomes, nursing action, nursing diagnosis explanation as an indicator of nursing service demand and complexity of care, representation of concepts through mental maps and suggestion of use of restriction models for nursing actions. It describes that the Nursing Process is constituted by nursing diagnosis, nursing action and nurse sensitive outcomes. FINAL CONSIDERATIONS: Indicating a nursing diagnosis as an indicator will bring benefits for knowledge production and decision-making. Although care outcomes are not exclusive responses to nursing action, the modifiable attributes of a nursing diagnosis generate knowledge about clinical practice, nursing action effectiveness and subjects of care' health state. There is coherence in understanding the Nursing Process concept evolution.

Identification of critical links based on the optimal reliable path in stochastic traffic networks.

In urban stochastic transportation networks, there are specific links that hold great importance. Disruptions or failures in these critical links can lead to reduced connectivity within the road network. Under this circumstance, this manuscript proposed a novel identification of critical links mathematical optimization model based on the optimal reliable path with consideration of link correlations under demand uncertainty. The method presented in this paper offers a solution to bypass the necessity of conducting a full scan of the entire road network. Due to the non-additive and non-linear properties of the proposed model, a modified heuristic algorithm based on K-shortest algorithm and inequality technical is presented. The numerical experiments are conducted to show that improve a certain road link may not necessarily improve the overall traffic conditions. Moreover, the results indicate that if the travel time reliability is not considered, it will bring errors to the identification of key links.

Untangling the Molecular Interactions Underlying Intracellular Phase Separation Using Combined Global Sensitivity Analyses.

Liquid-liquid phase separation is an intracellular mechanism by which molecules, usually proteins and RNAs, interact and then rapidly demix from the surrounding matrix to form membrane-less compartments necessary for cellular function. Occurring in both the cytoplasm and the nucleus, properties of the resulting droplets depend on a variety of characteristics specific to the molecules involved, such as valency, density, and diffusion within the crowded environment. Capturing these complexities in a biologically relevant model is difficult. To understand the nuanced dynamics between proteins and RNAs as they interact and form droplets, as well as the impact of these interactions on the resulting droplet properties, we turn to sensitivity analysis. In this work, we examine a previously published mathematical model of two RNA species competing for the same protein-binding partner. We use the combined analyses of Morris Method and Sobol' sensitivity analysis to understand the impact of nine molecular parameters, subjected to three different initial conditions, on two observable LLPS outputs: the time of phase separation and the composition of the droplet field. Morris Method is a screening method capable of highlighting the most important parameters impacting a given output, while the variance-based Sobol' analysis can quantify both the importance of a given parameter, as well as the other model parameters it interacts with, to produce the observed phenomena. Combining these two techniques allows Morris Method to identify the most important dynamics and circumvent the large computational expense associated with Sobol', which then provides more nuanced information about parameter relationships. Together, the results of these combined methodologies highlight the complicated protein-RNA relationships underlying both the time of phase separation and the composition of the droplet field. Sobol' sensitivity analysis reveals that observed spatial and temporal dynamics are due, at least in part, to high-level interactions between multiple (3+) parameters. Ultimately, this work discourages using a single measurement to extrapolate the value of any single rate or parameter value, while simultaneously establishing a framework in which to analyze and assess the impact of these small-scale molecular interactions on large-scale droplet properties.

Exploring optimal deep tunnel sewer systems to enhance urban pluvial flood resilience in the gangnam region, South Korea.

Urban pluvial flooding is becoming a global concern, exacerbated by urbanization and climate change, especially in rapidly developing areas where existing sewer systems lag behind growth. In order to minimize a system's functional failures during extreme rainfalls, localized engineering solutions are required for urban areas chronically suffering from pluvial floods. This study critically evaluates the Deep Tunnel Sewer System (DTSS) as a robust grey infrastructure solution for enhancing urban flood resilience, with a case study in the Gangnam region of Seoul, South Korea. To do so, we integrated a one-dimensional sewer model with a rapid flood spreading model to identify optimal routes and conduit diameters for the DTSS, focusing on four flood-related metrics: the total flood volume, the flood duration, the peak flooding rate, and the number of flooded nodes. Results indicate that, had the DTSS been in place, it could have reduced historical flood volumes over the last decade by 50.1-99.3%, depending on the DTSS route. Regarding the conduit diameter, an 8 m diameter was found to be optimal for minimizing all flood-related metrics. Our research also developed the Intensity-Duration-Frequency (IDF) surfaces in three dimensions, providing a correlation between simulated flood-related metrics and design rainfall characteristics to distinguish the effect of DTSS on flood risk reduction. Our findings demonstrate how highly engineered solutions can enhance urban flood resilience, but they may still face challenges during extreme heavy rainfalls with a 80-year frequency or above. This study contributes to rational decision-making and emergency management in the face of increasing urban pluvial flood risks.

Improving new energy subsidy efficiency considering learning effect: A case study on wind power.

Subsidy policies are instrumental in driving the development of new energy. However, the effective allocation of new energy subsidies over time is challenging given fiscal constraints. This study addresses this challenge by considering the learning effect associated with the new energy industry. A two-stage dynamic programming model is proposed to capture the investment decision-making process of companies under new energy subsidy policies and government subsidy setups. Theoretical findings suggest that company investment decisions in new energy are influenced by a guiding principle: The subsidy rate should be negatively correlated with the variation rate of production scale increment (VRPSI). We calibrate this investment decision principle using wind power data from 14 countries. According to this principle, excessive subsidy rates may result in a low VRPSI, thereby diminishing future investment profitability in the new energy industry and leading to subsidy inefficiency. Upon investigating the efficiency of annual subsidy allocation, we find that the subsidy rates were potentially set too high in 2014, 2016, and 2017. Furthermore, the government should exercise caution regarding an inefficient subsidy pattern whereby companies invest in new energy only when the subsidy rate exceeds a certain threshold, neglecting traditional power sources. It is crucial to note that although this study uses wind power industry data for calibration and simulation, the theoretical model can be broadly applied to other new energy industries and emerging industries with increasing marginal net profit.

The research of river basin ecological compensation based on water emissions trading mechanism.

By integrating the successful case of the European Union emissions trading system, this study proposes a water emissions trading system, a novel method of reducing water pollution. Assuming that upstream governments allocate initial quotas to upstream businesses as the compensation standard, this approach defines the foundational principles of market trading mechanisms and establishes a robust watershed ecological compensation model to address challenges in water pollution prevention. To be specific, the government establishes a reasonable initial quota for upstream enterprises, which can be used to limit the emissions of upstream pollution. When enterprises exceed their allocated emissions quota, they face financial penalties. Conversely, these emissions rights can be transformed into profitable assets by participating in the trading market as a form of ecological compensation. Numerical simulations demonstrate that various pollutant emissions from upstream businesses will have various effects on the profits of other businesses. Businesses in the upstream region received reimbursement from the assigned emission rights through the market mechanism, demonstrating that ecological compensation for the watershed can be achieved through the market mechanism. This novel market trading system aims at controlling emissions management from the perspectives of individual enterprises and ultimately optimizing the aquatic environment.

Sex-structured disease transmission model and control mechanisms for visceral leishmaniasis (VL).

BACKGROUND: Leishmaniasis are a group of diseases caused by more than 20 species of the protozoan that are transmitted through the bite of female sand fly. The disease is endemic to 98 countries of the world. It affects most commonly the poorest of the poor and mainly males. Several research has been conducted to propose disease control strategies. Effective medical care, vector control, environmental hygiene, and personal protection are the mainstays of the current preventative and control methods. The mathematical models for the transmission dynamics of the disease studied so far did not consider the sex-biased burden of the disease into consideration. METHODOLOGY: Unlike the previous VL works, this study introduces a new deterministic sex-structured model for understanding the transmission dynamics of visceral leishmaniasis. Basic properties of the model including basic reproduction number ([Formula: see text]), and conditions for the existence of backward bifurcation of the model are explored. Baseline parameter values were estimated after the model was fitted to Ethiopia's VL data. Sensitivity analysis of the model was performed to identify the parameters that significantly impact the disease threshold. Numerical simulations were performed using baseline parameter values, and scenario analysis is performed by changing some of these parameters as appropriate. CONCLUSION: The analysis of the model shows that there is a possibility for a backward bifurcation for [Formula: see text], which means bringing [Formula: see text] to less than unity may not be enough to eradicate the disease. Our numerical result shows that the implementation of disease-preventive strategies, as well as effectively treating the affected ones can significantly reduce the disease prevalence if applied for more proportion of the male population. Furthermore, the implementation of vector management strategies also can considerably reduce the total prevalence of the disease. However, it is demonstrated that putting more effort in treating affected reservoir animals may not have any significant effect on the overall prevalence of the disease as compared to other possible mechanisms. The numerical simulation infers that a maximum of 60% of extra preventative measures targeted to only male population considerably reduces the total prevalence of VL by 80%. It is also possible to decrease the total prevalence of VL by 69.51% when up to 50% additional infected males receive treatment with full efficacy. Moreover, applying a maximum of 15% additional effort to reduce the number of vectors, decreases the total VL prevalence by 57.71%. Therefore, in order to reduce the disease burden of visceral leishmaniasis, public health officials and concerned stakeholders need to give more emphasis to the proportion of male humans in their intervention strategies.

The Demographic-Wealth model for cliodynamics.

Cliodynamics is a still a relatively new research area with the purpose of investigating and modelling historical processes. One of its first important mathematical models was proposed by Turchin and called "Demographic-Fiscal Model" (DFM). This DFM was one of the first and is one of a few models that link population with state dynamics. In this work, we propose a possible alternative to the classical Turchin DFM, which contributes to further model development and comparison essential for the field of cliodynamics. Our "Demographic-Wealth Model" (DWM) aims to also model link between population and state dynamics but makes different modelling assumptions, particularly about the type of possible taxation. As an important contribution, we employ tools from nonlinear dynamics, e.g., existence theory for periodic orbits as well as analytical and numerical bifurcation analysis, to analyze the DWM. We believe that these tools can also be helpful for many other current and future models in cliodynamics. One particular focus of our analysis is the occurrence of Hopf bifurcations. Therefore, a detailed analysis is developed regarding equilibria and their possible bifurcations. Especially noticeable is the behavior of the so-called coexistence point. While changing different parameters, a variety of Hopf bifurcations occur. In addition, it is indicated, what role Hopf bifurcations may play in the interplay between population and state dynamics. There are critical values of different parameters that yield periodic behavior and limit cycles when exceeded, similar to the "paradox of enrichment" known in ecology. This means that the DWM provides one possible avenue setup to explain in a simple format the existence of secular cycles, which have been observed in historical data. In summary, our model aims to balance simplicity, linking to the underlying processes and the goal to represent secular cycles.

Optimal sizing and power losses reduction of photovoltaic systems using PSO and LCL filters.

The integration of renewable energy systems into electricity grids is a solution for strengthening electricity distribution networks (SEDNs). Renewable energies such as solar photovoltaics are suitable for reinforcing a low-voltage line by offering an electrical energy storage system. However, the integration of photovoltaic systems can lead to problems of harmonic distortion due to the presence of direct current or non-linear feedback in networks from other sources. Therefore, connection standards exist to ensure the quality of the energy before injection at a point of common coupling (PCC). In this work, particle swarm optimization (PSO) is used to control a boost converter and to evaluate the power losses and the harmonic distortion rate. The test on the IEEE 14 bus standard makes it possible to determine the allocation or integration nodes for other sources such as biomass, wind or hydrogen generators, in order to limit the impact of harmonic disturbances (LIHs). The evaluation of the harmonic distortion rate, the power losses as well as the determination of the system size is done using an objective function defined based on the integration and optimization constraints of the system. The proposed model performs better since the grid current and voltage are stabilized in phase after the photovoltaic source is injected.

Drug Distribution After Intravitreal Injection: A Mathematical Model.

Purpose: Intravitreal injection of drugs is commonly used for treatment of chorioretinal ocular pathologies, such as age-related macular degeneration. Injection causes a transient increase in the intraocular volume and, consequently, of the intraocular pressure (IOP). The aim of this work is to investigate how intravitreal flow patterns generated during the post-injection eye deflation influence the transport and distribution of the injected drug. Methods: We present mathematical and computational models of fluid motion and mass transport in the vitreous chamber during the transient phase after injection, including the previously unexplored effects of globe deflation as ocular volume decreases. Results: During eye globe deflation, significant fluid velocities are generated within the vitreous chamber, which can possibly contribute to drug transport. Pressure variations within the eye globe are small compared to IOP. Conclusions: Even if significant fluid velocities are generated in the vitreous chamber after drug injection, these are found to have negligible overall effect on drug distribution.

Exploring local and global stability of COVID-19 through numerical schemes.

Respiratory sensitivity and pneumonia are possible outcomes of the coronavirus (COVID-19). Surface characteristics like temperature and sunshine affect how long the virus survives. This research article analyzes COVID-19 mathematical model behavior based on symptomatic and non-symptomatic individuals. In the reproductive model, the best result indicates the intensity of the epidemic. Our model remained stable at a certain point under controlled conditions after we evaluated a specific element. This approach is in place of traditional approaches such as Euler's and Runge-Kutta's. An unusual numerical approach known as the non-standard finite difference (NSFD) scheme is used in this article. This numerical approach gives us positivity. A dependable numerical analysis allowed us to evaluate different approaches and verify our theoretical results. Unlike the widely used Euler and RK4 approaches, we investigated the benefits of implementing NSFD schemes. By numerically simulating COVID-19 in a variety of scenarios, we demonstrated how our theoretical concepts work. The simulation findings support the usefulness of both approaches.

Anti-Inflammatory Properties of the Citrus Flavonoid Diosmetin: An Updated Review of Experimental Models.

Inflammation is an essential contributor to various human diseases. Diosmetin (3',5,7-trihydroxy-4'-methoxyflavone), a citrus flavonoid, can be used as an anti-inflammatory agent. All the information in this article was collected from various research papers from online scientific databases such as PubMed and Web of Science. These studies have demonstrated that diosmetin can slow down the progression of inflammation by inhibiting the production of inflammatory mediators through modulating related pathways, predominantly the nuclear factor-κB (NF-κB) signaling pathway. In this review, we discuss the anti-inflammatory properties of diosmetin in cellular and animal models of various inflammatory diseases for the first time. We have identified some deficiencies in current research and offer suggestions for further advancement. In conclusion, accumulating evidence so far suggests a very important role for diosmetin in the treatment of various inflammatory disorders and suggests it is a candidate worthy of in-depth investigation.

A variable speed limit control approach for freeway tunnels based on the model-based reinforcement learning framework with safety perception.

To improve the traffic safety and efficiency of freeway tunnels, this study proposes a novel variable speed limit (VSL) control strategy based on the model-based reinforcement learning framework (MBRL) with safety perception. The MBRL framework is designed by developing a multi-lane cell transmission model for freeway tunnels as an environment model, which is built so that agents can interact with the environment model while interacting with the real environment to improve the sampling efficiency of reinforcement learning. Based on a real-time crash risk prediction model for freeway tunnels that uses random deep and cross networks, the safety perception function inside the MBRL framework is developed. The reinforcement learning components fully account for most current tunnels' application conditions, and the VSL control agent is trained using a deep dyna-Q method. The control process uses a safety trigger mechanism to reduce the likelihood of crashes caused by frequent changes in speed. The efficacy of the proposed VSL strategies is validated through simulation experiments. The results show that the proposed VSL strategies significantly increase traffic safety performance by between 16.00% and 20.00% and traffic efficiency by between 3.00% and 6.50% compared to a fixed speed limit approach. Notably, the proposed strategies outperform traditional VSL strategy based on the traffic flow prediction model in terms of traffic safety and efficiency improvement, and they also outperform the VSL strategy based on model-free reinforcement learning framework when sampling efficiency is considered together. In addition, the proposed strategies with safety triggers are safer than those without safety triggers. These findings demonstrate the potential for MBRL-based VSL strategies to improve traffic safety and efficiency within freeway tunnels.

Mid-ocean ridge unfaulting revealed by magmatic intrusions.

Mid-ocean ridges (MORs) are quintessential sites of tectonic extension1-4, at which divergence between lithospheric plates shapes abyssal hills that cover about two-thirds of the Earth's surface5,6. Here we show that tectonic extension at the ridge axis can be partially undone by tectonic shortening across the ridge flanks. This process is evidenced by recent sequences of reverse-faulting earthquakes about 15 km off-axis at the Mid-Atlantic Ridge and Carlsberg Ridge. Using mechanical models, we show that shallow compression of the ridge flanks up to the brittle failure point is a natural consequence of lithosphere unbending away from the axial relief. Intrusion of magma-filled fractures, which manifests as migrating swarms of extensional seismicity along the ridge axis, can provide the small increment of compressive stress that triggers reverse-faulting earthquakes. Through bathymetric analyses, we further find that reverse reactivation of MOR normal faults is a widely occurring process that can reduce the amplitude of abyssal hills by as much as 50%, shortly after they form at the ridge axis. This 'unfaulting' mechanism exerts a first-order influence on the fabric of the global ocean floor and provides a physical explanation for reverse-faulting earthquakes in an extensional environment.

Mathematical modeling of transdermal delivery of topical drug formulations in a dynamic microfluidic diffusion chamber in health and disease.

Mathematical models of epidermal and dermal transport are essential for optimization and development of products for percutaneous delivery both for local and systemic indication and for evaluation of dermal exposure to chemicals for assessing their toxicity. These models often help directly by providing information on the rate of drug penetration through the skin and thus on the dermal or systemic concentration of drugs which is the base of their pharmacological effect. The simulations are also helpful in analyzing experimental data, reducing the number of experiments and translating the in vitro investigations to an in-vivo setting. In this study skin penetration of topically administered caffeine cream was investigated in a skin-on-a-chip microfluidic diffusion chamber at room temperature and at 32°C. Also the transdermal penetration of caffeine in healthy and diseased conditions was compared in mouse skins from intact, psoriatic and allergic animals. In the last experimental setup dexamethasone, indomethacin, piroxicam and diclofenac were examined as a cream formulation for absorption across the dermal barrier. All the measured data were used for making mathematical simulation in a three-compartmental model. The calculated and measured results showed a good match, which findings indicate that our mathematical model might be applied for prediction of drug delivery through the skin under different circumstances and for various drugs in the novel, miniaturized diffusion chamber.

Modeling single cell trajectory using forward-backward stochastic differential equations.

Recent advances in single-cell sequencing technology have provided opportunities for mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. Optimal transport has emerged as a promising theoretical framework for this task by computing pairings between cells from different time points. However, optimal transport methods have limitations in capturing nonlinear trajectories, as they are static and can only infer linear paths between endpoints. In contrast, stochastic differential equations (SDEs) offer a dynamic and flexible approach that can model non-linear trajectories, including the shape of the path. Nevertheless, existing SDE methods often rely on numerical approximations that can lead to inaccurate inferences, deviating from true trajectories. To address this challenge, we propose a novel approach combining forward-backward stochastic differential equations (FBSDE) with a refined approximation procedure. Our FBSDE model integrates the forward and backward movements of two SDEs in time, aiming to capture the underlying dynamics of single-cell developmental trajectories. Through comprehensive benchmarking on multiple scRNA-seq datasets, we demonstrate the superior performance of FBSDE compared to other methods, highlighting its efficacy in accurately inferring developmental trajectories.

Generating PET scan patterns in Alzheimer's by a mathematical model.

Alzheimer disease (AD) is the most common form of dementia. The cause of the disease is unknown, and it has no cure. Symptoms include cognitive decline, memory loss, and impairment of daily functioning. The pathological hallmarks of the disease are aggregation of plaques of amyloid-ß (Aß) and neurofibrillary tangles of tau proteins (τ), which can be detected in PET scans of the brain. The disease can remain asymptomatic for decades, while the densities of Aß and τ continue to grow. Inflammation is considered an early event that drives the disease. In this paper, we develop a mathematical model that can produce simulated patterns of (Aß,τ) seen in PET scans of AD patients. The model is based on the assumption that early inflammations, R and [Formula: see text], drive the growth of Aß and τ, respectively. Recently approved drugs can slow the progression of AD in patients, provided treatment begins early, before significant damage to the brain has occurred. In line with current longitudinal studies, we used the model to demonstrate how to assess the efficacy of such drugs when given years before the disease becomes symptomatic.

Experimental and theoretical model of microvascular network remodeling and blood flow redistribution following minimally invasive microvessel laser ablation.

Overly dense microvascular networks are treated by selective reduction of vascular elements. Inappropriate manipulation of microvessels could result in loss of host tissue function or a worsening of the clinical problem. Here, experimental, and computational models were developed to induce blood flow changes via selective artery and vein laser ablation and study the compensatory collateral flow redistribution and vessel diameter remodeling. The microvasculature was imaged non-invasively by bright-field and multi-photon laser microscopy, and optical coherence tomography pre-ablation and up to 30 days post-ablation. A theoretical model of network remodeling was developed to compute blood flow and intravascular pressure and identify vessels most susceptible to changes in flow direction. The skin microvascular remodeling patterns were consistent among the five specimens studied. Significant remodeling occurred at various time points, beginning as early as days 1-3 and continuing beyond day 20. The remodeling patterns included collateral development, venous and arterial reopening, and both outward and inward remodeling, with variations in the time frames for each mouse. In a representative specimen, immediately post-ablation, the average artery and vein diameters increased by 14% and 23%, respectively. At day 20 post-ablation, the maximum increases in arterial and venous diameters were 2.5× and 3.3×, respectively. By day 30, the average artery diameter remained 11% increased whereas the vein diameters returned to near pre-ablation values. Some arteries regenerated across the ablation sites via endothelial cell migration, while veins either reconnected or rerouted flow around the ablation site, likely depending on local pressure driving forces. In the intact network, the theoretical model predicts that the vessels that act as collaterals after flow disruption are those most sensitive to distant changes in pressure. The model results correlate with the post-ablation microvascular remodeling patterns.