Global dynamics of discrete mathematical models of tuberculosis

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional R 0 which is based on the disease-free equilibrium, and a new net reproduction number R 0 ( E ∗ ) based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if R 0 ≤   1 and unstable if R 0 > 1 . Moreover, the endemic equilibrium is locally asymptotically stable if R 0 ( E ∗ ) < 1 < R 0 .

Modeling and analysis of a multilayer solid tumour with cell physiological age and resource limitations

We study an avascular spherical solid tumour model with cell physiological age and resource constraints in vivo. We divide the tumour cells into three components: proliferating cells, quiescent cells and dead cells in necrotic core. We assume that the division rate of proliferating cells is nonlinear due to the nutritional and spatial constraints. The proportion of newborn tumour cells entering directly into quiescent state is considered, since this proportion can respond to the therapeutic effect of drug. We establish a nonlinear age-structured tumour cell population model. We investigate the existence and uniqueness of the model solution and explore the local and global stabilities of the tumour-free steady state. The existence and local stability of the tumour steady state are studied. Finally, some numerical simulations are performed to verify the theoretical results and to investigate the effects of different parameters on the model.

Degradation behaviors of Nabumetone and its metabolite during UV/monochloramine process: Experimental and theoretical study

This study investigated degradation behaviors of a nonsteroidal anti-inflammatory drug Nabumetone (NMT) and its major metabolite 6-methoxy-2-naphthylacetic acid (MNA) in the coupling process of ultraviolet and monochloramine (UV/NH2Cl). The second-order rate constants of the contaminants reacting with reactive radicals (HO•, Cl•, Cl2•⁻, and CO3•⁻) were determined by laser flash photolysis experiments. HO• and Cl• contributed predominantly with 52.3% and 21.7% for NMT degradation and 60.8% and 22.3% for MNA degradation. The presence of chlorides retarded the degradation of NMT, while promoted the destruction of MNA, which was ascribed to the photosensitization effects of MNA under UV irradiation. Density functional theory (DFT) calculations revealed that radical adduct formation (RAF) was dominant pathway for both HO• and Cl• reacting with the contaminants, and hydrogen atom transfer (HAT) preferred to occur on side chains of NMT and MNA. NMT reacted with NO2• through single electron transfer (SET) with the second-order rate constant calculated to be 5.35 × 107 (mol/L)-1 sec-1, and the contribution of NO2• was predicted to be 13.0% of the total rate constant of NMT in pure water, which indicated that NO2• played a non-negligible role in the degradation of NMT. The acute toxicity and developmental toxicity of NMT were enhanced after UV/NH2Cl treatment, while those of MNA were alleviated. The transformation products of both NMT and MNA exhibited higher mutagenicity than their parent compounds. This study provides a deep understanding of the mechanism of radical degradation of NMT and MNA in the treatment of UV/NH2Cl.

The Impact of the Fluid-Solid Coupling Behavior of Macro and Microstructures in the Spiral Cochlea on Hearing

The cilia of the outer hair cells (OHCs) are the key microstructures involved in cochlear acoustic function, and their interactions with lymph in the cochlea involve complex, highly nonlinear, coupled motion and energy conversions, including macroscopic fluid-solid coupling. Recent optical measurements have shown that the frequency selectivity of the cochlea at high sound levels is entirely mechanical and is determined by the interactions of the hair bundles with the surrounding fluid. In this paper, an analytical mathematical model of the spiral cochlea containing macro- and micromeasurements was developed to investigate how the phonosensitive function of OHCs' motions is influenced by the macrostructural and microstructural fluid-solid coupling in the spiral cochlea. The results showed that the macrostructural and microstructural fluid-solid coupling exerted the radial forces of OHCs through the flow field, deflecting the cilia and generating frequency-selective properties of the microstructures. This finding showed that microstructural frequency selectivity arises from the radial motions of stereocilia hair bundles and enhances the hearing of sound signals at specific frequencies. It also implied that the macrostructural and microstructural fluid-solid couplings influence the OHCs' radial forces and that this is a key factor in the excitation of ion channels that enables their activity in helping the brain to detect sound.

Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI

PURPOSE

This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approach and a T2-based pore size estimation technique.

THEORY AND METHODS

A general diffusion-relaxation theoretical model for the spherical mean signal from water molecules within a distribution of cylinders with varying radii was introduced, encompassing the evaluated models as particular cases. Additionally, a new numerical approach was presented for estimating effective radii (i.e., MRI-visible mean radii) from the ground truth radii distributions, not reliant on previous theoretical approximations and adaptable to various acquisition sequences. The ground truth radii were obtained from scanning electron microscope images.

RESULTS

Both methods show a linear relationship between effective radii estimated from MRI data and ground-truth radii distributions, although some discrepancies were observed. The spherical mean power-law method overestimated fiber radii. Conversely, the T2-based method exhibited higher sensitivity to smaller fiber radii, but faced limitations in accurately estimating the radius in one particular phantom, possibly because of material-specific relaxation changes.

CONCLUSION

The study demonstrates the feasibility of both techniques to predict pore sizes of hollow microfibers. The T2-based technique, unlike the spherical mean power-law method, does not demand ultra-high diffusion gradients, but requires calibration with known radius distributions. This research contributes to the ongoing development and evaluation of neuroimaging techniques for fiber radius estimation, highlights the advantages and limitations of both methods, and provides datasets for reproducible research.

Irradiation-induced hair graying in mice: an experimental model to evaluate the effectiveness of interventions targeting oxidative stress, DNA damage prevention, and cellular senescence

Hair graying, also known as canities or achromotrichia, is a natural phenomenon associated with aging and is influenced by external factors such as stress, environmental toxicants, and radiation exposure. Understanding the mechanisms underlying hair graying is an ideal approach for developing interventions to prevent or reverse age-related changes in regenerative tissues. Hair graying induced by ionizing radiation (γ-rays or X-rays) has emerged as a valuable experimental model to investigate the molecular pathways involved in this process. In this review, we examine the existing evidence on radiation-induced hair graying, with a particular focus on the potential role of radiation-induced cellular senescence. We explore the current understanding of hair graying in aging, delve into the underlying mechanisms, and highlight the unique advantages of using ionizing-irradiation-induced hair graying as a research model. By elucidating the molecular pathways involved, we aim to deepen our understanding of hair graying and potentially identify novel therapeutic targets to address this age-related phenotypic change.

Numerical and Analytical Simulation of the Growth of Amyloid-β Plaques

Numerical and analytical solutions were employed to calculate the radius of an amyloid-β (Aβ) plaque over time. To the author's knowledge, this study presents the first model simulating the growth of Aβ plaques. Findings indicate that the plaque can attain a diameter of 50 μm after 20 years of growth, provided the Aβ monomer degradation machinery is malfunctioning. A mathematical model incorporates nucleation and autocatalytic growth processes using the Finke-Watzky model. The resulting system of ordinary differential equations was solved numerically, and for the simplified case of infinitely long Aβ monomer half-life, an analytical solution was found. Assuming that Aβ aggregates stick together and using the distance between the plaques as an input parameter of the model, it was possible to calculate the plaque radius from the concentration of Aβ aggregates. This led to the "cube root hypothesis," positing that Aβ plaque size increases proportionally to the cube root of time. This hypothesis helps explain why larger plaques grow more slowly. Furthermore, the obtained results suggest that the plaque size is independent of the kinetic constants governing Aβ plaque agglomeration, indicating that the kinetics of Aβ plaque agglomeration is not a limiting factor for plaque growth. Instead, the plaque growth rate is limited by the rates of Aβ monomer production and degradation.

An experimental and theoretical study on cell swelling for osmotic imbalance induced by electroporation

The cellular membrane serves as a pivotal barrier in regulating intra- and extracellular matter exchange. Disruption of this barrier through pulsed electric fields (PEFs) induces the transmembrane transport of ions and molecules, creating a concentration gradient that subsequently results in the imbalance of cellular osmolality. In this study, a multiphysics model was developed to simulate the electromechanical response of cells exposed to microsecond pulsed electric fields (μsPEFs). Within the proposed model, the diffusion coefficient of the cellular membrane for various ions was adjusted based on electropore density. Cellular osmolality was governed and described using Van't Hoff theory, subsequently converted to loop stress to dynamically represent the cell swelling process. Validation of the model was conducted through a hypotonic experiment and simulation at 200 mOsm/kg, revealing a 14.2% increase in the cell's equivalent radius, thereby confirming the feasibility of the cell mechanical model. With the transmembrane transport of ions induced by the applied μsPEF, the hoop stress acting on the cellular membrane reached 179.95 Pa, and the cell equivalent radius increased by 11.0% when the extra-cellular medium was supplied with normal saline. The multiphysics model established in this study accurately predicts the dynamic changes in cell volume resulting from osmotic imbalance induced by PEF action. This model holds theoretical significance, offering valuable references for research on drug delivery and tumor microenvironment modulation.

Exploring the potential anti-thyroid activity of Acetyl-L-carnitine: Lactoperoxidase inhibition profile, iodine complexation and scavenging power against H2O2. Experimental and theoretical studies

L-Acetylcarnitine (ALC), a versatile compound, has demonstrated beneficial effects in depression, Alzheimer's disease, cognitive impairment, and other conditions. This study focuses on its antithyroid activity. The precursor molecule, L-carnitine, inhibited the uptake of triiodothyronine (T3) and thyroxine (T4), and it is possible that ALC may reduce the iodination process of T3 and T4. Currently, antithyroid drugs are used to control the excessive production of thyroid hormones (TH) through various mechanisms: (i) forming electron donor-acceptor complexes with molecular iodine, (ii) eliminating hydrogen peroxide, and (iii) inhibiting the enzyme thyroid peroxidase. To understand the pharmacological properties of ALC, we investigated its plausible mechanisms of action. ALC demonstrated the ability to capture iodine (Kc = 8.07 ± 0.32 x 105 M-1), inhibit the enzyme lactoperoxidase (LPO) (IC50 = 17.60 ± 0.76 µM), and scavenge H2O2 (39.82 ± 0.67 mM). A comprehensive physicochemical characterization of ALC was performed using FTIR, Raman, and UV-Vis spectroscopy, along with theoretical DFT calculations. The inhibition process was assessed through fluorescence spectroscopy and vibrational analysis. Docking and molecular dynamics simulations were carried out to predict the binding mode of ALC to LPO and to gain a better understanding into the inhibition process. Furthermore, albumin binding experiments were also conducted. These findings highlight the potential of ALC as a therapeutic agent, providing valuable insights for further investigating its role in the treatment of thyroid disorders.

Precision epidemiology at the nexus of mathematics and nanotechnology: Unraveling the dance of viral dynamics

The intersection of mathematical modeling, nanotechnology, and epidemiology marks a paradigm shift in our battle against infectious diseases, aligning with the focus of the journal on the regulation, expression, function, and evolution of genes in diverse biological contexts. This exploration navigates the intricate dance of viral transmission dynamics, highlighting mathematical models as dual tools of insight and precision instruments, a theme relevant to the diverse sections of Gene. In the context of virology, ethical considerations loom large, necessitating robust frameworks to protect individual rights, an aspect essential in infectious disease research. Global collaboration emerges as a critical pillar in our response to emerging infectious diseases, fortified by the predictive prowess of mathematical models enriched by nanotechnology. The synergy of interdisciplinary collaboration, training the next generation to bridge mathematical rigor, biology, and epidemiology, promises accelerated discoveries and robust models that account for real-world complexities, fostering innovation and exploration in the field. In this intricate review, mathematical modeling in viral transmission dynamics and epidemiology serves as a guiding beacon, illuminating the path toward precision interventions, global preparedness, and the collective endeavor to safeguard human health, resonating with the aim of advancing knowledge in gene regulation and expression.

Stomatal conductance reduction tradeoffs in maize leaves: A theoretical study

As the leading global grain crop, maize significantly impacts agricultural water usage. Presently, photosynthesis (A net ${A}_{\text{net}}$ ) in leaves of modern maize crops is saturated withCO 2 ${\text{CO}}_{2}$ , implying that reducing stomatal conductance (g s ${g}_{{\rm{s}}}$ ) would not affectA net ${A}_{\text{net}}$ but reduce transpiration (τ $\tau $ ), thereby increasing water use efficiency (WUE). Whileg s ${g}_{{\rm{s}}}$ reduction benefits upper canopy leaves under optimal conditions, the tradeoffs in low light and nitrogen-deficient leaves under nonoptimal microenvironments remain unexplored. Moreover,g s ${g}_{{\rm{s}}}$ reduction increases leaf temperature (T leaf ${T}_{\text{leaf}}$ ) and water vapor pressure deficit, partially counteracting transpiratory water savings. Therefore, the overall impact ofg s ${g}_{{\rm{s}}}$ reduction on water savings remains unclear. Here, we use a process-based leaf model to investigate the benefits of reducedg s ${g}_{{\rm{s}}}$ in maize leaves under different microenvironments. Our findings show that increases inT leaf ${T}_{\text{leaf}}$ due tog s ${g}_{{\rm{s}}}$ reduction can diminish WUE gains by up to 20%. However,g s ${g}_{{\rm{s}}}$ reduction still results in beneficial WUE tradeoffs, where a 29% decrease ing s ${g}_{{\rm{s}}}$ in upper canopy leaves results in a 28% WUE gain without loss inA net ${A}_{\text{net}}$ . Lower canopy leaves exhibit superior tradeoffs ing s ${g}_{{\rm{s}}}$ reduction with 178% gains in WUE without loss inA net ${A}_{\text{net}}$ . Our simulations show that these WUE benefits are resilient to climate change.

Quantitative analyses of RBC movement in whole blood exposed to DC and ELF electric field

For the study of biological effects of direct current (DC) and extremely low frequency (ELF) electric fields, we have quantitatively analyzed red blood cell (RBC) movement in whole blood. Considering the inhomogeneous distribution of electric fields in vivo, five different electric field distributions were generated under a microscope. For theoretical analyses, we assumed electrophoresis and dielectrophoresis as basic motive forces and obtained the spatial distribution of blood cell velocity. The RBC velocity was measured using video image analysis. The spatial dependence of the velocity showed good agreement with that predicted by theoretical analysis. This result suggests the validity of the theoretical model based on electrophoresis and dielectrophoresis for the study of ELF electric field exposure to inhomogeneous animal and human bodies. Next, using the same measurement system, we attempted to find the electric field strength at which these effects occur. The threshold values were found to be 0.40 and 1.6 kV/m, respectively, for DC and AC electric field exposures. Furthermore, we investigated the reproducibility of the field effects in more realistic conditions of human exposure. The RBCs in microchannels were exposed to the electric field generated in capacitive coupling using electrodes separated by an air gap. Even in the new condition, similar effects were observed, which also verified the validity of the analysis described above. These results will provide useful information for the safety assessment of field exposure and for the future biomedical applications of electric fields to manipulate RBCs in vivo.

The Bobath Clinical Reasoning Framework: A systems science approach to the complexity of neurodevelopmental conditions, including cerebral palsy

The current recommended developmental Bobath practice within the Bobath Clinical Reasoning Framework (BCRF) can be conceptualized using the lens of systems science, thereby providing a holistic perspective on the interrelatedness and interconnectedness of the variables associated with childhood-onset disability. The BCRF is defined as an in-depth clinical reasoning framework that can be applied to help understand the relationships between the domains of the International Classification of Functioning, Disability and Health, how those domains can be influenced, and how they impact each other. The BCRF is a transdisciplinary observational system and practical reasoning approach that results in an intervention plan. This provides a holistic understanding of the complexity of situations associated with disorders such as cerebral palsy (CP) and the basis for the lifelong management and habilitation of people living with neurological disorders. The clinical reasoning used by the BCRF draws on the important contextual factors of the individual and their social environment, primarily the family unit. It is rooted in an understanding of the interrelationships between typical and atypical development, pathophysiology (sensorimotor, cognitive, behavioural), and neuroscience, and the impact of these body structure and function constructs on activity and participation. The systems science model integral to the BCRF is a useful way forward in understanding and responding to the complexity of CP, the overarching goal being to optimize the lived experience of any individual in any context.

Application of colorimetric sensor array coupled with chemometric methods for monitoring the freshness of snakehead fillets

Total volatile basic nitrogen content (TVB-N) is an important index of freshness for snakehead. This paper attempted the feasibility of determining TVB-N content level in snakehead fillets by a colorimetric sensor array (CSA) composed of twelve porphyrin materials and eight pH indicators. The nine feature variables in RGB, HSV and CIE L*a*b* color spaces were obtained by differentiating the images of the CSA before and after exposure to the headspace-gas of the samples. Competitive adaptive reweighted sampling combined with partial least squares regression (CARS-PLS) was used to build the relationship between the TVB-N content and the feature variables of CSA, and to select meaningful color-sensitive materials. The results showed that CARS-PLS had a correlation coefficient of 0.9325 in the prediction set and selected 13 informative color-sensitive materials. This study demonstrated that the CSA with CARS-PLS algorithm could be used successfully to quantify and monitor the TVB-N in snakehead fillets.

Performance evaluation and optimization of a suspension-type reactor for use in heterogeneous catalytic ozonation

Packed fixed-bed reactors are traditionally used for heterogeneous catalytic ozonation. However, a high solid-to-liquid requirement, poor ozone dissolution, ineffective utilization of catalyst surface area, and production of large amounts of catalyst waste impede application of such reactors. In this study, we designed a suspension catalytic ozonation reactor and compared the performance of this reactor with that of a traditional fixed-bed catalytic ozonation reactor employing oxalic acid (OA) as the target contaminant. Our results showed that total O3 dissolved into the suspension reactor (117-134 mg.L-1) was much higher compared to that measured in the fixed-bed reactor (53 mg.L-1) due to a higher O3(g) interphase mass transfer rate in the suspension reactor. In accordance with the higher O3(g) interphase mass transfer, we observed a much higher proportional OA removal (32 %) compared to that achieved in the fixed-bed reactor (10%) employing an Fe-oxide catalyst supported on Al2O3 (Fe-oxide@Al2O3) in both reactors. Use of a double-layered Cu-Al hydroxide (Cu-Al LDHs) catalyst in the suspension reactor further enhanced the performance with nearly 90 % OA removal observed. Given the superior performance of the suspension reactor, we investigated the impact of operating conditions (catalyst dosage, hydraulic retention time and ozone dosage) employing Cu-Al LDHs as the catalyst. We also developed a mathematical kinetic model to describe the performance of the suspension reactor and, through use of the kinetic model, showed that O3(g) interphase transfer rate was the rate-limiting step in OA removal. Thus, improvement in ozone gas diffuser design is required to improve the performance of the suspension reactor. Overall, the present study demonstrated that suspension reactors were more effective than fixed-bed reactors for oxidation of surface-active organic compounds such as OA due to the higher ozone interphase mass transfer rate and effective utilization of the catalyst surface area that can be achieved. As such, further research on suspension reactor design and development of catalysts suitable for use in suspension reactors should facilitate large-scale application of catalytic ozonation processes by the wastewater treatment industry.

Effects of road width, radii and speeds on collisions at three-arm priority intersections

Simulation and observational studies have identified the importance of intersection geometries and vehicle speeds in collisions. However, the causal mechanisms of such collisions in low-speed areas and for different collision types remain unclear. This observational study investigates the complex relationships between geometries, speeds, visibilities, and road traffic collisions in the context of low-speed urban areas.Data were collected from 120 three-arm priority intersections in Portsmouth, UK. In 2007, Portsmouth became the first city in the UK to adopt a 20mph speed limit on all residential streets. The city has also adopted the UK's Manual for Streets (MfS) as the design standard for all new priority intersections in low-speed residential areas.Piecewise structural equation models (pSEM) were developed to represent the causal mechanisms that relate to geometries, speeds, speed limits and collisions. Findings indicate the role of combinations of approach lane width, corner radii, speed limit, and type of collision. The interaction of wider approach lanes on the minor arm and larger radii of turns for left-turning vehicles (left-hand driving perspective) was associated with higher numbers of road traffic collisions for right-turning vehicles. It is posited here that this is due to the orientation of the left-turning vehicle blocking the left visibility of the right-turning vehicle. These results give weight to the introduction of the 20mph speed limit zone in Portsmouth and some of the changes brought about by MfS. However, the combined effect of approach width and radii on collisions is novel and could form the basis of further guidance on reducing specific types of collisions at three-arm priority intersections.

Quasi-synchronization for variable-order fractional complex dynamical networks with hybrid delay-dependent impulses

This paper focuses on addressing the problem of quasi-synchronization in heterogeneous variable-order fractional complex dynamical networks (VFCDNs) with hybrid delay-dependent impulses. Firstly, a mathematics model of VFCDNs with short memory is established under multi-weighted networks and mismatched parameters, which is more diverse and practical. Secondly, under the framework of variable-order fractional derivative, a novel fractional differential inequality has been proposed to handle the issue of quasi-synchronization with hybrid delay-dependent impulses. Additionally, the quasi-synchronization criterion for VFCDNs is developed using differential inclusion theory and Lyapunov method. Finally, the practicality and feasibility of this theoretical analysis are demonstrated through numerical examples.

Team Care for the Care Team: A Scoping Review of the Relational Dimensions of Collaboration in Healthcare Contexts

Examining team care for the care team, this scoping literature review highlights the relational and compassionate dimensions of collaboration and teamwork that can alleviate healthcare worker suffering and promote well-being in challenging contexts of care. Its goal is to provide greater conceptual clarity about team care and examine the contextual dimensions regarding the needs and facilitators of team care. Analysis of the 48 retained texts identified three broad types of communicative practice that constitute team care: sharing; supporting; and leading with compassion. The environmental conditions facilitating team care included a caring team culture and specific and accessible organizational supports. These results are crystallized into a conceptual model of team care that situates team care within a system of team and organizational needs and anticipated outcomes. Gaps in the literature are noted and avenues for future research are suggested.

Multispecies comparative prostate anatomy by imaging: Implications for experimental models of prostatic disease

BACKGROUND

There is an increasing interest in using preclinical models for development and assessment of medical devices and imaging techniques for prostatic disease care. Still, a comprehensive assessment of the prostate's radiological anatomy in primary preclinical models such as dogs, rabbits, and mice utilizing human anatomy as a reference point remains necessary with no optimal model for each purpose being clearly defined in the literature. Therefore, this study compares the anatomical characteristics of different animal models to the human prostatic gland from the imaging perspective.

METHODS

We imaged five Beagle laboratory dogs, five New Zealand White rabbits, and five mice, all sexually mature males, under Institutional Animal Care and Use Committee (IACUC) approval. Ultrasonography (US) was performed using the Vevo® F2 for mice (57 MHz probe). Rabbits and dogs were imaged using the Siemens® Acuson S3000 (17 MHz probe) and endocavitary (8 MHz) probes, respectively. Magnetic resonance imaging (MRI) was also conducted with a 7T scanner in mice and 3T scanner in rabbits and dogs.

RESULTS

Canine transrectal US emerged as the optimal method for US imaging, depicting a morphologically similar gland to humans but lacking echoic zonal differentiation. MRI findings in canines indicated a homogeneously structured gland similar to the human peripheral zone on T2-weighted images (T2W) and apparent diffusion coefficient (ADC). In rabbits, US imaging faced challenges due to the pubic symphysis, whereas MRI effectively visualized all structures with the prostate presenting a similar aspect to the human peripheral gland on T2W and ADC maps. Murine prostate assessment revealed poor visualization of the prostate glands in ultrasound due to its small size, while 7T MRI delineated the distinct prostates and its lobes, with the lateral and dorsal prostate resembling the peripheral zone and the anterior prostate the central zone of the human gland.

CONCLUSION

Dogs stand out as superior models for advanced preclinical studies in prostatic disease research. However, mice present as a good model for early stage studies and rabbits are a cost-effective alternative and serve as valuable tools in specific research domains when canine research is not feasible.

Creatine supplementation increases postnatal growth and strength and prevents overexpression of pro-inflammatory interleukin 6 in the hippocampus in an experimental model of cerebral palsy

ABSTRACTObjectives: The aim of this study was thus to evaluate the effect of Cr supplementation on morphological changes and expression of pro-inflammatory cytokines in the hippocampus and on developmental parameters. Methods: Male Wistar rat pups were submitted to an experimental model of CP. Cr was administered via gavage from the 21st to the 28th postnatal day, and in water after the 28th, until the end of the experiment. Body weight (BW), food consumption (FC), muscle strength, and locomotion were evaluated. Expression of interleukin-1β (IL-1β), interleukin-6 (IL-6), and tumor necrosis factor α (TNF-α) were assessed in the hippocampus by quantitative real-time polymerase chain reaction. Iba1 immunoreactivity was assessed by immunocytochemistry in the hippocampal hilus. Results: Experimental CP caused increased density and activation of microglial cells, and overexpression of IL-6. The rats with CP also presented abnormal BW development and impairment of strength and locomotion. Cr supplementation was able to reverse the overexpression of IL-6 in the hippocampus and mitigate the impairments observed in BW, strength, and locomotion. Discussion: Future studies should evaluate other neurobiological characteristics, including changes in neural precursor cells and other cytokines, both pro- and anti-inflammatory.

CPhaMAS: An online platform for pharmacokinetic data analysis based on optimized parameter fitting algorithm

BACKGROUND AND OBJECTIVE

Clinical pharmacological modeling and statistical analysis software is an essential basic tool for drug development and personalized drug therapy. The learning curve of current basic tools is steep and unfriendly to beginners. The curve is even more challenging in cases of significant individual differences or measurement errors in data, resulting in difficulties in accurately estimating pharmacokinetic parameters by existing fitting algorithms. Hence, this study aims to explore a new optimized parameter fitting algorithm that reduces the sensitivity of the model to initial values and integrate it into the CPhaMAS platform, a user-friendly online application for pharmacokinetic data analysis.

METHODS

In this study, we proposed an optimized Nelder-Mead method that reinitializes simplex vertices when trapped in local solutions and integrated it into the CPhaMAS platform. The CPhaMAS, an online platform for pharmacokinetic data analysis, includes three modules: compartment model analysis, non-compartment analysis (NCA) and bioequivalence/bioavailability (BE/BA) analysis. Our proposed CPhaMAS platform was evaluated and compared with existing WinNonlin.

RESULTS

The platform was easy to learn and did not require code programming. The accuracy investigation found that the optimized Nelder-Mead method of the CPhaMAS platform showed better accuracy (smaller mean relative error and higher R2) in two-compartment and extravascular administration models when the initial value was set to true and abnormal values (10 times larger or smaller than the true value) compared with the WinNonlin. The mean relative error of the NCA calculation parameters of CPhaMAS and WinNonlin was <0.0001 %. When calculating BE for conventional, high-variability and narrow-therapeutic drugs. The main statistical parameters of the parameters Cmax, AUCt, and AUCinf in CPhaMAS have a mean relative error of <0.01% compared to WinNonLin.

CONCLUSIONS

In summary, CPhaMAS is a user-friendly platform with relatively accurate algorithms. It is a powerful tool for analysing pharmacokinetic data for new drug development and precision medicine.

A mathematical model of ENaC and Slc26a6 regulation by CFTR in salivary gland ducts

Cystic fibrosis (CF) is a genetic disease caused by the mutations of cystic fibrosis transmembrane conductance regulator (CFTR), the cystic fibrosis transmembrane conductance regulator gene. Cftr is a critical ion channel expressed in the apical membrane of mouse salivary gland striated duct cells. Although Cftr is primarily a Cl- channel, its knockout leads to higher salivary Cl- and Na+ concentrations and lower pH. Mouse experiments show that the activation of Cftr upregulates epithelial Na+ channel (ENaC) protein expression level and Slc26a6 (a 1Cl-:2[Formula: see text] exchanger of the solute carrier family) activity. Experimentally, it is difficult to predict how much the coregulation effects of CFTR contribute to the abnormal Na+, Cl-, and [Formula: see text] concentrations and pH in CF saliva. To address this question, we construct a wild-type mouse salivary gland model and simulate CFTR knockout by altering the expression levels of CFTR, ENaC, and Slc26a6. By reproducing the in vivo and ex vivo final saliva measurements from wild-type and CFTR knockout animals, we obtain computational evidence that ENaC and Slc26a6 activities are downregulated in CFTR knockout in salivary glands.NEW & NOTEWORTHY This paper describes a salivary gland mathematical model simulating the ion exchange between saliva and the salivary gland duct epithelium. The novelty lies in the implementation of CFTR regulating ENaC and Slc26a6 in a CFTR knockout gland. By reproducing the experimental saliva measurements in wild-type and CFTR knockout glands, the model shows that CFTR regulates ENaC and Slc26a6 anion exchanger in salivary glands. The method could be used to understand the various cystic fibrosis phenotypes.

Different policies constrained agricultural non-point pollutants emission trading management for water system under interval, fuzzy, and stochastic information

Formulating suitable policies is essential for resources and environmental management. In this study, an agricultural pollutants emission trading management model driven by water resources and pollutants control is developed to search reasonable policies for agricultural water resources allocation under multiple uncertainties. Random-fuzzy and interval information in water resources system that have directly impact on the effectiveness of management schemes is reflected through interval two-stage stochastic fuzzy-probability programming. The model was root from regional agricultural water resources system in Jining City, China under considering the relationship among effective precipitation, crop water demand, and pollutants emission. Two types policies (water consumption-control and pollutants emission-control) are designed for searching the related interaction on water resources management and water quality improvement. The results indicated that water resources policies would be of water and environmental double benefits, and a large rainfall would reduce irrigation amount from water sources and lead to a larger pollutants emission trading. The results will help for defining scientific and effective water resources protection and management policies and analyzing the related interacted effects on water consumption, pollutants control and system benefit.

Transition from child to adult services for young people with cerebral palsy in Ireland: Influencing factors at multiple ecological levels

AIM

To explore the factors that influence the process of transitioning from child to adult services in Ireland among young people with cerebral palsy, their parents, and service providers.

METHOD

This study followed a qualitative descriptive approach. Semi-structured interviews were conducted with 54 participants, including young people with cerebral palsy aged 16 to 22 years (n = 13), their parents (n = 14), and service providers (n = 27). Data were analysed using the Framework Method. Findings were categorized using an ecological model across four levels: individual, microsystem, mesosystem, and exosystem.

RESULTS

Limited awareness, preparation, and access to information hindered successful transition. Microsystem factors such as family knowledge, readiness, resilience, and health professional expertise influenced transition experience. Mesosystem factors encompassed provider-family interaction, interprofessional partnerships, and interagency collaboration between child and adult services. Exosystem factors included inadequate availability and distribution of adult services, limited referral options, coordination challenges, absence of transition policies, staffing issues, and funding allocation challenges.

INTERPRETATION

Transition is influenced by diverse factors at multiple ecological levels, including interactions within families, between health professionals, and larger systemic factors. Given the complexity of transition, a comprehensive multi-level response is required, taking into account the interactions among individuals, services, and systems.

Effectiveness evaluation of mosquito suppression strategies on dengue transmission under changing temperature and precipitation

Widespread resurgence of dengue outbreaks has seriously threatened the global health. Due to lack of treatments and vaccines, one key strategy in dengue control is to reduce the vector population size. As an environment-friendly mosquito control approach, releasing male mosquitoes transinfected with specific Wolbachia strain into the field to suppress the wild mosquito population size has become wildly accepted. The current study evaluates the effectiveness of this suppression strategy on dengue control under changing temperature and precipitation profiles. We formulate a mathematical model which includes larval intra-specific competition, the maturation period for mosquitoes, the extrinsic incubation period (EIP) and intrinsic incubation period (IIP). The persistence of mosquitoes and disease is discussed in terms of two basic reproduction numbers (RM and R0) and the release ratio pw. Further numerical simulations are carried out to not only validate theoretical results, but also provide interesting quantitative observations. Sensitivity analysis on the reproduction numbers, peak size, peak time and the final epidemic size is performed with respect to model parameters, which highlights effective control measures against dengue transmission. Moreover, by assuming temperature and precipitation dependent mosquito-related parameters, the model can be used to project the effectiveness of releasing Wolbachia-carrying males under climatic variations. It is shown that the effectiveness of various control strategies is highly dependent on the changing temperature and precipitation profiles. In particular, the model projects that it is most challenging to control the disease at the favorable temperature (around 27∼30∘C) and precipitation (5∼8mm/day) range, during which the basic reproduction number R0 is very high and more Wolbachia-infected males should be released.

Revisiting the Modularity-Disease transmission Link: Uncovering the importance of intra-modular structure

Studies have shown that the internal structure of modules is hardly important for the spread of epidemics. However, most of these studies have assumed that intra-module connectivity and inter-module connectivity do not affect each other. In reality, changes in the internal structure of modules may affect inter-module links and thus change the modularity of the entire network. Therefore, we have developed a theoretical network model with adjustable modularity to investigate the impact of this situation on disease transmission. Our findings indicate that the intra-module structure plays a crucial role in disease outbreaks. Changes in intra-module structure lead to significant numerical changes in peak prevalence and duration of disease. This implies that the potential impact of changes in exposure patterns within modules should also be considered when investigating the exact impact of modular social networks on disease burden.

Coupling dynamic response of saturated soil with anisotropic thermal conductivity under fractional order thermoelastic theory

In this paper, a two-dimensional (2D) thermo-hydro-mechanical dynamic (THMD) coupling analysis in the presence of a half-space medium is studied using Ezzat's fractional order generalized theory of thermoelasticity. Using normal mode analysis (NMA), the influence of the anisotropy of the thermal conduction coefficient, fractional derivatives, and frequency on the THMD response of anisotropy, fully saturated, and poroelastic subgrade is then analyzed with a time-harmonic load including mechanical load and thermal source subjected to the surface. The general relationships among the dimensionless physical variables such as the vertical displacement, excess pore water pressure, vertical stress, and temperature distribution are graphically illustrated. The NMA method does not require the integration and inverse transformation, increases the decoupling speed, and eliminates the limitation of numerical inverse transformation. The obtained results can guide the geotechnical engineering construction according to different values of load frequency, fractional order coefficient, and anisotropy of thermal conduction coefficient. This improves the subgrade stability and enriches the theoretical studies on thermo-hydro-mechanical coupling.

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-β (Aβ) 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 Aβ 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 (Aβ,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 Aβ 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.

A comprehensive study of settlement during the filling and post-closure phases at a landfill in Québec, Canada: Field data and TMB modelling

In Northern climates, waste placed curbside the evening before waste collection can lead to partially frozen waste at placement, which delays biodegradation and biodegradation-induced settlement. A 12-year settlement dataset collected during the filling and post-closure phases at a landfill in Québec, Canada was analyzed. The dataset showed a delay in biodegradation-induced settlement due to the first three waste lifts being placed in the winter months and exhibited an increase in the settlement rate at later times when the waste temperatures increased to values that support biodegradation. The field data also demonstrated that the stiffness of MSW increased in response to confined stress as subsequent waste lifts were added. A thermal-mechanical-biological (TMB) model was developed, in COMSOL Multiphysics, to simulate the settlement dataset. TMB integrates a Generalized Kelvin-Voigt (GKV) model, simulating instantaneous and mechanical creep settlements, with a biodegradation-induced settlement model that relates heat/gas generation with time to biodegradation-induced settlement. The thermal model simulates heat transfer through conduction and includes a biodegradation heat generation source term. The GKV stiffness parameters are expressed as a function of the applied stress to account for waste compressibility effects on mechanical response, which is consistent with field data and the research literature. The paper focuses solely on the MSW settlement field data and model predictions, with thermal response analysis presented in a separate publication. The TMB model effectively predicted waste behaviour, including resistance to compressibility under higher stress and the delay in waste settlement for waste placed in winter. The temperature and settlement data provide a valuable dataset to validate different models that can be used to predict waste settlement in cold regions.

Interactions of deprotonated phenylalanine with gold Clusters: Theoretical study with prospects for amino acid detection

Nanomaterials are widely used nowadays in industry and medicine. The specific properties of gold nanoclusters (Au NCs) are chemical stability, low cytotoxicity, low photobleaching, high sensitivity to the molecular environment. This set of properties allows to use Au NCs as nanosensors in bioimaging and diagnostics. We have investigated gold cluster complexes with proteinogenic amino acid phenylalanine (Phe). Detection of phenylalanine is essential for diagnostics of phenylketonuria, vitiligo, sclerosis, cancer, tuberculosis, etc. We have studied the complexes of Phe with Aunq clusters with atomic number equal 1-6, 8, 20 and a charge equal 0-2. We have established that the clusters Au40, Au21+ and Au32+ form the most stable complexes with Phe among NCs with charge 0, +1 and + 2, respectively. Intracomplex interactions have been studied using Atoms-In-Molecules (AIM) theory and Natural Bond Orbital (NBO) analysis. It has been shown that metal-ligand intracomplex interactions are partially covalent and partially electrostatic. Also, we have simulated the UV-vis absorption and Raman spectra of the Phe-Au NCs. We have established that the clusters possess prospective features if being used for colorimetric and Raman detection of Phe. Au20 cluster is remarkable for its six-times enhancement of the Raman signal. Moreover, our study provides insights into metal-ligand interactions for clusters synthesized inside a polypeptide globula. Hence, to the best of our knowledge this is a first attempt to perform a detailed analysis of Phe interactions with gold using quantum chemical calculations.

Automatic procedure for modelling, calibration, and optimization of a three-component chromatographic separation

The current landscape of biopharmaceutical production necessitates an ever-growing set of tools to meet the demands for shorter development times and lower production costs. One path towards meeting these demands is the implementation of digital tools in the development stages. Mathematical modelling of process chromatography, one of the key unit operations in the biopharmaceutical downstream process, is one such tool. However, obtaining parameter values for such models is a time-consuming task that grows in complexity with the number of compounds in the mixture being purified. In this study, we tackle this issue by developing an automated model calibration procedure for purification of a multi-component mixture by linear gradient ion exchange chromatography. The procedure was implemented using the Orbit software (Lund University, Department of Chemical Engineering), which both generates a mathematical model structure and performs the experiments necessary to obtain data for model calibration. The procedure was extended to suggest operating points for the purification of one of the components in the mixture by means of multi-objective optimization using three different objectives. The procedure was tested on a three-component protein mixture and was able to generate a calibrated model capable of reproducing the experimental chromatograms to a satisfactory degree, using a total of six assays. An additional seventh experiment was performed to validate the model response under one of the suggested optimum conditions, respecting a 95 % purity requirement. All of the above was automated and set in motion by the push of a button. With these results, we have taken a step towards fully automating model calibration and thus accelerating digitalization in the development stages of new biopharmaceuticals.

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.

A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system

Impaired cardiac function has been described as a frequent complication of COVID-19-related pneumonia. To investigate possible underlying mechanisms, we represented the cardiovascular system by means of a lumped-parameter 0D mathematical model. The model was calibrated using clinical data, recorded in 58 patients hospitalized for COVID-19-related pneumonia, to make it patient-specific and to compute model outputs of clinical interest related to the cardiocirculatory system. We assessed, for each patient with a successful calibration, the statistical reliability of model outputs estimating the uncertainty intervals. Then, we performed a statistical analysis to compare healthy ranges and mean values (over patients) of reliable model outputs to determine which were significantly altered in COVID-19-related pneumonia. Our results showed significant increases in right ventricular systolic pressure, diastolic and mean pulmonary arterial pressure, and capillary wedge pressure. Instead, physical quantities related to the systemic circulation were not significantly altered. Remarkably, statistical analyses made on raw clinical data, without the support of a mathematical model, were unable to detect the effects of COVID-19-related pneumonia in pulmonary circulation, thus suggesting that the use of a calibrated 0D mathematical model to describe the cardiocirculatory system is an effective tool to investigate the impairments of the cardiocirculatory system associated with COVID-19.

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.

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.

Discipline and punishment in panoptical public goods games

In Public Goods Games (PGG), the temptation to free-ride on others' contributions poses a significant threat to the sustainability of cooperative societies. Therefore, societies strive to mitigate this through incentive systems, employing rewards and punishments to foster cooperative behavior. Thus, peer punishment, in which cooperators sanction defectors, as well as pool punishment, where a centralized punishment institution executes the punishment, is deeply analyzed in previous works. Although the literature indicates that these methods may enhance cooperation on social dilemmas under particular contexts, there are still open questions, for instance, the structural connection between graduated punishment and the monitoring of public goods games. Our investigation proposes a compulsory PGG framework under Panoptical surveillance. Inspired by Foucault's theories on disciplinary mechanisms and biopower, we present a novel mathematical model that scrutinizes the balance between the severity and scope of punishment to catalyze cooperative behavior. By integrating perspectives from evolutionary game theory and Foucault's theories of power and discipline, this research uncovers the theoretical foundations of mathematical frameworks involved in punishment and discipline structures. We show that well-calibrated punishment and discipline schemes, leveraging the panoptical effect for universal oversight, can effectively mitigate the free-rider dilemma, fostering enhanced cooperation. This interdisciplinary approach not only elucidates the dynamics of cooperation in societal constructs but also underscores the importance of integrating diverse methodologies to address the complexities of fostering cooperative evolution.

A microdosimetry analysis of reversible electroporation in scattered, overlapping, and cancerous cervical cells

We present a numerical method for studying reversible electroporation on normal and cancerous cervical cells. This microdosimetry analysis builds on a unique approach for extracting contours of free and overlapping cervical cells in the cluster from the Extended Depth of Field (EDF) images. The algorithm used for extracting the contours is a joint optimization of multiple-level set function along with the Gaussian mixture model and Maximally Stable Extremal Regions. These contours are then exported to a multi-physics domain solver, where a variable frequency pulsed electric field is applied. The trans-Membrane voltage (TMV) developed across the cell membrane is computed using the Maxwell equation coupled with a statistical approach, employing the asymptotic Smoluchowski equation. The numerical model was validated by successful replication of existing experimental configurations that employed low-frequency uni-polar pulses on the overlapping cells to obtain reversible electroporation, wherein, several overlapping clumps of cervical cells were targeted. For high-frequency calculation, a combination of normal and cancerous cells is introduced to the computational domain. The cells are assumed to be dispersive and the Debye dispersion equation is used for further calculations. We also present the resulting strength-duration relationship for achieving the threshold value of electroporation between the normal and cancerous cervical cells due to their size and conductivity differences. The dye uptake modulation during the high-frequency electric field electroporation is further advocated by a mathematical model.

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.

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.

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.

Dynamical model of antibiotic responses linking expression of resistance genes to metabolism explains emergence of heterogeneity during drug exposures

Antibiotic responses in bacteria are highly dynamic and heterogeneous, with sudden exposure of bacterial colonies to high drug doses resulting in the coexistence of recovered and arrested cells. The dynamics of the response is determined by regulatory circuits controlling the expression of resistance genes, which are in turn modulated by the drug's action on cell growth and metabolism. Despite advances in understanding gene regulation at the molecular level, we still lack a framework to describe how feedback mechanisms resulting from the interdependence between expression of resistance and cell metabolism can amplify naturally occurring noise and create heterogeneity at the population level. To understand how this interplay affects cell survival upon exposure, we constructed a mathematical model of the dynamics of antibiotic responses that links metabolism and regulation of gene expression, based on the tetracycline resistancetetoperon inE. coli. We use this model to interpret measurements of growth and expression of resistance in microfluidic experiments, both in single cells and in biofilms. We also implemented a stochastic model of the drug response, to show that exposure to high drug levels results in large variations of recovery times and heterogeneity at the population level. We show that stochasticity is important to determine how nutrient quality affects cell survival during exposure to high drug concentrations. A quantitative description of how microbes respond to antibiotics in dynamical environments is crucial to understand population-level behaviors such as biofilms and pathogenesis.

The spiral wave frequency effect in atrial fibrillation

A spiral wavefront (WF), generated by a cardiac rotor that drifts between surface electrodes during atrial fibrillation, exhibits frequency changes inconsistent with classical Doppler effect (CDE) phenomena. Recent clinical studies reveal three repeatedly observed events--1) side-dependent frequency changes across the path of the rotor, 2) one additional WF strike on the higher frequency side, and 3) a reversal of WF strike sequence--which constitute a diametrical property of spinning WF sources. A linear ray model is first used to reveal and develop the diametrical phenomena. Mathematical models of an Archimedean spiral and a spiral generated by the diffusion equation are developed and compared. Each formulation predicts the diametrical property that CDE does not capture and illuminates the occurrence of a strong side and weak side with respect to the rotor path. Whereas CDE exhibits higher and lower frequencies from approaching and receding sources of WFs, respectively, spiral rotors generate higher and lower frequencies on opposite sides of the migration path. This motivates the reconsideration of mapping and ablation strategies that have traditionally been based on identifying sites of the dominant frequency. While this research aims to characterize the path of a spiral rotor during atrial fibrillation accurately, the results are applicable in other fields of science and engineering in which rotating spiral waves occur.

Highly efficient molecular film for inhibiting volatilization of hazardous nitric acid

Nitric acid, an important basic chemical raw material, plays an important role in promoting the development of national economy. However, such liquid hazardous chemicals are easy to cause accidental leakage during production, transportation, storage and use. The high concentration and corrosive toxic gas generated from decomposition shows tremendous harm to the surrounding environment and human life safety. Therefore, how to inhibit the volatilization of nitric acid and effectively control and block the generation of the toxic gas in the first time are the key to deal with the nitric acid leakage accident. Herein, a new method of molecular film obstruction is proposed to inhibit the nitric acid volatilization. The molecular film inhibitor spontaneously spread and form an insoluble molecular film on the gas-liquid interface, changing the state of nitric acid liquid surface and inhibiting the volatilization on the molecular scale. The inhibition rate up to 96% can be achieved below 45 °C within 400 min. Cluster structure simulation and energy barrier calculation is performed to elucidate the inhibition mechanism. Theoretical analysis of energy barrier shows that the specific resistance of the inhibitor significantly increased to 460 s·cm-1 at 45 °C, and the generated energy barrier is about 17,000 kJ·mol-1, which is much higher than the maximum energy required for nitric acid volatilization of 107.97 kJ·mol-1. The molecular film obstruction strategy can effectively inhibit the volatilization of nitric acid. This strategy paves the way for preventing the volatilization of liquid hazardous chemicals in accidental leakage treatment.

Opinion Evolution with Information Quality of Public Person and Mass Acceptance Threshold

Public persons are nodes with high attention to public events, and their opinions can directly affect the development on events. However, because of rationality, the followers' acceptance to the public persons' opinions will depend on the information trait on public persons' opinions and own comprehension. To study how different opinions of the public persons guide different followers, we build an opinion dynamics model, which would provide a theoretical method for public opinion management. Based on the classical bounded confidence model, we extract the information quality variables and individual trust threshold and introduce them to construct our two-stage opinion evolution model. And then in the simulation experiments, we analyze the different effects of opinion information quality, opinion release time, and frequency on public opinion by adjusting the different parameters. Finally, we added a case to compare real data, the data from classical model simulation and the data from improved model simulation to verify the effectiveness on our model. The research found that the more sufficient the argument and the more moderate the attitude, the more likely to guide the public opinion. If public person holds different opinions and different information quality, he should choose different time to present his opinion to achieve ideal guide effect. When public person holds neutral opinion and the information quality is relatively general, he/she can intervene in public opinion as soon as possible to control final public opinion; when public person holds extreme opinion and the information quality is relatively high, he/she can choose to express opinion after a certain period on public opinion evolution, which is conducive to improve the guidance effect on public opinion. The frequency of releasing opinions of public person consistently has a positive impact on the final public opinion.

Comparison of stochastic and deterministic models for gambiense sleeping sickness at different spatial scales: A health area analysis in the DRC

The intensification of intervention activities against the fatal vector-borne disease gambiense human African trypanosomiasis (gHAT, sleeping sickness) in the last two decades has led to a large decline in the number of annually reported cases. However, while we move closer to achieving the ambitious target of elimination of transmission (EoT) to humans, pockets of infection remain, and it becomes increasingly important to quantitatively assess if different regions are on track for elimination, and where intervention efforts should be focused. We present a previously developed stochastic mathematical model for gHAT in the Democratic Republic of Congo (DRC) and show that this same formulation is able to capture the dynamics of gHAT observed at the health area level (approximately 10,000 people). This analysis was the first time any stochastic gHAT model has been fitted directly to case data and allows us to better quantify the uncertainty in our results. The analysis focuses on utilising a particle filter Markov chain Monte Carlo (MCMC) methodology to fit the model to the data from 16 health areas of Mosango health zone in Kwilu province as a case study. The spatial heterogeneity in cases is reflected in modelling results, where we predict that under the current intervention strategies, the health area of Kinzamba II, which has approximately one third of the health zone's cases, will have the latest expected year for EoT. We find that fitting the analogous deterministic version of the gHAT model using MCMC has substantially faster computation times than fitting the stochastic model using pMCMC, but produces virtually indistinguishable posterior parameterisation. This suggests that expanding health area fitting, to cover more of the DRC, should be done with deterministic fits for efficiency, but with stochastic projections used to capture both the parameter and stochastic variation in case reporting and elimination year estimations.

New Azo Derivative of β-Diketones and Its Cu(II), Co(II) Complexes: Synthesis, Theoretical Study and Biological Activity

The paper is focused on biological activity and theoretical study of the structure and properties of a new azo derivative of β-diketones and its complexes with some metals. The aim of our work was to study the structure and properties of the newly synthesized compound as well as to theoretically determine the possibility of complex formation with the Cu(II) or Co(II) ions. A compound with the same substituents R1=R2=CH3 was chosen for the study. A synthesized azo compound based on 4-amino antipyrine and its complexes with Cu(II), Co(II) in solution and solid phase is reported. The structures of these compounds have been testified by X-ray, IR and  NMR spectroscopy. The combined experimental and theoretical approach was used. To study the structure and properties of the synthesized compound, as well as its possible complex formation with the Cu(II), quantum-chemical calculations were carried out the 6-31G basis set and the electron density functional theory (DFT) method. These 3-(1-phenyl-2,3-dimethyl-pyrazolone-5) azopentadione-2,4 (PDPA) with Cu(II) and Co(II) complexes had effective inhibition against butyrylcholinesterase and acetylcholinesterase. IC50 values were found as 19.03, 3.64 μM for AChE and 28.47, 8.01 μM for BChE, respectively. Cholinesterase inhibitors work to slow down the acetylcholine's deterioration.