Search Results (219)

The role of poverty, specifically the urban poor, in shaping the urban landscape is often solely linked to slums and informal settlements in urban centers. However, contrary to this common perception, this study aims to elucidate how urban poor residents contribute to shaping urban sprawl in developing countries. After identifying patterns of urban sprawl and poverty in the Jakarta Metropolitan Area (JMA) in Indonesia, the study used the Structural Equation Model (SEM) method to analyze survey data from 195 respondents with a per capita income of less than USD 2.15 (IDR 34,000) daily in Tangerang Regency, a western suburb of the JMA. This study shows that urban sprawl and poverty concentration overlap. The urban poor contribute to urban sprawl by purchasing affordable land on the urban periphery, traveling there with their motorized vehicles, and taking advantage of government subsidies. However, rather than gaining more land, they face increased public service costs, a lack of basic facilities, and habitat destruction. Most respondents own their own homes, but almost half of the respondents (41.54%) state that these homes are less than 48 m² in size. It can be concluded that economically vulnerable populations can contribute to urban sprawl when confronted with ineffective planning institutions. Full article

This study explores the spread of malware within a digital framework by introducing a unique fractional-order model that employs the Atangana–Baleanu–Caputo (ABC) derivative. As cyber threats grow increasingly sophisticated and widespread, traditional models using classical differential equations often prove inadequate, particularly in capturing long-term memory effects and historical dependencies inherent in real-world systems. To address these challenges, the proposed approach utilizes the non-local characteristics of fractional calculus, offering a more comprehensive framework for understanding malware behavior. The model includes the derivation of the basic reproduction number, ${\Re }_0$, to evaluate conditions for malware persistence or elimination, sensitivity analysis and examines equilibrium states to assess overall system stability. Theoretical analysis ensures the existence and uniqueness of solutions through fixed-point techniques. Through numerical simulations, the theoretical results are validated, emphasizing the significant impact of antidotal and recovery measures in controlling malware spread. These findings provide essential guidance for enhancing the protection and robustness of sophisticated cyber-physical and humanoid infrastructures. Full article

We present a comprehensive mathematical analysis of a within-host dual-target HIV dynamics model, which explicitly incorporates the virus’s interactions with its two primary cellular targets: CD4⁺ T cells and macrophages. The model is formulated as a system of five nonlinear delay differential equations, integrating three distinct discrete time delays to account for critical intracellular processes such as the development of productively infected cells and the maturation of new virions. We first establish the model’s biological well-posedness by proving the non-negativity and boundedness of solutions, ensuring all trajectories remain within a feasible region. The basic reproduction number, ${\mathcal{R}}_0^d$, is derived using the next-generation matrix method and serves as a sharp threshold for disease dynamics. Analytical results demonstrate that the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0^d\le 1$, guaranteeing viral eradication from any initial state. Conversely, when ${\mathcal{R}}_0^d>1$, a unique endemic equilibrium emerges and is proven to be GAS, representing a state of chronic infection. These global stability properties are rigorously established for both the non-delayed and delayed systems using carefully constructed Lyapunov functions and functionals, coupled with LaSalle’s invariance principle. A sensitivity analysis identifies viral production rates ($p_1,p_2$) and infection rates (${\beta }_1,{\beta }_2$) as the most influential parameters on ${\mathcal{R}}_0^d$, while the viral clearance rate (m) and maturation delay (${\tau }_3$) have a suppressive effect. The model is extended to evaluate antiretroviral therapy (ART), revealing a critical treatment efficacy threshold ${ϵ}^{cr}$ required to suppress the virus. Numerical simulations validate all theoretical findings and further investigate the dynamics under varying treatment efficacies and maturation delays, highlighting how these factors can shift the system from persistence to clearance. This study provides a rigorous mathematical framework for understanding HIV dynamics, with actionable insights for designing targeted treatment protocols aimed at achieving viral suppression. Full article

This paper is dedicated to the analytical investigation of the global dynamics of an SEIR epidemiological model that incorporates latency age (the time spent by an individual in the exposed class before becoming infectious) and a general nonlinear incidence rate. In this model, to reflect the dependence of disease progress on the latency age, the exposed class is structured by the latency age, and the rate at which the latent individual becomes infected, and the removal rate are assumed to depend on the latency age. By analyzing the characteristic equations associated with each equilibrium, we study the local stability of both the disease-free and endemic steady states of the model. Moreover, it is proven that the semiflow generated by this system is asymptotically smooth, and if the basic reproduction number is greater than unity, the system is uniformly persistent. Furthermore, based on Lyapunov functional and LaSalle’s invariance principle, the global dynamics of the model are established. It is obtained that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable and hence the disease dies out; however, if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable, and the disease persists. Numerical simulations are carried out to illustrate the main analytic results. Full article

Student dropout prediction remains critical in higher education, where timely identification enables effective interventions. Learning Management Systems (LMSs) capture rich temporal data reflecting student behavioral evolution, yet existing approaches underutilize this sequential information. Traditional machine learning methods aggregate behavioral data into static features, discarding dynamic patterns that distinguish successful from at-risk students. While Long Short-Term Memory (LSTM) networks model sequences, they assume discrete time steps and struggle with irregular LMS observation intervals. To address these limitations, we introduce Completion-aware Risk Neural Ordinary Differential Equations (CR-NODE), integrating continuous-time dynamics with completion-focused features for early dropout prediction. CR-NODE employs Neural ODEs to model student behavioral evolution through continuous differential equations, naturally accommodating irregular observation patterns. Additionally, we engineer three completion-focused features: completion rate, early warning score, and engagement variability, derived from root cause analysis. Evaluated on Canvas LMS data from 100,878 enrollments across 89,734 temporal sequences, CR-NODE achieves Macro F1 of 0.8747, significantly outperforming LSTM (0.8123), Extreme Gradient Boosting (XGBoost) (0.8300), and basic Neural ODE (0.8682). McNemar’s test confirms statistical significance ($p<0.0001$). Cross-dataset validation on the Open University Learning Analytics Dataset (OULAD) demonstrates generalizability, achieving 84.44% accuracy versus state-of-the-art LSTM (83.41%). To support transparent decision-making, SHapley Additive exPlanations (SHAP) analysis reveals completion patterns as the primary prediction drivers. Full article

The basic reproduction number ($R_0$) is an epidemiological metric that represents the average number of new infections caused by a single infectious individual in a completely susceptible population. The methodology for calculating this metric is well-defined for numerous model types, including, most prominently, Ordinary Differential Equations (ODEs). The basic reproduction number is used in disease modeling to predict the potential of an outbreak and the transmissibility of a disease, as well as by governments to inform public health interventions and resource allocation for controlling the spread of diseases. A Petri Net (PN) is a directed bipartite graph where places, transitions, arcs, and the firing of the arcs determine the dynamic behavior of the system. Petri Net models have been an increasingly used tool within the epidemiology community. However, no generalized method for calculating $R_0$ directly from PN models has been established. Thus, in this paper, we establish a generalized computational framework for calculating $R_0$ directly from Petri Net models. We adapt the next-generation matrix method to be compatible with multiple Petri Net formalisms, including both deterministic Variable Arc Weight Petri Nets (VAPNs) and stochastic continuous-time Petri Nets (SPNs). We demonstrate the method’s versatility on a range of complex epidemiological models, including those with multiple strains, asymptomatic states, and nonlinear dynamics. Crucially, we numerically validate our framework by demonstrating that the analytically derived $R_0$ values are in strong agreement with those estimated from simulation data, thereby confirming the method’s accuracy and practical utility. Full article

In this paper, we develop a mathematical model to investigate HIV infection dynamics, where we focus on the virus’s dual-target mechanism involving both CD$4^{+}$ T cells and macrophages. Our model is structured as a system of seven nonlinear ordinary differential equations describing the interactions between susceptible, latent, and infected cells, alongside free virus particles. We derive the basic reproduction number, ${\mathcal{R}}_0$, as two components, ${\mathcal{R}}_{01}$ and ${\mathcal{R}}_{02}$, which quantify the respective contributions of CD$4^{+}$ T cells and macrophages to viral spread. It is deduced that the infection-free steady state is globally asymptotically stable once ${\mathcal{R}}_0\le 1$, ensuring viral eradication. For ${\mathcal{R}}_0>1$, a stable endemic steady state emerges, indicating the persistence of the infection. Later, we develop an optimal control strategy to study the impact of reverse transcriptase and protease inhibitors. This analysis identifies a critical drug efficacy threshold, ${ϵ}^{\ast }=1-{\displaystyle \frac{1}{{\mathcal{R}}_0}}$, necessary for viral eradication. The numerical simulations and the sensitivity analysis provide key parameters that drive viral dynamics, offering practical insights for designing targeted therapies, particularly during the early stages of infection. Full article

Integration in non-integer-dimensional spaces (NIDS) is actively used in quantum field theory, statistical physics, and fractal media physics. The integration over the entire momentum space with non-integer dimensions was first proposed by Wilson in 1973 for dimensional regularization in quantum field theory. However, self-consistent calculus of integrals and derivatives in NIDS and the vector calculus in NIDS, including the fundamental theorems of these calculi, have not yet been explicitly formulated. The construction of precisely such self-consistent calculus is the purpose of this article. The integral and differential operators in NIDS are defined by using the generalization of the Wilson approach, product measure, and metric approaches. To derive the self-consistent formulation of the NIDS calculus, we proposed some principles of correspondence and self-consistency of NIDS integration and differentiation. In this paper, the basic properties of these operators are described and proved. It is proved that the proposed operators satisfy the NIDS generalizations of the first and second fundamental theorems of standard calculus; therefore, these NIDS operators form a calculus. The NIDS derivative satisfies the standard Leibniz rule; therefore, these derivatives are integer-order operators. The calculation of the NIDS integral over the ball region in NIDS gives the well-known equation of the volume of a non-integer dimension ball with arbitrary positive dimension. The volume, surface, and line integrals in D-dimensional spaces are defined, and basic properties are described. The NIDS generalization of the standard vector differential operators (gradient, divergence, and curl) and integral operators (the line and surface integrals of vector fields) are proposed. The NIDS generalizations of the standard gradient theorem, the divergence theorem (the Gauss–Ostrogradsky theorem), and the Stokes theorem are proved. Some basic elements of the calculus of differential forms in NIDS are also proposed. The proposed NIDS calculus can be used, for example, to describe fractal media and the fractal distribution of matter in the framework of continuum models by using the concept of the density of states. Full article

The linear stability of convection in a vertical two-layer porous structure representing a building external wall is studied. The wall is confined by two open vertical boundaries kept at different but uniform temperatures and is composed of two homogeneous porous layers, characterized by different values of permeability and thermal conductivity. The aim of this paper is investigating whether the wall can undergo the transition to thermal instability, namely, the onset of a multicellular convective pattern. The basic stationary state, given by the fully developed buoyant flow in the vertical direction, is perturbed by means of small-amplitude disturbances, and the resulting eigenvalue problem for neutrally stable modes is studied numerically. The solution of the perturbed governing equations shows that, for suitable values of the governing parameters, thermal instability can arise. The results highlight that the ratio of the permeabilities of the two layers as well as the ratio of their thermal conductivities, together with the aspect ratio between their thicknesses, are key parameters for the possible onset of instability. The temperature difference between the two open boundaries that can trigger instability is determined with reference to practical cases, namely, insulated walls that fulfill the Italian requirements in terms of overall thermal transmittance. Full article

Rod-pumping systems represent complex nonlinear systems. Traditional soft-sensing methods used for efficiency prediction in such systems typically rely on complicated fractional-order partial differential equations, severely limiting the real-time capability of efficiency estimation. To address this limitation, we propose an approximate efficiency prediction model for nonlinear fractional-order differential systems based on selective heterogeneous ensemble learning. This method integrates electrical power time-series data with fundamental operational parameters to enhance real-time predictive capability. Initially, we extract critical parameters influencing system efficiency using statistical principles. These primary influencing factors are identified through Pearson correlation coefficients and validated using p-value significance analysis. Subsequently, we introduce three foundational approximate system efficiency models: Convolutional Neural Network-Echo State Network-Bidirectional Long Short-Term Memory (CNN-ESN-BiLSTM), Bidirectional Long Short-Term Memory-Bidirectional Gated Recurrent Unit-Transformer (BiLSTM-BiGRU-Transformer), and Convolutional Neural Network-Echo State Network-Bidirectional Gated Recurrent Unit (CNN-ESN-BiGRU). Finally, to balance diversity among basic approximation models and predictive accuracy, we develop a selective heterogeneous ensemble-based approximate efficiency model for nonlinear fractional-order differential systems. Experimental validation utilizing actual oil-well parameters demonstrates that the proposed approach effectively and accurately predicts the efficiency of rod-pumping systems. Full article

Designing an effective electrical model for charged water bodies is of great significance in reducing the risk of electric shock in water and enhancing the safety and reliability of electrical equipment. Aiming to resolve the problems faced in using existing charged water body modeling methods, a practical circuit model of a charged water body is developed. The basic units of the model are simply constructed using fractional-order resistance–capacitance (RC) parallel circuits. The state variables of the model can be obtained by solving the circuit equations. In addition, a practical method for obtaining the circuit model parameters is also developed. This enables the estimation of the characteristics of charged water bodies under different conditions through model simulation. The effectiveness of the proposed method is verified by comparing the estimated voltage and leakage current of the model with the actual measured values. The comparison results show that the estimated value of the model is close to the actual characteristics of the charged water body. Full article

With the rapid development of hydrogen fuel cell vehicles, the research on the throttling effect of high-pressure hydrogen is crucial to the safety of hydrogen circulation systems for fuel cells. This paper studies the Joule-Thomson coefficients (${\mathrm{\mu }}_{\mathrm{J}\mathrm{T}}$) of ten gas state equations. The four equations, Van Der Waals (VDW), Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), and Beattie Bridgeman (BB), were selected for calculation. These were compared with the database of the National Institute of Standards and Technology (NIST), aiming to determine the optimal state equation under different temperature and pressure conditions. The empirical formula of the ${\mathrm{\mu }}_{\mathrm{J}\mathrm{T}}$ pressure and temperature was compounded, and the temperature rise effect was further calculated using the empirical formula of compounding. The results show that the calculated value of ${\mathrm{\mu }}_{\mathrm{J}\mathrm{T}}$ by using the VDW equation in the low-pressure range (0–2 MPa) is closer to the value in the NIST database with an error less than 0.056 $\mathrm{K}·{\mathrm{M}\mathrm{P}\mathrm{a}}^{-1}$. The tendency of ${\mathrm{\mu }}_{\mathrm{J}\mathrm{T}}$ described by the RK equation corresponds to the NIST database; meanwhile, the maximum error in the SRK equation is 0.143916 $\mathrm{K}·{\mathrm{M}\mathrm{P}\mathrm{a}}^{-1}$. The BB equation is more applicable within the pressure range of 20 to 50 MPa with a maximum error of 0.042853 $\mathrm{K}·{\mathrm{M}\mathrm{P}\mathrm{a}}^{-1}$. The fitting error of the empirical formula is within 9.52%, and the relative error of the calculated temperature rise is less than 4%. This research might provide several technical ideas for the study of the throttling effect of hydrogen refueling stations and the hydrogen circulation system of on-board hydrogen fuel cells. Full article

Maintaining the required relative humidity values in the vehicle cabin is an important HVAC task, along with considerations related to the temperature, velocity, air pressure and noise. Deviation from the optimal values worsens the psycho-physiological state of the driver and affects the energy efficiency of the train. In this study, a model of liquid film formation on and removal from various cabin surfaces was constructed using the fundamental Navier–Stokes hydrodynamic equations. A special transport model based on the liquid vapor diffusion equation was used to simulate the air environment inside the cabin. The evaporation and condensation of surface films were simulated using the Euler film model, which directly considers liquid–gas and gas–liquid transitions. Numerical results were obtained using the RANS equations and a turbulence model by means of the finite volume method in Ansys CFD. Conjugate fields of temperature, velocity and moisture concentration were constructed for various time intervals, and the dependence values for the film thicknesses on various surfaces relative to time were determined. The verification was conducted in comparison with the experimental data, based on the protocol for measuring the microclimate indicators in workplaces, as applied to the train cabin: the average ranges encompassed temperature changes from 11% to 18%, and relative humidity ranges from 16% to 26%. Comparison with the results of other studies, without considering the phase transition and condensation, shows that, for the warm mode, the average air temperature in the cabin with condensation is 12.5% lower than without condensation, which is related to the process of liquid evaporation from the heated walls. The difference in temperature values for the model with and without condensation ranged from −12.5% to +4.9%. We demonstrate that, with an effective mode of removing condensate film from the window surface, including recirculation modes, the energy consumption of the climate control system improves significantly, but this requires a more accurate consideration of thermodynamic parameters and relative humidity. Thus, considering the moisture condensation model reveals that this variable can significantly affect other parameters of the microclimate in cabins: in particular, the temperature. This means that it should be considered in the numerical modeling, along with the basic heat transfer equations. Full article

CO₂ transport is a crucial part of CCUS. Nonetheless, due to the physical property differences between CO₂ and natural gas and oil, CO₂ pipeline transport is distinct from natural gas and oil transport. Gaseous CO₂ transportation has become the preferred scheme for transporting impurity-containing CO₂ tail gas in purification plants due to its advantages of simple technology, low cost, and high safety, which are well suited to the scenarios of low transportation volume and short distance in purification plants. The research on its physical property and state parameters is precisely aimed at optimizing the process design of gaseous transportation so as to further improve transportation efficiency and safety. Therefore, it has important engineering practical significance. Firstly, this paper collected and analyzed the research cases of CO₂ transport both domestically and internationally, revealing that phase state and physical property testing of CO₂ gas containing impurities is the basic condition for studying CO₂ transport. Subsequently, the exhaust gas captured by the purification plant was captured after hydrodesulfurization treatment, and the characteristics of the exhaust gas components were obtained by comparing before and after treatment. By preparing fluid samples with varied CO₂ content and conducting the flash evaporation test and PV relationship test, the compression factor and density of natural gas under different temperatures and pressures were obtained. It is concluded that under the same pressure in general, the higher the CO₂ content, the smaller the compression factor. Except for pure CO_2, the higher the CO₂ content, the higher the density under constant pressure, which is related to the content of C₂ and heavier hydrocarbon components. At the same temperature, the higher the CO₂ content, the higher the viscosity under the same pressure; the lower the pressure, the slower the viscosity growth slows down. The higher the CO₂ content at the same temperature, the higher the specific heat at constant pressure. With the decrease in temperature, the CO₂ content reaching the highest specific heat at the identical pressure gradually decreases. Finally, BWRS, PR, and SRK equations of state were utilized to calculate the compression factor and density of the gas mixture with a molar composition of 50% CO₂ and the gas mixture with a molar composition of 100% CO₂. Compared with the experimental results, the most suitable equation of state is selected as the PR equation, which refers to the parameter setting of critical nodes of CO₂ gas transport. Full article

In this paper, we establish an age-structured SEIAR epidemic model that incorporates media effects and employ the exponential function approach to demonstrate the crucial role of media influence in disease prevention and control. Notably, our model accounts for the possibility of recessive infected individuals becoming dominant through contact with infectious individuals. Theoretical analysis yields the explicit expression for the basic reproduction number $R_0$, which serves as a critical threshold for disease dynamics. Through comprehensive threshold analysis, we investigate the existence and stability of both disease-free and endemic equilibrium states. By applying characteristic equation analysis and the method of characteristics, we establish the following: (1) when $R_0<1$, the disease-free equilibrium is globally asymptotically stable; (2) when $R_0>1$, a unique endemic equilibrium exists and maintains local asymptotic stability under specific conditions. This study shows that strengthening media promotion, raising awareness, and reducing the density of recessive infected individuals can effectively control the further spread of a disease. To validate our theoretical results, we present numerical simulations that quantitatively assess the impact of varying media reporting intensities on epidemic containment measures. These simulations provide practical insights for public health intervention strategies. Full article