Mathematical Modeling Approach Research Articles

Mathematical Modeling Approach and Simulation in Food Drying Applications

Recent developments in the branch of food drying involve advancements in the development of mathematical models [...]

The Development of “Batik Sendang” and Integrated Marketing Communication Strategy using a Mathematical Model Approach

The aim of this research are to ascertain, investigate, and evaluate the degree to which the creation of innovative economic products for Sendang Paciran batik clothing and the use of an integrated marketing communication strategy have an impact on the tourism appeal of Sendang Agung and Sendang Duwur Villages Paciran District. The explanatory survey method is employed in this research. The results of the research show that even though the villages of Sendang Agung and Sendang Duwur Paciran have built an integrated marketing communication plan for creative economic products, more work has to be done on it. This is evident from the responses of the vast majority of respondents who concurred with the posed questions. However, of the four forming parts of integrated marketing communications, public relations, publicity, and advertising are the forming factors with the strongest role and are the ones that have been executed the best.

Sub-inhibitory antibiotic treatment selects for enhanced metabolic efficiency.

Bacterial growth and metabolic rates are often closely related. However, under antibiotic selection, a paradox in this relationship arises: antibiotic efficacy decreases when bacteria are metabolically dormant, yet antibiotics select for resistant cells that grow fastest during treatment. That is, antibiotic selection counterintuitively favors bacteria with fast growth but slow metabolism. Despite this apparent contradiction, antibiotic resistant cells have historically been characterized primarily in the context of growth, whereas the extent of analogous changes in metabolism is comparatively unknown. Here, we observed that previously evolved antibiotic-resistant strains exhibited a unique relationship between growth and metabolism whereby nutrient utilization became more efficient, regardless of the growth rate. To better understand this unexpected phenomenon, we used a simplified model to simulate bacterial populations adapting to sub-inhibitory antibiotic selection through successive bottlenecking events. Simulations predicted that sub-inhibitory bactericidal antibiotic concentrations could select for enhanced metabolic efficiency, defined based on nutrient utilization: drug-adapted cells are able to achieve the same biomass while utilizing less substrate, even in the absence of treatment. Moreover, simulations predicted that restoring metabolic efficiency would re-sensitize resistant bacteria exhibiting metabolic-dependent resistance; we confirmed this result using adaptive laboratory evolutions of Escherichia coli under carbenicillin treatment. Overall, these results indicate that metabolic efficiency is under direct selective pressure during antibiotic treatment and that differences in evolutionary context may determine both the efficacy of different antibiotics and corresponding re-sensitization approaches.IMPORTANCEThe sustained emergence of antibiotic-resistant pathogens combined with the stalled drug discovery pipelines highlights the critical need to better understand the underlying evolution mechanisms of antibiotic resistance. To this end, bacterial growth and metabolic rates are often closely related, and resistant cells have historically been characterized exclusively in the context of growth. However, under antibiotic selection, antibiotics counterintuitively favor cells with fast growth, and slow metabolism. Through an integrated approach of mathematical modeling and experiments, this study thereby addresses the significant knowledge gap of whether antibiotic selection drives changes in metabolism that complement, and/or act independently, of antibiotic resistance phenotypes.

Comparative analysis of standard mathematical modeling approaches to solve Einstein’s field equations in spherically symmetric static background for compact stars

This study examines Einstein’s field equations in the context of general relativity, comparing five distinct methodologies: (a) vanishing complexity, (b) embedding class one or the Karmarkar condition, (c) conformally flat spacetime, (d) conformal killing symmetry, and (e) the Karmarkar scalar condition. The first four methods reveal a significant connection between two metric potentials, while the fifth method provides a coordinate-independent condition expressed in terms of structural scalars. The paper provides a comprehensive comparative analysis of a new exact solution derived by assuming a common metric function and solving the remaining metric functions through corresponding bridge equations to evaluate their effectiveness and validity. Critical parameters such as thermodynamic factors, causality conditions, stability, and mass function analysis are investigated.

Unsupervised Deep Anomaly Detection for Industrial Multivariate Time Series Data

With the rapid development of deep learning, researchers are actively exploring its applications in the field of industrial anomaly detection. Deep learning methods differ significantly from traditional mathematical modeling approaches, eliminating the need for intricate mathematical derivations and offering greater flexibility. Deep learning technologies have demonstrated outstanding performance in anomaly detection problems and gained widespread recognition. However, when dealing with multivariate data anomaly detection problems, deep learning faces challenges such as large-scale data annotation and handling relationships between complex data variables. To address these challenges, this study proposes an innovative and lightweight deep learning model—the Attention-Based Deep Convolutional Autoencoding Prediction Network (AT-DCAEP). The model consists of a characterization network based on convolutional autoencoders and a prediction network based on attention mechanisms. The AT-DCAEP exhibits excellent performance in multivariate time series data anomaly detection without the need for pre-labeling large-scale datasets, making it an efficient unsupervised anomaly detection method. We extensively tested the performance of AT-DCAEP on six publicly available datasets, and the results show that compared to current state-of-the-art methods, AT-DCAEP demonstrates superior performance, achieving the optimal balance between anomaly detection performance and computational cost.

Exploring the impact of how criminals interact with cyber-networks—a mathematical modeling approach

Exploring the impact of how criminals interact with cyber-networks—a mathematical modeling approach

Mathematical Modeling Approach to the Optimization of Biomass Storage Park Management

This paper addresses the critical issue of managing biomass parks, a key component in the shift towards sustainable energy sources. The research problem centers on optimizing the management of these parks to enhance production and economic viability. Our aim was to bridge the gap in current research by developing and applying mathematical models tailored for biomass park management. The study commenced by constructing a basic model based on assumptions such as uniform biomass and steady input rates. Progressing from this initial model, we explored sophisticated control strategies, including Pontryagin’s maximum principle and dynamic programming, and employed numerical methods to tackle the nonlinearities and complexities inherent in biomass management. Our approach’s scope extended to predicting and managing biomass flow, highlighting each method’s distinct advantages. The simple model laid the groundwork for understanding, while optimal control techniques revealed the system’s intricate dynamics. The numerical methods provided practical solutions to complex equations. We found that while each method is beneficial on its own, their combined use can significantly improve decision-making in biomass park management. This research emphasizes the importance of aligning the chosen method with specific operational challenges and desired outcomes for optimal efficacy, offering both theoretical insights and practical applications in the field of renewable energy management.

Modeling of Shear Flows over Superhydrophobic Surfaces: From Newtonian to Non-Newtonian Fluids.

The design and use of superhydrophobic surfaces have gained special attentions due to their superior performances and advantages in many flow systems, e.g., in achieving specific goals including drag reduction and flow/droplet handling and manipulation. In this work, we conduct a brief review of shear flows over superhydrophobic surfaces, covering the classic and recent studies/trends for both Newtonian and non-Newtonian fluids. The aim is to mainly review the relevant mathematical and numerical modeling approaches developed during the past 20 years. Considering the wide ranges of applications of superhydrophobic surfaces in Newtonian fluid flows, we attempt to show how the developed studies for the Newtonian shear flows over superhydrophobic surfaces have been evolved, through highlighting the major breakthroughs. Despite the fact that, in many practical applications, flows over superhydrophobic surfaces may show complex non-Newtonian rheology, interactions between the non-Newtonian rheology and superhydrophobicity have not yet been well understood. Therefore, in this Review, we also highlight emerging recent studies addressing the shear flows of shear-thinning and yield stress fluids in superhydrophobic channels. We focus on reviewing the models developed to handle the intricate interaction between the formed liquid/air interface on superhydrophobic surfaces and the overlying flow. Such an intricate interaction will be more complex when the overlying flow shows nonlinear non-Newtonian rheology. We conclude that, although our understanding on the Newtonian shear flows over superhydrophobic surfaces has been well expanded via analyzing various aspects of such flows, the non-Newtonian counterpart is in its early stages. This could be associated with either the early applications mainly concerning Newtonian fluids or new complexities added to an already complex problem by the nonlinear non-Newtonian rheology. Finally, we discuss the possible directions for development of models that can address complex non-Newtonian shear flows over superhydrophobic surfaces.

Review of Mathematical Modeling Research: A Descriptive Content Analysis Study

Recently, mathematical models and modeling practices have become popular in associating mathematics with real-life problems and, hence understanding this relationship. Accordingly, the mathematical modeling skill has been adopted in the standards and by researchers. Understanding the use of mathematical modeling in the learning and teaching processes of mathematics education will contribute to the future of the field. This study aimed to review the trends in mathematical modeling literature using leading research studies. This study reviewed the various types of studies indexed in the Web of Science database between 2000 and 2021 regarding how they addressed modeling. As well as mathematical modeling approaches used, the studies were reviewed in terms of basic characteristics such as publication year, sample, and research method. We evaluated studies using a form developed by the researchers, and the study revealed an increase in the number of studies over the years, and the studies were conducted mostly with pre-service teachers. In addition, we observed that research studies employed mostly small samples to closely monitor the modeling process.

Logistic Model for Predicting Coliform Growth in Wastewater Effluent From the Chambo River (Ecuador)

Purpose: The objective of this work is to apply a predictive model of bacterial growth to determine the concentration of total coliforms, under controlled laboratory conditions, in wastewater from the city of Riobamba that flows into the Chambo River (Ecuador). Theoretical Framework: Wastewater pollution is a global problem that affects water quality and public health. Population growth has a drastic impact on the contamination of water bodies, particularly in Ecuador, since most of the effluents are not adequately treated, which becomes a public health and environmental problem. For this reason, over the years, total and fecal coliforms have been used as indicators of water quality. Design/Methodology/Approach: The study used a mathematical modeling approach of a logistic and deterministic type, and calculated through an executable command designed in the integrated development environment (IDE) with the Visual C# programming language (logic) and the XAML design language (interface). Findings: The results achieved are 1) the theoretical construction of a mathematical model (logistic model) starting from a differential equation and the taking of three experimental measurements, 2) the computer construction of the bacterial growth model and 3) it has been demonstrated that there is agreement between the values obtained from the model of total coliform growth and the experimental results with a margin of error of less than 1%. Research, Practical & Social Implications: This information can be used by stakeholders to determine actions that could improve current conditions. Originality/Value: The result of this study emphasizes that the model proposed can reproduce the growth of coliforms up to a maximum growth point, it is necessary to continue with the development of the same in the stationary phase of bacterial growth and then in the decay phase.

Logistic Model for Predicting Coliform Growth in Wastewater Effluent From the Chambo River (Ecuador)

Purpose: The objective of this work is to apply a predictive model of bacterial growth to determine the concentration of total coliforms, under controlled laboratory conditions, in wastewater from the city of Riobamba that flows into the Chambo River (Ecuador). Theoretical Framework: Wastewater pollution is a global problem that affects water quality and public health. Population growth has a drastic impact on the contamination of water bodies, particularly in Ecuador, since most of the effluents are not adequately treated, which becomes a public health and environmental problem. For this reason, over the years, total and fecal coliforms have been used as indicators of water quality. Design/Methodology/Approach: The study used a mathematical modeling approach of a logistic and deterministic type, and calculated through an executable command designed in the integrated development environment (IDE) with the Visual C# programming language (logic) and the XAML design language (interface). Findings: The results achieved are 1) the theoretical construction of a mathematical model (logistic model) starting from a differential equation and the taking of three experimental measurements, 2) the computer construction of the bacterial growth model and 3) it has been demonstrated that there is agreement between the values obtained from the model of total coliform growth and the experimental results with a margin of error of less than 1%. Research, Practical & Social Implications: This information can be used by stakeholders to determine actions that could improve current conditions. Originality/Value: The result of this study emphasizes that the model proposed can reproduce the growth of coliforms up to a maximum growth point, it is necessary to continue with the development of the same in the stationary phase of bacterial growth and then in the decay phase.

Transmission Dynamics of Monkeypox Virus With Age‐Structured Human Population: A Mathematical Modeling Approach

This study presents a deterministic mathematical model of monkeypox disease transmission dynamics with an age‐structured human population divided into two subgroups of children (Group 1) and adults (Group 2). Two equilibrium points, monkeypox‐free, E0, and a unique monkeypox‐endemic equilibrium point, E1, are established. The age‐structured monkeypox basic reproduction number, ℝ0, is computed using the next‐generation matrix approach and established to be ℝ0 = 1.2448. The Lyapunov functions are constructed; together with LaSalle’s invariance principle, the monkeypox‐free equilibrium point, E0, is established to be globally asymptotically stable whenever ℝ0 ≤ 1, as confirmed by the Lyapunov stability method, and the monkeypox‐endemic equilibrium point, E1, is globally asymptotically stable whenever ℝ0 > 1. Sensitivity analysis of the threshold quantity ℝ0 is performed using the Latin hypercube sampling method and Pearson’s partial rank correlation coefficient, and the results showed that the parameters β11, β22, μ, ν1, Λ1, ν2 were the most sensitive to the spread of monkeypox infection in an age‐structured population. It is, therefore, suggested that the rate of monkeypox infection can be reduced by ensuring that the rate of interaction between susceptible children and infected children and between susceptible adults and infected adults is minimized. Moreover, the spread of monkeypox infection can be curbed by emphasizing controls such as early diagnosis and treatment and hospitalization of critically ill infectives.

Dynamical analysis of COVID-19 and tuberculosis co-infection using mathematical modelling approach

<abstract><p>Both tuberculosis (TB) and COVID-19 are infectious diseases with similar clinical manifestations, which mainly affect the lungs. Clinical studies have revealed that the immunosuppressive drugs taken by COVID-19 patients can affect the immunological functions in the body, which can cause the patients to contract active TB via a new infection or reinfection, and the co-infection of the two diseases portends a clinical complexity in the management of the patients. Thus, this paper presents a mathematical model to study the dynamics and control of COVID-19-TB co-infection. The full model of the co-infection is split into two submodels, namely, the TB-only and the COVID-19-only models. The equilibria of the disease-free and endemic situations of the two sub-models are shown to be globally asymptotically stable when their control reproduction numbers $ R_{o}^{TV}, R_{o}^{CV} < 1 $ and $ \tilde {R}_{o}^{TV}, \tilde {R}_{o}^{CV} > 1 $, respectively. However, the disease-free equilibrium of the co-infection model was found to lose its global stability property when the reproduction number $ R_{o}^{F} < 1 $, therefore exhibiting a backward bifurcation. Uncertainty and sensitivity analysis of the associated reproduction number of the full model has been performed by using the Latin hypercube sampling/Pearson rank correlation coefficient (LHS/PRCC) method. The rate of transmission of COVID-19 and the proportions of individuals vaccinated with Bacillus Calmette-Guérin (BCG) and against COVID-19 were found to be highly significant in the spread and control of COVID-19-TB co-infection. Furthermore, the simulation results show that decreasing the COVID-19 transmission rate and increasing the proportion of people vaccinated with BCG and against COVID-19 can lower the number of cases of COVID-19-TB co-infection. Therefore, measures to reduce the transmission rate and the provision of adequate resources to increase the proportions of people vaccinated against TB and COVID-19 should be implemented to minimize the cases of co-infection.</p></abstract>

Enhancing cooking banana preservation: A mathematical model approach

Enhancing cooking banana preservation: A mathematical model approach

Leveraging Guerrilla Intelligence Gathering Technique for Optimal Counterterrorism Operations: A Mathematical Perspective

The research aims to explore the potential of leveraging guerrilla intelligence techniques for the optimization of counterterrorism (CT) operations, by taking a mathematical modeling approach. This study focuses on undermining the structural dynamics of a hierarchically structured terrorist organization consisting of three distinct classes of operatives: leaders, foot-soldiers, and recruiters. By developing a mathematical framework, this research seeks to provide insights into disrupting the operational capabilities and effectiveness of such organizations. The study began with analysis of the organization’s hierarchical structure, recognizes the critical roles played by each class of operatives in the evolution of terrorist activities. Leaders provide strategic guidance, foot-soldiers execute operations, and recruiters facilitate the expansion and replenishment of the organization's ranks. Understanding the interactions and dependencies among these classes is crucial for formulating effective CT strategies. Drawing inspiration from guerrilla intelligence gathering techniques, we formulated a system of differential equation model to capture the dynamics of the organization's structure. The model incorporates variables representing the population sizes of the three operatives’ class, as well as the rates of recruitment, promotion, commission, attrition, and defection. By considering these factors, the model aims to assess the impact of different strategies on the organization's viability and resilience. Furthermore, the research investigates the necessary and sufficient strategies for disrupting the organizational structure, - targeting at least two classes of operatives simultaneously. It also explores the effects of intelligence gathering, and the sabotaging effect of “syndromnized intelligence optimizing pseud-terrorist” (SIOP) agents. This allows for the evaluation of various scenarios and strategies, enabling the identification of optimal approaches to undermine the organization's structural dynamics. The study also recognizes the complex nature of terrorist organizations, including their adaptability and resilience. As such, we incorporated elements of organizational resilience evaluations. By considering the organization's response to CT efforts, the study aims to inform strategies that can effectively counteract potential recalcitrant operatives. The results of the analyses shows that the infiltration of at least 5% SIOP agents in a given “enemy-centric” CT environment has the potential to boost attrition accuracy by 60%, internal personnel defection (IPD) by 25%, vulnerability index by 81.71 %, and operational efficiency by 81.91%. Specifically, targeting all three classes of operatives simultaneously under this optimal CT option would yield 96.48% efficiency than other strategies. This level of interdiction is necessary and sufficient to optimally degrade a given organization to extinction within a period of 10 years, as well as inhibiting any propensity of sudden future strength resurgence. The targeting at least two classes of operative simultaneously was also highlighted and appraised empirically, to be necessary and sufficient for undermining the ingenious bureaucratic structure, high popularity and self-enforcing equilibrium that drive the resilience characteristics of most contemporary organizations. The outcomes of this study have significant implications for CT operations and policy formulation. By leveraging the insights gained from the model, decision-makers can develop targeted and evidence-based approaches to disrupt terrorists’ hierarchically structures. Ultimately, the findings from this study can contribute to enhancing the effectiveness of CT efforts, leading to improved security and stability in affected regions. In conclusion, this research proposes a mathematical model to explore the optimization of CT operations by leveraging guerrilla intelligence technique.

Analysis of the Strategic Value of Electric Vehicles Based on Mathematical Modeling Approach

Analysis of the Strategic Value of Electric Vehicles Based on Mathematical Modeling Approach

A research on mathematical model approaches in biomass supply chain

A research on mathematical model approaches in biomass supply chain

Enhancing efficiency and adaptability in mixed model line balancing through the fusion of learning effects and worker prerequisites

This research introduces a comprehensive scheme to tackle the Mixed-Model Assembly Line Balancing Problem (MALBPLW) within manufacturing contexts. The primary aim is to optimize assembly line task assignments by integrating both the learning effect and worker prerequisites. The learning effect recognizes the enhanced efficiency of workers over time due to learning and experience. A novel mathematical model and solution approach are proposed, encompassing factors like cycle time, task interdependencies, worker classifications, and the learning effect. The model endeavors to minimize the overall costs related to both workers and workstations while simultaneously maximizing production efficiency. Experimental assessments are conducted to evaluate the efficacy of this proposed approach. Diverse manufacturing scenarios are inspected, comparing and analyzing cost reductions and production efficiency. The outcomes highlight the effectiveness of this approach in achieving enhanced cost-effectiveness and resource utilization in contrast to conventional methods. This study contributes significantly to advancing assembly line balancing and production planning techniques by presenting a pragmatic framework for optimizing resource usage and reducing costs in manufacturing environments. The knowledge extracted from these discoveries can significantly assist professionals in the industry seeking to improve manufacturing processes and strengthen competitiveness.

Mathematical modelling and mechanics approaches in investigation of structural failure causes

An approach has been proposed for analyzing the causes of failure of parts, which is based on the use of mathematical modeling in calculating mechanical loads and strength parameters by finite-element analysis, followed by an assessment of the durability of the structure using methods of mechanics of damaged media that take into account the accumulation of structural defects in the material of products. The developed approach was used to calculate critical loads that led to the destruction of the crankshaft of a passenger car engine, and to establish the reasons for their appearance, and also allowed to propose technical solutions to eliminate such emergency situations.

Evolutionary dynamics of glucose-deprived cancer cells: insights from experimentally informed mathematical modelling.

Glucose is a primary energy source for cancer cells. Several lines of evidence support the idea that monocarboxylate transporters, such as MCT1, elicit metabolic reprogramming of cancer cells in glucose-poor environments, allowing them to re-use lactate, a by-product of glucose metabolism, as an alternative energy source with serious consequences for disease progression. We employ a synergistic experimental and mathematical modelling approach to explore the evolutionary processes at the root of cancer cell adaptation to glucose deprivation, with particular focus on the mechanisms underlying the increase in MCT1 expression observed in glucose-deprived aggressive cancer cells. Data from in vitro experiments on breast cancer cells are used to inform and calibrate a mathematical model that comprises a partial integro-differential equation for the dynamics of a population of cancer cells structured by the level of MCT1 expression. Analytical and numerical results of this model suggest that environment-induced changes in MCT1 expression mediated by lactate-associated signalling pathways enable a prompt adaptive response of glucose-deprived cancer cells, while fluctuations in MCT1 expression due to epigenetic changes create the substrate for environmental selection to act upon, speeding up the selective sweep underlying cancer cell adaptation to glucose deprivation, and may constitute a long-term bet-hedging mechanism.