Mathematical Modeling Approach Research Articles

Mathematical Modelling Approaches for Integrated Single Machine Scheduling and Electric Vehicle Routing Problem

Mathematical Modelling Approaches for Integrated Single Machine Scheduling and Electric Vehicle Routing Problem

A Systematic Review of Sustainable Supply Chain Network Design: Optimization Approaches and Research Trends

In response to the ever-increasing pursuit of competitiveness among organizations in today’s global business landscape, the subject of supply chain management has become a vital domain encompassing a wide range of sectors and industries across the economy. The growing concern about sustainable development has prompted public and private supply chain players to incorporate the three pillars of sustainability, namely, economic, environmental, and social, into the design of their supply chain networks. This study reviews and examines the content of 102 relevant papers to discuss the mathematical models, modeling approaches, and solutions that have been explored in the existing literature on forward sustainable supply chain network design. This paper also investigates the sustainability elements and supply chain network peculiarities including design factors and decision levels. In this review, several limitations in the current literature on sustainable supply chain network design optimization models are highlighted. According to the analysis, it was found that a better understanding of the industry and its sustainability requirements and priorities is essential for designing sustainable supply chain networks that are tailored to the needs of a specific industry rather than achieving general sustainability objectives. In addition, integrating strategic, tactical, and operational decision levels in the design of supply chain networks is critical for evaluating their impact on each other in terms of sustainability. More sophisticated mathematical solution methods for dealing with real-life scenarios including nonlinearity and uncertainty sources are required. The paper concludes with new prospects of research to promote a better integration of sustainability into supply chain networks.

Flight dynamic modeling and stability of a small-scale side-by-side helicopter for Urban Air Mobility

This paper aims to explore the development of a flight dynamics model for a small-scale side-by-side helicopter and describe its trim and stability characteristics. The helicopter is considered a suitable candidate for Urban Air Mobility (UAM) solutions, because of its reliable design and low noise characteristics, but still very small knowledge is present on the mathematical modeling approaches and dynamic properties. A 14 degrees of freedom nonlinear mathematical model is developed and semi-analytical models are employed to account for the presence of the shrouds. An iterative trim routine is developed and applied with a suitable control mix that allows the use of classic helicopter controls. To control the vertical speed and roll rate, the paper assumes an equal collective pitch and lateral cyclic in the two rotors, while a uniform plus a differential longitudinal cyclic is adopted for pitch and yaw maneuvers. The paper discusses unique characteristics of the side-by-side configuration as obtained from the stability analysis: an unstable high-frequency mode, governed by the vertical velocity and pitch angle arises when the center of gravity (CG) of the vehicle is aligned or placed in front of the two main rotors. Similarly, both lateral phugoid and roll subsidence modes are sensitive to the CG location. The side-by-side configuration presents also a stable spiral mode which needs to be carefully designed.

CNS Viral Infections-What to Consider for Improving Drug Treatment: A Plea for Using Mathematical Modeling Approaches.

Neurotropic viruses may cause meningitis, myelitis, encephalitis, or meningoencephalitis. These inflammatory conditions of the central nervous system (CNS) may have serious and devastating consequences if not treated adequately. In this review, we first summarize how neurotropic viruses can enter the CNS by (1) crossing the blood-brain barrier or blood-cerebrospinal fluid barrier; (2) invading the nose via the olfactory route; or (3) invading the peripheral nervous system. Neurotropic viruses may then enter the intracellular space of brain cells via endocytosis and/or membrane fusion. Antiviral drugs are currently used for different viral CNS infections, even though their use and dosing regimens within the CNS, with the exception of acyclovir, are minimally supported by clinical evidence. We therefore provide considerations to optimize drug treatment(s) for these neurotropic viruses. Antiviral drugs should cross the blood-brain barrier/blood cerebrospinal fluid barrier and pass the brain cellular membrane to inhibit these viruses inside the brain cells. Some antiviral drugs may also require intracellular conversion into their active metabolite(s). This illustrates the need to better understand these mechanisms because these processes dictate drug exposure within the CNS that ultimately determine the success of antiviral drugs for CNS infections. Finally, we discuss mathematical model-based approaches for optimizing antiviral treatments. Thereby emphasizing the potential of CNS physiologically based pharmacokinetic models because direct measurement of brain intracellular exposure in living humans faces ethical restrictions. Existing physiologically based pharmacokinetic models combined with in vitro pharmacokinetic/pharmacodynamic information can be used to predict drug exposure and evaluate efficacy of antiviral drugs within the CNS, to ultimately optimize the treatments of CNS viral infections.

PIEZO1 regulates leader cell formation and cellular coordination during collective keratinocyte migration.

The collective migration of keratinocytes during wound healing requires both the generation and transmission of mechanical forces for individual cellular locomotion and the coordination of movement across cells. Leader cells along the wound edge transmit mechanical and biochemical cues to ensuing follower cells, ensuring their coordinated direction of migration across multiple cells. Despite the observed importance of mechanical cues in leader cell formation and in controlling coordinated directionality of cell migration, the underlying biophysical mechanisms remain elusive. The mechanically-activated ion channel PIEZO1 was recently identified to play an inhibitory role during the reepithelialization of wounds. Here, through an integrative experimental and mathematical modeling approach, we elucidate PIEZO1's contributions to collective migration. Time-lapse microscopy reveals that PIEZO1 activity inhibits leader cell formation at the wound edge. To probe the relationship between PIEZO1 activity, leader cell formation and inhibition of reepithelialization, we developed an integrative 2D continuum model of wound closure that links observations at the single cell and collective cell migration scales. Through numerical simulations and subsequent experimental validation, we found that coordinated directionality plays a key role during wound closure and is inhibited by upregulated PIEZO1 activity. We propose that PIEZO1-mediated retraction suppresses leader cell formation which inhibits coordinated directionality between cells during collective migration.

Strategic Planning and Ecological Safety Evaluation of University Campuses on Green Marketing Principles

Strategic planning of university campuses (UC) aims to harmonize nature, humans, and architectural complexes, enhancing the positive university image through specialized green and recreation zones. Highly urbanized UC areas, particularly with nearby roads, encounter increased technogenic load and pose additional health hazards. The purpose of the paper is the evaluation of the environmental safety level of the UC recreational territories on the example of campuses of Kyiv universities, located nearby highly loaded roads, using a complex of express methods of analysis, mathematical modeling and criterion-based approach, considering the main green economy principles. The scientific novelty of the paper and the authors’ contribution is in the assessment of the environmental safety level of city-type UC recreational territories being under the significant technogenic load from vehicle emissions. Such express analysis methods as densimetry, viscometry, stalagmometry, conductometry, potentiometry and optical methods, and in particular, refractometric studies have been used to assess the impact of vehicle emissions. The mathematical modeling and computational experiment have been carried out for dispersion fields of the main vehicle emissions pollutants. Ecologically acceptable distances from the road considering the specifics of recreational territory have been determined using the integral index of technogenic load. Propositions for minimizing human health hazards and improving the system of environmental monitoring of such territories have been provided and substantiated. The study also confirms the positive effects of environmental management and green marketing principles synergy, benefiting both nature and humans as well as the university image. Obtained results can be used for the design and reconstruction of UC and their recreational areas, as well as for planning roads located nearby the campuses, improving traffic on them. It is also convenient to foresee the enhancement of the environmental activities in the student research work and create student communities for monitoring the UC environmental state and the development of eco-startup projects.

Understanding the spread of typhoid fever: Combining vaccination and sanitation methods for better public health policies

Typhoid fever remains a major public health concern, affecting over nine million individuals globally each year. Mathematical modeling approaches can provide valuable insights into typhoid transmission dynamics and inform preventive strategies. In this study, we developed a compartmental model incorporating key features of typhoid epidemiology and two crucial interventions: vaccination and sanitation practices. The model stratifies the population into susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered compartments and tracks the bacterial load in the environment. We established a disease-free equilibrium and basic reproduction number R0. We also identified the endemic equilibrium and analyzed its existence. Numerical simulations demonstrated the critical impact of enhanced sanitation and vaccination in curtailing infections. Our model underscores the need for multifaceted control measures that encompass vaccine coverage, sanitation enforcement, and healthcare capacity building to mitigate typhoid in high-risk regions. This study provides a comprehensive framework to model the intricate transmission dynamics of typhoid fever, supporting informed public health policies and decision-making.

A fractional mathematical model approach on glioblastoma growth: tumor visibility timing and patient survival

In this paper, we introduce a mathematical model given by
 \begin{equation}
 { }^c \mathfrak{D}_t^\alpha u = \nabla \cdot \mathrm{D} \nabla u + \rho f(u) \quad \text{in } \Omega,
 \end{equation}
 where $f(u)=\frac{1}{1-u/\mathrm{K}}, \, u/\mathrm{K} \neq 1, \, \mathrm{K} > 0$, to enhance established mathematical methodologies for better understanding glioblastoma dynamics at the macroscopic scale. The tumor growth model exhibits an innovative structure even within the conventional framework, including a proliferation term, $f(u)$, presented in a different form compared to existing macroscopic glioblastoma models. Moreover, it represents a further refined model by incorporating a calibration criterion based on the integration of a fractional derivative, $\alpha$, which differs from the existing models for glioblastoma. Throughout this study, we initially discuss the modeling dynamics of the tumor growth model. Given the frequent recurrence observed in glioblastoma cases, we then track tumor mass formation and provide predictions for tumor visibility timing on medical imaging to elucidate the recurrence periods. Furthermore, we investigate the correlation between tumor growth speed and survival duration to uncover the relationship between these two variables through an experimental approach. To conduct these patient-specific analyses, we employ glioblastoma patient data and present the results via numerical simulations. In conclusion, the findings on tumor visibility timing align with empirical observations, and the investigations into patient survival further corroborate the well-established inter-patient variability for glioblastoma cases.

A mathematical modeling approach to analyzing and addressing customer service inefficiencies in an international company

This paper presents a novel and in-depth mathematical approach to analyzing the inefficiencies and shortcomings of customer service in an international company based in China. By employing advanced mathematical concepts such as set theory, graph theory, probability theory, and stochastic processes, we develop a comprehensive and multi-faceted model that captures the various aspects of customer service, including unfairness, bureaucracy, failure to perform duties, irresponsibility, untruthfulness, and untrustworthiness. Our findings suggest that these issues are deeply rooted in the company's organizational structure and culture, and we propose potential solutions to address these problems. We also introduce new mathematical techniques, such as the use of hypergraphs and multi-objective optimization, to provide a more nuanced understanding of the complex dynamics at play within the customer service department.

Quantifying in vitro B. anthracis growth and PA production and decay: a mathematical modelling approach

Protective antigen (PA) is a protein produced by Bacillus anthracis. It forms part of the anthrax toxin and is a key immunogen in US and UK anthrax vaccines. In this study, we have conducted experiments to quantify PA in the supernatants of cultures of B. anthracis Sterne strain, which is the strain used in the manufacture of the UK anthrax vaccine. Then, for the first time, we quantify PA production and degradation via mathematical modelling and Bayesian statistical techniques, making use of this new experimental data as well as two other independent published data sets. We propose a single mathematical model, in terms of delay differential equations (DDEs), which can explain the in vitro dynamics of all three data sets. Since we did not heat activate the B. anthracis spores prior to inoculation, germination occurred much slower in our experiments, allowing us to calibrate two additional parameters with respect to the other data sets. Our model is able to distinguish between natural PA decay and that triggered by bacteria via proteases. There is promising consistency between the different independent data sets for most of the parameter estimates. The quantitative characterisation of B. anthracis PA production and degradation obtained here will contribute towards the ambition to include a realistic description of toxin dynamics, the host immune response, and anti-toxin treatments in future mechanistic models of anthrax infection.

A Risk-Structured Model for the Transmission Dynamics of Anthrax Disease

Anthrax, a zoonotic disease with serious public health consequences, has been the subject of rigorous mathematical and statistical modeling to better understand its dynamics and to devise effective control techniques. In this study, we propose a novel mathematical risk-structured model for anthrax disease spread that includes both qualitative and quantitative evaluations. Our research focuses on the complex interplay between host–anthrax interactions and zoonotic transmission. Our mathematical approach incorporates bifurcation analysis and stability considerations. We investigate the dynamic behavior of the proposed model under various settings, shedding light on the important parameters that determine anthrax transmission and persistence. The normalized forward sensitivity analysis method is used to determine the parameters that are relevant to reducing Rc and, by extension, disease spread. Through scenario simulation of our model, we identify intervention techniques, such as enlightenment of the populace, that will effectively minimize disease transmission. Our findings provide insights into anthrax epidemiology and emphasize the importance of effective disease management. Bifurcation investigations reveal the existence and stability of numerous equilibria, allowing for a better understanding of the behavior of the system under various scenarios. This study adds to the field of anthrax modeling by providing a foundation for informed decision-making regarding public health measures. The use of a mathematical modeling approach improves our ability to anticipate and control anthrax epidemics, ultimately helping to protect both human and animal populations.

Collaboration of thermal sensors and drones in fighting wildfires; Mathematical model and heuristic approach

The forest temperature is monitored utilizing thermal sensors. In the event of a temperature increase, these sensors promptly notify firefighters, enabling timely intervention against fires. Drones offer a potential solution for fire containment by swiftly addressing them in their nascent stages, as identified by temperature fluctuations detected by these sensors. Alternatively, if left unchecked, the situation may necessitate protracted aerial operations like the deployment of fixed-wing air tankers, helicopters, smokejumpers, and rappellers. Regrettably, such measures consume invaluable time that could be better spent combating the blaze. Recent literature on wildfires underscores the significance of collaborative approaches and the seamless integration of contemporary technologies in mitigating the expenses associated with forest fires. This study builds upon the temperature data acquired through thermal sensors to propose an all-encompassing mathematical framework designed to identify and facilitate the early extinguishment of fires using drones. The initial step involves formulating the problem through a mixed-integer linear programming model. To solve the model within expansive dimensions, a heuristic approach inspired by Clark and Wright is posited. The efficacy of this algorithm is gauged through the resolution of diverse scenarios. Promisingly, the results show the viability of collaboration of thermal sensors and drones to accurately pinpoint and extinguish forest fires. The outcomes underscore not only the protective capabilities of the suggested methodology but also its cost-effectiveness. Moreover, the approach's pioneering nature is underscored as it offers a fiscally prudent strategy that rapidly curbs uncontrollable fires.

The analysis of a novel COVID-19 model with the fractional-order incorporating the impact of the vaccination campaign in Nigeria via the Laplace-Adomian Decomposition Method

This study underscores the crucial role of COVID-19 vaccinations in managing the pandemic, with a specific focus on Nigeria. Employing a fractional-order mathematical modeling approach, the research assesses vaccination efficacy, minimum effectiveness, and duration. The model’s numerical solution is derived through the Laplace Adomian Decomposition Method (LADM), utilizing rapidly converging infinite series. Simulation results illustrate the impact of COVID-19 transmission and vaccination rates. The study concludes that implementing a vaccination strategy in an integer order proves to be the most effective approach to controlling the spread of COVID-19. These findings have significant implications for researchers, policymakers, and healthcare workers. They emphasize the central role of fractional calculus in facilitating vaccine implementation in the ongoing battle against COVID-19. The study calls for global efforts to maximize vaccination implementation for the overall benefit of public health.

Fuzzy Modeling Framework Using Sector Non-Linearity Techniques for Fixed-Wing Aircrafts

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed-wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprising fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed-wing aircraft systems. Here, the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity red techniques to recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models, like parallel and non-parallel distributed compensation control laws using linear matrix inequality optimization, enables the development of control algorithms that guarantee stability conditions for a wide range of operations points, avoiding the classical gain scheduling schemes, where the stability issues can be extremely challenging.

Propagation of solitary waves in origami-inspired metamaterials

We propose a design strategy for creating origami-like mechanical metamaterials with diverse non-linear mechanical properties and capable of remote actuation. The proposed triangulated cylindrical origami (TCO)-inspired metamaterials enable the highly desirable strain-softening/hardening and snap-through behaviors via a multi-material and highly deformable hinge design. Moreover, we couple these novel non-linear mechanical properties of the TCO origami-inspired metamaterials with the transformative ability of hard-magnetic active materials, allowing for untethered shape- and property-actuation in the developed metamaterials. We develop a mathematical modeling framework for the proposed TCO origami-inspired metamaterials, building on approximating the highly deformable hinges as a combination of longitudinal and rotational springs. We validate the accuracy of the developed mathematical modeling approach by comparing the analytically predicted compressive response of a unit cell structure with the corresponding numerical and experimental results. Using the developed mathematical modeling framework, we investigate the magnetic field-induced large deformation and superimposed solitary wave propagation in the TCO origami-inspired metamaterial system. We show that the proposed metamaterial allows us to tune the key characteristics of the enabled non-linear solitary waves, including their characteristic width and amplitude. The proposed design strategy for readily manufacturable origami-inspired metamaterial systems paves a novel path for practical engineering applications. Our studies also underscore the potential of magneto-mechanical interaction in the design of reconfigurable metamaterial systems with superior non-linear mechanical and elastic wave properties.

A Comparative Study on Various ANN Optimization Algorithms for Magnetorheological Elastomer Carbonyl Iron Particle Concentration Estimation

Estimation particle composition such as particle shape, size, and concentration are crucial prior to the fabrication process of magnetorheological elastomer (MRE) to avoid process repetition due to inaccurate formulation. Currently, most of MRE prediction model were purposely used to predict the rheological properties such as shear stress and dynamic modulus, known as forward model. Nonetheless, very few studies have been reported to be capable able of predicting particle composition particularly in MR materials, which known as inverse model. Therefore, this paper proposed a carbonyl iron particle (CIP) concentration based MRE prediction model using neural network algorithm. Neural network-based machine learning model is more approachable compared to conventional mathematical modelling approach due to easily identify trends and pattern while handling multi-variety data. Various optimization algorithms have been employed such as Adam, RMSprop, SGD, AdaGrad, and Nadam throughout the modelling process. As the results, given shear strain amplitude, magnetic flux density, storage modulus, and loss factor as model input, SGD gave the maximum prediction accuracy with 0.95 and 3.038 MPa of R2 and RMSE, respectively. Hence, this model can be the basis to the MRE material and devices development particularly as the tool to reduce costing and time consuming.

Assessing the impact of information-induced self-protection on Zika transmission: A mathematical modeling approach

Abstract As per the World Health Organization’s (WHO’s) suggestions, personal protection via adopting precautionary measures is one of the most effective control aspects to avoid Zika infection in the absence of suitable medical treatment. This personal protection further can be enhanced and explored by propagating information about disease prevalence. Therefore, in this study, we wish to see the effect of information on Zika transmission by formulating a compartmental mathematical model that quantifies the effect of an individual’s behavioral response as self-protection due to information. Furthermore, the basic reproduction number was calculated using the next-generation matrix technique. The model analysis was carried out to determine the local and global stability properties of equilibrium points. In addition, the model shows the occurrence of forward bifurcation when the reproduction number crosses unity. To understand the impact of various model parameters, we conducted a sensitivity analysis using both the normalized sensitivity index and the partial rank correlation coefficient methods. Moreover, we performed numerical simulations to assess the influence of important parameters on the model’s behavior for Zika prevalence. Our study accentuates that as information-induced self-protection increases, the prevalence of Zika infection will be at a very minimum level, and this observation is in line with WHO suggestions.

Assessing botanical compatibility in gin production: A mathematical model and network analysis approach

This study introduces a novel methodology for evaluating volatile-compound-based compatibility in 160 botanicals essential for gin production. It establishes a comprehensive botanical pairing system through network analysis, mathematical modeling, and indicator development. Key findings include the benefits of strategic botanical inclusions to recipes for compatibility improvement and a numerical compatibility assessment, revealing an average indicator of 1.78 across thirty validated gin recipes, with a significant threshold at 1.36 indicating superior compatibility. Additionally, two distinct indicators were formulated—one focusing on the percentage of shared compounds due to a specific botanical and another on the botanical’s representation in the recipe. A visual network analysis replaces the traditional aroma classification wheel, offering a comprehensive view of aromatic profiles. This research transforms gin formulation, supported by an extensive database and validated methods.

A Deep Neural Network-Fused Mathematical Modeling Approach for Reliable Flight Control of Small Unmanned Aerial Vehicles

In order to ensure the flight safety of small unmanned aerial vehicles (UAVs), a deep neural network-fused mathematical modeling approach is put up for reliable flight control of small UAVs. First, engine torque, thrust eccentricity and initial stop angle are taken into full consideration. A six-degree-of-freedom nonlinear model is formulated for small UAVs, concerning both ground taxiing and air flight status. Then, the model was linearized using the principle of small disturbances. The linearized model expressions for both ground taxiing and air flight were provided. In addition, radial basis function neural networks are used for online approximation to address the nonlinearity and uncertainty caused by changes in aircraft aerodynamic parameters. At the same time, to compensate for the external disturbance and the approximation error of the neural network, the system robustness is improved by selecting reasonable design parameters. This helps the whole flight control system obtain better tracking control performance. At last, some simulation experiments are carried out to evaluate the performance of the proposed mathematical modeling framework. The simulation results show that the proposal has stronger convergence ability, smaller prediction error, and better performance. Thus, proper proactivity can be acknowledged.

Novel mathematical modelling approaches and a new lower bounding scheme for multi-manned assembly line balancing problems with walking workers

This article suggests two novel mathematical modelling approaches and a lower bound calculation method for the number of workstations to balance multi-manned assembly lines with walking workers. While new formulations include more variables, they require fewer constraints than the existing one. The performances of all formulations are compared each other using benchmark test instances from the literature as well as the instances produced in this study. Comparison results showed that one of novel modelling approaches exhibits superior performance than the existing one in all aspects. It has been demonstrated that the proposed model can be applied to practical-sized instances of the problem. Also, the advantages of the proposed lower bounding scheme have been shown.