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This paper presents a modeling practical works project of electrical engineering, proposed to the first-year students of the University Institute of Technology in France, during the COVID-19 pandemic. The objective of this paper is twofold. The first objective is to present to the students the opportunities of modeling and calculation development of a spreadsheet software in their professional lives. The second objective is to create a file that automatically calculates all the current and voltage values at each point of any alternative electrical circuit. The aim of this paper, geared toward students, is to bring them to build their own numerical remote lab, autonomously. Therefore, pedagogical keys are given along the reading of this document to help them to progress, both on electrical circuits conceptual understanding with series and parallel RLC circuits and on their computation in a spreadsheet software. As a conclusion, this paper can be used as a base to develop remote modeling practical works of many and different devices, as well as a database starting point of such analytical models. [ABSTRACT FROM AUTHOR]

The process of selecting suppliers is a critical and multifaceted aspect of supply chain management, involving numerous criteria and decision-making variables. This complexity escalates when integrating sustainable and resilient factors into supplier evaluation. This literature review paper explores various evaluation criteria that encompass economic, environmental, social, and resilience dimensions for supplier selection. Different methodologies to model and address these complexities are investigated in this research. This review synthesizes the findings of 143 publications spanning the last decade (2013–2023), highlighting the prevalent evaluation criteria and methodologies and identifying existing research gaps. In addition, the feasibility of combining multiple approaches to more accurately reflect real-world scenarios and manage uncertainties in supplier selection is examined. This paper also proposes a decision-making framework to assist practitioners in navigating the intricacies of this process. The paper concludes by suggesting seven potential directions for future research in this evolving field. [ABSTRACT FROM AUTHOR]

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [ABSTRACT FROM AUTHOR]

Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including deterministic, stochastic, and fractional order models, for this purpose. This article presents a comprehensive review and comparative study of the transmission dynamics of fractional order in epidemiological modeling. A significant portion of the paper is dedicated to the graphical simulation of these models, providing a visual representation of their behavior and characteristics. The article further embarks on a comparative analysis of fractional-order models with their integer-order counterparts. This comparison sheds light on the nuances and subtleties that differentiate these models, thereby offering valuable insights into their respective strengths and limitations. The paper also explores time delay models, non-linear incidence rate models, and stochastic models, explaining their use and significance in epidemiology. It includes studies and models that focus on the transmission dynamics of diseases using fractional order models, as well as comparisons with integer-order models. The findings from this study contribute to the broader understanding of epidemiological modeling, paving the way for more accurate and effective strategies in disease control and prevention. [ABSTRACT FROM AUTHOR]

Snake robots, inspired by the biology of snakes, are bionic robots with multiple degrees of freedom and strong robustness. These robots represent a current area of significant research interest within the field of robotics. Snake robots have a wide range of applications in many fields, advancing the integration of bionics, robotics, and cybernetics, while playing a crucial role in performing survey and rescue missions. This survey presents the latest technological advancements in modeling, motion control, and guidance laws for planar snake robots, and provides a unified perspective based on the existing results. To achieve target-tracking control of robots in complex environments, we present a feasible approach that integrates guided vector field technology and transforms the target-tracking and obstacle avoidance problem into a reference angle tracking issue. Finally, this paper analyzes and summarizes the development process and key technologies of snake robot control and provides an outlook on future development trends. [ABSTRACT FROM AUTHOR]

This paper proposes a mathematical model based on a mechanistic approach and previous research findings for the bacterial canker disease development in kiwifruit vines. This disease is a leading cause of severe damage to kiwifruit vines, particularly in humid regions, and contributes to significant economic challenges for growers in many countries. The proposed model contains three parts. The first one is the model of the kiwifruit vine describing its light interception, its carbon acquisition, and the partitioning dynamics. The carbon resource represents the chemical energy required for maintaining the necessary respiration of the living organs and their growth processes. The second part of the model is the dynamics of the pathogenic bacterial population living within the vine's tissues and competing with them for the carbon resource required for their proliferation. The third part of the model is the carbon dynamics described by a mass conservation formula which computes the remaining amount of carbon available for competition. The model was validated by comparing simulations with experimental results obtained from growth chambers. The results show that the proposed model can simulate reasonably well the functional part of the vine in both the healthy case and the disease case without plant defense mechanisms in which the bacteria are always dominant under favorable environmental conditions. They also show that the environmental effects on the vine's growth and the infection progress are taken into account and align with the previous studies. The model can be used to simulate the infection process, predict its outcomes, test disease management techniques, and support experimental analyses. [ABSTRACT FROM AUTHOR]

This research focuses on biological systems with sexual reproduction in which female and male individuals coexist together, forming female–male couples with the purpose of procreation. The couples can originate new females and males according to a certain probability law. Consequently, in this type of biological systems, two biological phases are involved: a mating phase in which the couples are formed, and a reproduction phase in which the couples, independently of the others, originate new offspring of both sexes. Due to several environmental factors of a random nature, these phases usually develop over time in a non-predictable (random) environment, frequently influenced by the numbers of females and males in the population and by the number of couples participating in the reproduction phase. In order to investigate the probabilistic evolution of these biological systems, in previous papers, by using a methodology based on branching processes, we had introduced a new class of two-sex mathematical models. Some probabilistic properties and limiting results were then established. Additionally, under a non-parametric statistical framework, namely, not assuming to have known the functional form of the offspring law, estimates for the main parameters affecting the reproduction phase were determined. We now continue this research line focusing the attention on the estimation of such reproductive parameters under a parametric statistical setting. In fact, we consider offspring probability laws belonging to the family of bivariate power series distributions. This general family includes the main probability distributions used to describe the offspring dynamic in biological populations with sexual reproduction. Under this parametric context, we propose accurate estimates for the parameters involved in the reproduction phase. With the aim of assessing the quality of the proposed estimates, we also determined optimal credibility intervals. For these purposes, we apply the Bayesian estimation methodology. As an illustration of the methodology developed, we present a simulated study about the demographic dynamics of Labord's chameleon populations, where a sensitivity analysis on the prior density is included. [ABSTRACT FROM AUTHOR]

Hot metal is loaded from the torpedo car to the ladle, where desulfurization is realized. The main aim of the desulfurization process is to reduce the amount of sulfur in hot metal. During this process, the temperature of desulfurized hot metal is changed. The continuous measurement of this temperature during the desulfurization process is not implemented due to the device's construction and the increasing costs. The temperature is measured only at the beginning and end of this process. For this reason, the paper focuses on the mathematical model proposal for the continuous measurement and the prediction of the desulfurized hot metal temperature. Information about this temperature will provide insight into the course of thermal processes and allow us to predict the temperature before pouring from the ladle into the oxygen converter. [ABSTRACT FROM AUTHOR]

Non-destructive techniques for the analysis of cultural heritage items are of the outmost importance in order to understand better the artworks, to assess their conservation conditions and to evaluate a possible restoration intervention. Among these techniques, pulsed infrared thermography plays an important role, since it is simple and quite powerful. A standard experimental setup employs flash lamps for the delivery of a pulse of visible light to heat the sample and an infrared camera to record the consequent radiation emission. In this study, this technique was applied for studying ancient manuscripts and, in particular, for revealing hidden text buried under the end leaves of the book. A mathematical model developed by the authors is briefly detailed. The finite element method was employed to numerically solve the model equations and perform numerical simulations. The numerical results highlight the influence of some parameters involved in this phenomenon and can be used for a quantitative analysis of the experimental findings. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to further investigate the mathematical structure of sentences—proposed in a recent paper—and its connections with human short–term memory. This structure is defined by two independent variables which apparently engage two short–term memory buffers in a series. The first buffer is modelled according to the number of words between two consecutive interpunctions—variable referred to as the word interval, I P —which follows Miller's 7 ± 2 law; the second buffer is modelled by the number of word intervals contained in a sentence, M F , ranging approximately for one to seven. These values result from studying a large number of literary texts belonging to ancient and modern alphabetical languages. After studying the numerical patterns (combinations of I P and M F ) that determine the number of sentences that theoretically can be recorded in the two memory buffers—which increases with the use of I P and M F —we compare the theoretical results with those that are actually found in novels from Italian and English literature. We have found that most writers, in both languages, write for readers with small memory buffers and, consequently, are forced to reuse sentence patterns to convey multiple meanings. [ABSTRACT FROM AUTHOR]

New sustainable technologies have been explored as potential solutions to address the global issue of water scarcity by enhancing water treatment processes. In this context, an innovative coagulation/flocculation unit known as the helically coiled tube flocculator (HCTF) has emerged, offering notable advantages such as high process efficiency, short detention time, and cost-effectiveness compared to conventional hydraulic units. The HCTF harnesses its flow energy to disperse coagulation/flocculation agents and facilitate the formation of flocs through collisions between destabilized particles. This paper introduces an assessment of the process efficiency, geometric properties, and hydraulic characteristics of an alternative and sustainable water clarification system incorporating an HCTF, with the aim of determining its optimal length. In HCTFs, the flocculator's length (referred to as L) can exert a significant influence on process efficiency, necessitating a comprehensive evaluation of this parameter for the rational design of such units. To accomplish this, the paper scrutinizes physical experimental findings from previous research articles, which are related to the efficiency of flocculation (indirectly estimated by analyzing turbidity removal efficiency). Additionally, it examines the geometric and hydraulic attributes across 48 distinct variations of HCTFs. This study culminates in the development of a model for determining the optimal length for HCTFs. Furthermore, it includes a probabilistic assessment that establishes a connection between the optimal length and other parameters involved in the clarification process—whether deterministic or probabilistic—and their impact on the final process efficiency, all with a 90% confidence level. This paper stands out by pioneering the determination of the optimal length of HCTFs, filling a gap in the existing literature, which previously only mentioned the importance of this parameter in process efficiency without providing a predictive model. The results highlight the robustness of the proposed alternative clarification system. Even in scenarios with substantial variations in dimensional hydraulic parameters (such as a worst-case relative standard deviation of 20%), the process efficiency fluctuations range between 1.3% and 5.2%. These outcomes lend support to the adoption of such alternative water clarification systems. They also underscore the potential of probabilistic evaluation as a valuable tool for investigating novel water and wastewater treatment units and enhancing existing ones. [ABSTRACT FROM AUTHOR]

This contribution aims to analyze compliance with the rules relating to disturbances in the domain of health due to exposure to electromagnetic fields (EMF). This concerns safety standards for exposed living tissue and the integrity of exposed medical devices acting on the body. This investigation is carried out by reviewing and analyzing these exposure effects. In the paper, the EMF exposure, the nature of sources and the characters of their interactions with objects are first illustrated. Then, EMF exposure restrictions accounting for living tissues safety standards as well as medical devices constancy are discussed. Exposure biological effects comprising both thermal and non-thermal effects are then detailed. The verification and control of EMF effects are next illustrated including mathematical modeling of EMF effects, governing equations and body tissues representation in the solution of these equations. At the end of the paper, two examples representing the cases of tissues and devices are given to check the rules under exposure to EMF: biological effects on exposed human tissues and integrity of a magnetic resonance imager under external disturbance. [ABSTRACT FROM AUTHOR]

This study looks at how travelers move between MADINA and JEDDA, using the UPPAAL Stratego tool to tackle the complexities of urban mobility. As cities grow, effective transportation planning becomes more challenging. Travelers have three options: car, bus, and train. The choices for car and bus travel are impacted by traffic conditions, which can vary between heavy and light, affecting both travel time and cost. We propose a detailed mathematical model that captures all possible scenarios related to these travel options, incorporating the uncertainties of real life. This allows us to simulate different traffic situations. By using UPPAAL Stratego, we evaluate three strategies: the Safe Strategy, which minimizes risk; the Fast Strategy, which aims to reduce travel time; and the Fast and Safe Strategy, which seeks a balance between speed and safety. This paper starts with an introduction to the Stochastic Priced Timed Games approach, highlighting its relevance in modeling dynamic travel environments. We then provide an overview of UPPAAL Stratego, showcasing its abilities in generating, optimizing, and comparing strategies. Next, we outline our mathematical model, explaining the assumptions, parameters, and data sources we used. Our simulation results illustrate how each strategy performs under different conditions, shedding light on traveler preferences and behaviors. The findings underscore the significance of accounting for traffic variability in travel planning and offer important insights for urban transportation policies aimed at improving the traveler experience and optimizing resource use. Additionally, we emphasize the theoretical contributions of our model by demonstrating its applicability to real-world scenarios and its potential to inform future research in urban mobility optimization. Ultimately, this research adds to the growing knowledge of smart transportation systems, demonstrating how formal mathematical modeling can address complex real-world challenges and inform future urban mobility strategies. [ABSTRACT FROM AUTHOR]

With China's urbanization, the construction industry has generated massive construction and demolition waste (C&DW), leading to severe environmental pollution and social problems. However, the currently proposed policies have not promoted the sustainable development of the C&DW recycling market. This paper constructs a tripartite evolutionary game model of construction production enterprises, construction enterprises, and the government. The decision-making evolution laws of relevant stakeholders at different stages of the development of the C&DW recycling market are identified through equilibrium stability analysis. The results show that in the initial stage, the government can help encourage enterprises to participate in C&DW recycling through appropriate subsidy and penalty measures. As the recycling market matures, enterprises achieve profits through market mechanisms and the proportion of enterprises participating in recycling increases. At this time, the government no longer plays a leading role, and the strategy evolves into non-supervision. In addition, the government should design carbon emission reduction policies for carbon quota and trading according to the market status to exert positive effects. Hence, this study provides a theoretical basis for the governments of developing countries to effectively manage C&DW market development. [ABSTRACT FROM AUTHOR]

This study aimed to show what role biomedical engineering can play in sexual health. A new concept of sexological ontology, an essential tool for building evidence-based models of sexual health, is proposed. This ontology should be based on properly validated mathematical models of sexual reactions identified using reliable measurements of physiological signals. This paper presents a review of the recommended measurement methods. Moreover, a general human sexual reaction model based on dynamic systems built at different levels of time × space × detail is presented, and the actual used modeling approaches are reviewed, referring to the introduced model. Lastly, examples of devices and computer programs designed for sexual therapy are described, indicating the need for legal regulation of their manufacturing, similar to that for other medical devices. [ABSTRACT FROM AUTHOR]

As the global energy structure undergoes transformation and the low-carbon development process continues to advance, integrated energy systems have progressively emerged as crucial technical support for achieving sustainable development. In this paper, a joint-day optimal scheduling model is put forward considering the existence of dispatchable resources in community integrated energy systems (CIES). The aim is to cut down the system operation cost and enhance energy utilization efficiency. This model is founded on the concept of energy hubs and combines the shiftable, transferable, and reducible characteristics of demand-side flexible loads. It includes gas turbine power generation systems, energy storage, as well as wind and solar renewable resources. System operation cost and carbon trading cost are comprehensively taken into account, and ultimately, the CIES low-carbon economic dispatch model with the lowest total cost as the optimization objective is established. The Yalmip toolbox and Cplex solver are employed to solve the model. The optimization results of flexible electric and thermal loads participating in dispatching under different scenarios are analyzed through simulation. The economic benefits of electric and thermal independent dispatching are compared and analyzed, and the economic benefits of electric and thermal coupled dispatching are verified. The study reveals that the rational scheduling of user-side flexible loads can notably reduce operating costs, lower the load peak-to-valley difference and carbon emissions, and boost the comprehensive economic and environmental benefits of the system. [ABSTRACT FROM AUTHOR]

In many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same period. Consequently, traditional production planning models enforce minimum demand constraints by product and period rather than by individual orders. An important drawback of this aggregation procedure is that it requires a fixed order fulfillment period, potentially missing opportunities for more efficient resource use through early completion. This paper introduces a novel mathematical formulation that preserves the integrity of customer orders, allowing for early fulfillment when possible. We compare a traditional linear programming model with a new mixed-integer programming approach using a sawmill case study. Although more complex than the traditional model, the proposed formulation reduces costs by approximately 6% by enabling early order completion and offers greater flexibility and control over the production process. This approach leads to better resource utilization and more precise order management, presenting a valuable alternative to conventional production planning models. [ABSTRACT FROM AUTHOR]

This paper presents the development of a numerical analysis model designed to estimate the lifespan of reduced-diameter wheels used in freight wagons based on their diameter, under quasi-static conditions. These wheels are increasingly being used in combined transport applications, where they are installed in various bogie configurations and subjected to different operational environments. However, due to the unique characteristics of reduced-diameter wheels, their lifespan has been scarcely studied. To accurately build this model, an in-depth investigation of the rolling phenomenon was required, addressing key issues in the track–vehicle interaction and establishing relationships between these factors. After constructing the rail–wheel interaction model, it was applied to calculate the lifespan of wheels with standard, medium, and reduced diameters under identical conditions for comparison. This approach makes it possible to determine the lifespan of reduced-diameter wheels relative to standard ones, as well as to observe how lifespan changes with wheel diameter, and it is observed how lifespan diminishes non-linearly with decreasing diameters. The underlying reasons for this variation are explained through a comprehensive understanding of the rolling phenomenon, enabled by the full analysis. [ABSTRACT FROM AUTHOR]

Sustainable management in high-tech enterprises is a key aspect of successfully operating modern companies, especially under conditions of risk and uncertainty. This study reviews the field of sustainable management and interval analysis and identifies the main trends and challenges facing high-tech enterprises in the modern world. This study emphasizes the importance of applying interval analysis in making strategic decisions and developing sustainable business models that can adapt to variable environments. This paper presents empirical data, illustrating the practical application of interval analysis tools in the management in high-tech enterprises. It analyzes the effectiveness and potential of this approach to increase the levels of sustainability and competitiveness of organizations in constantly changing business environments. In general, this article is a valuable contribution to the development of sustainable management theory and practice for high-tech enterprises, enriching the existing knowledge in this area and offering new perspectives for research and practical application. Our research has been validated and is presented in the results section. The purpose of this study is to present current developments in methodologies and tools for risk measurement within the probabilistic paradigm of uncertainty, which are supposed to be used in relation to the economic evaluation of real investment projects. The methodological directions or approaches to risk measurement formed in this context are (1) based on quantile measures, within which the quantitative aspect of risk is modeled using quantile quantiles of the distribution of a random variable describing the possible (predicted) results of economic activity; (2) the Monte Carlo method, which is a tool for evaluating the indicators of economic efficiency and risk in justifying real investments, taking into account different distribution laws and mutual relations for the financial and economic parameters of the investment project, as well as its computational and instrumental elaboration. [ABSTRACT FROM AUTHOR]

Featured Application: The results of this work can be used for solving medical problems in emergency and reconstructive surgery, as well as to build intelligent surgical decision-making systems. In this paper, the problems of modeling the human bladder and its stress–strain state under an external static influence are considered. A method for the identification of the anisotropic biomechanical characteristics of the bladder tissue is proposed. An FEM model was created, which takes into account the fact that the bladder is surrounded by fiber, affected by surrounding organs, and partially protected by pelvic bones. The model considers the presence of constant hydrostatic pressure on the walls of the bladder when it is full. It has been shown that the isotropic mechanical characteristics of biological tissue can be used for studying the deformed state of a filled bladder if a filled bladder of 300 mL is considered as the initial non-deformed stage. This was shown by the modeling and verification of the effect of the external static force on the bladder. Numerical experiments were conducted based on the constructed model. To validate the results obtained, a series of natural experiments on the effect of external pressure on the bladder under ultrasound control were conducted. In the future, there are plans to use the constructed model to study rupture deformations of the bladder under the influence of static and dynamic loads. [ABSTRACT FROM AUTHOR]

The sustainable implementation of resources and the transition to low-carbon construction is on the world's daily agenda. This paper describes the development of criteria for the efficient management of material resources in low-carbon construction. Net income, gross profit, balance sheets, and equity are proposed as indicators that serve as criteria for assessing the efficient use of resources. Nonlinear regression models were the methodological basis for the establishment of cause-and-effect relationships of the volume of construction of transport structures. It was established that since construction companies do not purchase materials for storage, the cost of materials for use in low-carbon technological construction work is directly proportional to the cost of construction. The volume of production in the construction industry is determined by construction costs. More efficient use of low-carbon materials reduces cost and construction waste. In this paper, we have established the relationship between the indicator of efficiency for the functioning of the construction enterprises in Ukraine and the use of low-carbon materials for the construction of transport structures. The practical value of the obtained results for low-carbon construction management lies in proving the relationship between the performance indicators of the construction enterprise (net profit, gross profit, output volume, balance sheets, and equity capital) and the use of low-carbon material resources. Our results form the basis for future research into the use of a cost-based model for low-carbon economy transition in municipalities and regions. [ABSTRACT FROM AUTHOR]

This paper examines the relationship between the magnetization behavior and crystal lattice orientations of Fe–Si alloys intended for magnetic applications. A novel approach is introduced to assess anisotropy of the magnetic losses and first magnetization curves. This method links the magnetocrystalline anisotropy energy of single crystal structures to the textures of polycrystalline materials through a vectorial space description of the crystal unit cell, incorporating vectors for external applied field and saturation magnetization. This study provides a preliminary understanding of how texture influences magnetic loss rates and the first magnetization curves. Experimental results from Electron Back-Scattered Diffraction (EBSD) and Single-Sheet Tests (SSTs), combined with energy considerations and mathematical modeling, reveal the following key findings: (i) a higher density of cubic texture components, whether aligned or rotated relative to the rolling direction, decreases magnetic anisotropy, suggesting that optimizing cubic texture can enhance material performance; (ii) at high magnetic fields, there is no straightforward correlation between energy losses and polarization; and (iii) magnetization rates significantly impact magnetization loss rates, highlighting the importance of considering these rates in optimizing Fe–Si sheet manufacturing processes. These findings offer valuable insights for improving the manufacturing and performance of Fe–Si sheets, emphasizing the need for further exploration of texture effects on magnetic behavior. [ABSTRACT FROM AUTHOR]

There is uncertainty in the results of any mathematical model due to different reasons. It is important to estimate this uncertainty. Sensitivity analysis is commonly used to estimate how the changes in the input parameters affect the solutions of the model. In this paper, we discuss different ways of performing local and global sensitivity analyses and apply them to two models: an epidemic model and a new myocardial infarction model, both based on ordinary differential equations. The first model is a simple model used to explain the ideas, while the second one shows how to apply them to a model with more state variables and parameters. We find that if the parameters are not accurately known, local sensitivity analysis can be misleading and that global sensitivity methods that sample the whole parameter space, varying all the values of the parameters at the same time, are the most reliable. We also show how the sensitivity analysis results can be used to determine the uncertainty in the results of the model. We present numerical simulations. [ABSTRACT FROM AUTHOR]

Microscale robotics has emerged as a transformative field, offering unparalleled opportunities for innovation and advancement in various fields. Owing to the distinctive benefits of wireless operation and a heightened level of safety, magnetic actuation has emerged as a widely adopted technique in the field of microrobotics. However, factors such as Brownian motion, fluid dynamic flows, and various nonlinear forces introduce uncertainties in the motion of micro/nanoscale robots, making it challenging to achieve precise navigational control in complex environments. This paper presents an extensive review encompassing the trajectory from theoretical foundations of the generation and modeling of magnetic fields as well as magnetic field-actuation modeling to motion control methods of magnetic microrobots. We introduce traditional control methods and the learning-based control approaches for robotic systems at the micro/nanoscale, and then these methods are compared. Unlike the conventional navigation methods based on precise mathematical models, the learning-based control and navigation approaches can directly learn control signals for the actuation systems from data and without relying on precise models. This endows the micro/nanorobots with high adaptability to dynamic and complex environments whose models are difficult/impossible to obtain. We hope that this review can provide insights and guidance for researchers interested in automated magnetic microrobot control. [ABSTRACT FROM AUTHOR]

This paper analyzes healthcare supply chain shortcomings during the COVID-19 pandemic, specifically in supplying personal protective equipment (PPE) to healthcare personnel. It addresses the need for effective PPE stockpile strategies, considering past inadequacies. A linear programming model is presented to determine optimal PPE stockpile levels, factoring in unpredictable demand and variable supplier costs. The study includes a comparative analysis of scenarios with and without stockpiling strategies. Moreover, we employ the Morris method for comprehensive sensitivity analysis, focusing on key factors, namely: demand, supply from traditional and non-traditional sources, and stockpile capacity. These insights are vital for policymakers to develop better PPE stockpiling methods, thus improving healthcare crisis management. [ABSTRACT FROM AUTHOR]

The objective of this paper was to study the sCO2 cycle as a waste heat recovery system for a 180 kW biogas engine. The research methodology adopted was numerical simulations through two models built in different programs: Aspen HYSYS and GT Suite. The models were used to optimize the design and thermodynamic parameters of a CO2 cycle in terms of system power, system efficiency, expander, and compressor efficiency. Depending on the objective function, the sCO2 cycle could provide additional power ranging from 27.9 to 11.3 kW. Based on the calculation performed, "Recuperated cycle at maximum power" was selected for further investigation. The off-design analysis of the system revealed the optimum operating point. The authors designed the preliminary dimensions of the turbomachinery, i.e., the rotor dimension is 16 mm, which will rotate at 100,000 rpm. [ABSTRACT FROM AUTHOR]

Mathematical modeling has served as an epidemiological tool to enhance the modeling efforts of the social and economic impacts of the pandemic. This article reviews epidemiological network models, which are conceived as a flexible way of representing objects and their relationships. Many studies have used these models over the years, and they have also been used to explain COVID-19. Based on the information provided by the Web of Science database, exploratory, descriptive research based on the techniques and tools of bibliometric analysis of scientific production on epidemiological network models was carried out. The epidemiological models used in the papers are diverse, highlighting those using the SIS (Susceptible-Infected-Susceptible), SIR (Susceptible-Infected-Recovered) and SEIR (Susceptible-Exposed-Infected-Removed) models. No model can perfectly predict the future, but they provide a sufficiently accurate approximation for policy makers to determine the actions needed to curb the pandemic. This review will allow any researcher or specialist in epidemiological modeling to know the evolution and development of related work on this topic. [ABSTRACT FROM AUTHOR]

The paper presents a review of models that can be used to describe dynamics of lung cancer growth and its response to treatment at both cell population and intracellular processes levels. To address the latter, models of signaling pathways associated with cellular responses to treatment are overviewed. First, treatment options for lung cancer are discussed, and main signaling pathways and regulatory networks are briefly reviewed. Then, approaches used to model specific therapies are discussed. Following that, models of intracellular processes that are crucial in responses to therapies are presented. The paper is concluded with a discussion of the applicability of the presented approaches in the context of lung cancer. [ABSTRACT FROM AUTHOR]

Given that global amounts of waste are growing rapidly, it is extremely important to determine what amount of waste will be generated in the near future. Accurate waste forecasting is also important for planning and designing a sustainable municipal solid waste (MSW) management system. For that reason, there is a need to build a model to predict the amount of MSW generated in the near future. Based on previous research, artificial neural networks (ANN) show better results in predicting waste generation compared to other mathematical models. In this research, an ANN model using the iterative algorithm Broyden–Fletcher–Goldfarb–Shanno (BFGS) for the prediction of MSW fractions, based on the socio-demographic characteristics, economic and industrial data obtained in Croatia and summarized data of the member states of EU (EU-27 from 2020), showed good predictive capabilities. The coefficient of determination during the training cycle for the output variables; household and similar waste (HHS), paper and cardboard waste (PCW), wood waste (WW), textile waste (TW), plastic waste (PW) and glass waste (GW) were 0.993; 0.997; 0.999; 0.997; 0.998; and 0.998, respectively, while reduced chi-square, mean bias error, root mean square error, mean percentage error, average absolute relative deviation and sum of squared errors were found low. In this paper, Yoon′s method of interpretation shows the relationships between socio-demographic data and the amount of generated waste. The results indicate that the lowest level of education shows a negative impact on observed waste-types calculations, with a relative impact between −9.889 and −4.467%. The most pronounced positive impact on the calculation of HHS, PCW, WW, TW, PW and GW was observed for year variable, gross domestic product, exports of goods and services, imports of goods and services, wages and salaries, secondary income, arrivals in collective accommodation establishments, overnight stays in collective accommodation establishments and exports of petroleum and petroleum products to partner countries, with a relative influence of 4.063–7.028; 2828–4851; 5240–6197; 5.308–6.341; 4290–4810; 4533–5805; and 4.345–4.493, respectively. The obtained results indicate that the amount of HHS waste at the EU-27 level in 2025 will decrease by approximately 18% compared to the data from 2018. The quantities of other observed recyclable types of waste will increase by 34% for PCW, 310% for WW, 40% for TW, 276% for PW and about 67% for GW. The amount of waste generated provides the basic information needed to plan, operate and optimize the waste management system. It could also help in the transition to an environmentally friendly and economically profitable circular economy. The model created in this research could also help with the system of separate waste collection, which would lead to more efficient recycling and the achievement of the set goals for recycling 55% of municipal waste by 2025. [ABSTRACT FROM AUTHOR]

In this paper, we construct a more realistic mathematical model to study toxoplasmosis dynamics. The model considers two discrete time delays. The first delay is related to the latent phase, which is the time lag between when a susceptible cat has effective contact with an oocyst and when it begins to produce oocysts. The second discrete time delay is the time that elapses from when the oocysts become present in the environment to when they are able to infect. The main aim in this paper is to find the conditions under which the toxoplasmosis can disappear from the cat population and to study whether the time delays can affect the qualitative properties of the model. Thus, we investigate the impact of the combination of two discrete time delays on the toxoplasmosis dynamics. Using dynamical systems theory, we are able to find the basic reproduction number R 0 d that determines the global long-term dynamics of the toxoplasmosis. We prove that, if R 0 d < 1 , the toxoplasmosis will be eradicated and that the toxoplasmosis-free equilibrium is globally stable. We design a Lyapunov function in order to prove the global stability of the toxoplasmosis-free equilibrium. We also prove that, if the threshold parameter R 0 d is greater than one, then there is only one toxoplasmosis-endemic equilibrium point, but the stability of this point is not theoretically proven. However, we obtained partial theoretical results and performed numerical simulations that suggest that, if R 0 d > 1 , then the toxoplasmosis-endemic equilibrium point is globally stable. In addition, other numerical simulations were performed in order to help to support the theoretical stability results. [ABSTRACT FROM AUTHOR]

The paper presents the results of modeling the problem of injecting liquid sulfur dioxide into a porous reservoir initially saturated with methane and ice. The model presented in the paper assumes the formation of three different regions, namely the near one, saturated with liquid SO2 and its hydrate; the far one, containing methane and ice; and the intermediate one, saturated with methane and water. The effects of various parameters of the porous medium and injected SO2 on the nature of the course of the hydrate formation process have been studied. It is shown that with a decrease in reservoir permeability or injection pressure, the length of the intermediate region decreases, which, in the limiting case, means the formation of SO2 hydrate in the mode without the formation of an extended region saturated with methane and water. It is shown that such a regime is also typical for the case of high initial injection pressures, as well as low values of the initial reservoir temperature and injection temperature. [ABSTRACT FROM AUTHOR]

The issue of achieving controlled or targeted release of bioactive compounds with specific functional properties is a complex task that requires addressing several factors, including the type of bioactive, the nature of the delivery system, and the environmental conditions during transportation and storage. This paper deals with extensive reporting for the identification of original articles using Scopus and Google Scholar based on active packaging as a novel packaging technology that controls the release of antimicrobial agents encapsulated into carriers in the food packaging systems. For evidence-based search, the studies were extracted from 2015 to 2020 and screened using the 2020 Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Following the review and screening of publications, 32 peer-reviewed articles were subjected to systematic analysis. The preliminary search indicated that the encapsulation of bioactives enhances their bioavailability and stability. From a theoretical viewpoint, mathematical models play an important role in understanding and predicting the release behavior of bioactives during transportation and storage, thus facilitating the development of new packaging material by a systematic approach. However, only a few studies could formulate parameters for mathematical models in order to achieve the specific release mechanism regulated for the quality and safety of foods. Therefore, this paper will cover all encapsulation approaches, active packaging, and mathematical modeling in the food industry into structural form and analyze the challenges faced by the complex nature of active packaging in real food systems. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model of multiphase filtration in a deformable porous medium is presented. Based on the proposed model, the influence of the deformation of a porous medium on the filtration processes is studied. Numerical calculations are performed and the characteristics of the process are determined. This paper shows that an increase in the compressibility coefficient leads to a sharp decrease in porosity, absolute permeability and internal pressure of the medium near the well, and a decrease in the distance between wells leads to a sharp decrease in hydrodynamic parameters in the inter-well zone. [ABSTRACT FROM AUTHOR]

The Metaverse brings together components of parallel processing computing platforms, the digital development of physical systems, cutting-edge machine learning, and virtual identity to uncover a fully digitalized environment with equal properties to the real world. It possesses more rigorous requirements for connection, including safe access and data privacy, which are necessary with the advent of Metaverse technology. Traditional, centralized, and network-centered solutions fail to provide a resilient identity management solution. There are multifaceted security and privacy issues that hinder the secure adoption of this game-changing technology in contemporary cyberspace. Moreover, there is a need to dedicate efforts towards a secure-by-design Metaverse that protects the confidentiality, integrity, and privacy of the personally identifiable information (PII) of users. In this research paper, we propose a logical substitute for established centralized identity management systems in compliance with the complexity of the Metaverse. This research proposes a sustainable Self-Sovereign Identity (SSI), a fully decentralized identity management system to mitigate PII leaks and corresponding cyber threats on all multiverse platforms. The principle of the proposed framework ensures that the users are the only custodians and proprietors of their own identities. In addition, this article provides a comprehensive approach to the implementation of the SSI principles to increase interoperability and trustworthiness in the Metaverse. Finally, the proposed framework is validated using mathematical modeling and proved to be stringent and resilient against modern-day cyber attacks targeting Metaverse platforms. [ABSTRACT FROM AUTHOR]

In the realm of cementitious materials, integrating nanoclay shows promise in enhancing properties relevant to additive manufacturing. This paper presents a novel mathematical model that combines simple empirical dissolution/nucleation Avrami-like kinetics with a thixotropic kinetics equation. To analyze the initial exothermic peak, two sets of the calculation parameter function are built to describe the exothermic rate as a function of time, following an exponential pattern. This allows for the prediction of the changes in cumulative heat and heat rate during hydration, considering different concentrations of nanoclay. In the rheological aspect, the relationship between shear stress, shear rate, and time is modeled as a combination of exponential dependencies. This enables the prediction of the variations in shear stress with one variable while holding the other constant (either time or shear rate). By integrating these aspects, this model effectively describes both the first exothermal peak and the rheological behavior during cement hydration with the inclusion of nanoclay. Validated against experimental results, these models demonstrate good accuracy (overall below 3% error), reliability, and applicability. The findings offer valuable insights into the thermal and rheological aspects of concrete printing, enabling informed design decisions for both scientific and industrial applications. [ABSTRACT FROM AUTHOR]

Atomic Force Microscopy (AFM) nanoindentation is a powerful technique for determining the mechanical properties of soft samples at the nanoscale. The Hertz model is typically used for data processing when employing spherical indenters for small indentation depths (h) compared to the radius of the tip (R). When dealing with larger indentation depths, Sneddon's equations can be used instead. In such cases, the fitting procedure becomes more intricate. Nevertheless, as the h/R ratio increases, the force–indentation curves tend to become linear. In this paper the potential of using the linear segment of the curve (for h > R) to determine Young's modulus is explored. Force–indentation data from mouse and human lung tissues were utilized, and Young's modulus was calculated using both conventional and linear approximation methods. The linear approximation proved to be accurate in all cases. Gaussian functions were applied to the results obtained from both classic Sneddon's equations and the simplified approach, resulting in identical distribution means. Moreover, the simplified approach was notably unaffected by contact point determination. The linear segment of the force–indentation curve in deep spherical indentations can accurately determine the Young's modulus of soft materials at the nanoscale. [ABSTRACT FROM AUTHOR]

With the emergence of the fourth industrial revolution, the use of intelligent technologies in supply chains is becoming increasingly common. The aim of this research is to propose an optimal design for an intelligent supply chain of multiple perishable products under a vendor-managed inventory management policy aided by IoT-related technologies to address the challenges associated with traditional supply chains. Various levels of the intelligent supply chain employ technologies such as Wireless Sensor Networks (WSNs), Radio Frequency Identification (RFID), and Blockchain. In this paper, we develop a bi-objective nonlinear integer mathematical programming model for designing a four-level supply chain consisting of suppliers, manufacturers, retailers, and customers. The model determines the optimal network nodes, production level, product distribution and sales, and optimal choice of technology for each level. The objective functions are total cost and delivery times. The GAMS 24.2.1 optimization software is employed to solve the mathematical model in small dimensions. Considering the NP-Hard nature of the problem, the Grey Wolf Optimizer (GWO) algorithm is employed, and its performance is compared with the Multi-Objective Whale Optimization Algorithm (MOWOA) and NSGA-III. The results indicate that the adoption of these technologies in the supply chain can reduce delivery times and total supply chain costs. [ABSTRACT FROM AUTHOR]

The paper presents an original solution for modeling and simulation of the teeth movement biomedical processes which occur in the case of orthodontic treatments. The direct application of this method consists in the possibility to approximate, with high precision, the orthodontic treatment duration, depending on the physical characteristics of each patient. This aspect represents a novelty element in the biomedical processes' domain since, until now, the research activities in the mentioned field did not generate a solution for the approximation of the orthodontic treatment's duration. Analog modeling of the biomedical process operates with a fictional shaft defined to highlight the tooth symmetry axis. The tooth considered as an example is approximated as having a parabolic shape with an elliptical section. The digital simulation refers to the spatial-temporal evolution of this fictional shaft in the orthodontic dynamics, being made through the run of four computer programming algorithms. Interpretation of the obtained performance indicators will lead to an interesting study regarding the dynamics' process in orthodontics, having a pronounced unitary and systematic characteristic. Using the developed programs for obtaining the simulations results presented in the four tables and in the 18 figures shown in the paper, several case studies can be elaborated, associated with a wide variety of orthodontic treatments. [ABSTRACT FROM AUTHOR]

Cap-and-trade models have been largely studied in the literature when it comes to reducing emissions in a supply chain. In this paper, further pursuing the goal of analyzing the effectiveness of cap-and-trade strategies in reducing emissions in supply chains, we propose a mathematical model for sustainable supply chain management. This optimization program aims at reducing emissions and supply chain costs in an unregulated scenario w.r.t. the cap definition, i.e., trading CO2 is allowed but no formal limit on the CO2 emissions is imposed. Also, we considered an initial budget for technological investments by the facilities in the considered supply chain, allowing plants to reduce their unit production emissions at a different unit production cost. For this model, differently from what exists in the literature, we derive some theoretical conditions guaranteeing that, if obeyed, the emissions over time have a non-increasing trend meaning that decreasing caps over time can be attained with a self-regulated scenario. Computational results show the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Adequate mathematical description of magnetization curves is indispensable in engineering. The accuracy of the description has a significant impact on the design of electric machines and devices. The aim of this paper was to analyze the capability of Bézier curves systematically, to describe the nonlinear static magnetic properties of non-oriented electrical steels, and to compare this approach versus the established mathematical descriptions. First, analytic functions versus measurements were analyzed. The Bézier curves were then compared systematically with the most adequate analytic functions. Next, the most suitable orders of Bézier curves were determined for the approximation of nonlinear magnetic properties, where the influence of the range of the input measurement dataset on the approximation process was analyzed. Last, the extrapolation capabilities of the Bézier curves and analytic functions were evaluated. The general conclusion is that Bézier curves have adequate flexibility and significant potential for the approximation and extrapolation of nonlinear properties of non-oriented electrical steels. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper shows the development of a numerical analysis model, which enables the calculation of the cargo transport capacity of a vehicle that circulates through a vacuum tube at high speed, whose effectiveness in transport is analyzed. The simulated transportation system is based on vehicles moving in vacuum tubes at high speed, a concept commonly known as Hyperloop, but assuming the vehicles for cargo containers. For the specific vehicle proposed, which does not include a compressor and levitates on magnets, the system formed by the vehicle and the vacuum tube has been conceptually developed, establishing the corresponding mathematical relationships that define its behavior. To properly model the performance of this transport system, it has been necessary to establish the relationships between the design variables and the associated constraints, such as the Kantrowitz limit, aerodynamics, transport, energy consumption, etc. Once the model was built and validated, it was used to analyze the effects of the variation of the number of containers, the operating speed and the tube length, considering the total and specific consumption of energy. After finding the most efficient configuration regarding energy consumption and transport effectiveness, the complete system was calculated. The results obtained constitute a first approximation for the predesign of this transport system and the built model allows different alternatives to be compared according to the design variables. [ABSTRACT FROM AUTHOR]

The variation analysis is a key tool for ensuring the high quality assembly in the process of developing the technology for manufacturing of aircraft parts. One of the main factors in variations is the deviations in the positioning procedure. This paper is devoted to the development of an approach that allows taking into account the variations during positioning and merging it with the special algorithm of contact problem solving. The impact of varied boundary conditions is incorporated into an additional vector of forces that can be interpreted as reactions to the shift of supports. The obtained results are illustrated with a case of wing-to-fuselage assembly. [ABSTRACT FROM AUTHOR]

In this paper, we present an updated review on the mathematical modeling of different biological methods of hydrogen production. The presented mathematical modeling and methods range from inception to the current state-of-the-art developments in hydrogen production using biological methods. A comparative study was performed along with indications for future research and shortcomings of earlier research. This review will be helpful for all researchers working on different methods of hydrogen production. However, we only covered biological methods such as biophotolysis, fermentation and microbial electrolysis cells, and this list is not exhaustive of all other methods of hydrogen production. [ABSTRACT FROM AUTHOR]

Background: In container terminals, optimizing the scheduling of external trucks and yard cranes is crucial as it directly impacts the truck turnaround time, which is one of the most critical performance measures. Furthermore, proper scheduling of external trucks contributes to reducing CO 2 emissions. Methods: This paper proposes a new approach based on a mixed integer programming model to schedule external trucks and yard cranes with the objective of minimizing CO 2 emissions and reducing truck turnaround time, the gap between trucking companies' preferred arrival time and appointed time, and the energy consumption of yard cranes. The proposed approach combines data analysis and operations research techniques. Specifically, it employs a K-means clustering algorithm to reduce the number of necessary truck trips for container handling. Additionally, a two-stage mathematical model is applied. The first stage employs a bi-objective mathematical model to plan the arrival of external trucks at the terminal gates. The second stage involves a mathematical model that schedules yard cranes' movements between different yard blocks. Results: The results show that implementing this methodology in a hypothetical case study may lead to a substantial daily reduction of approximately 31% in CO 2 emissions. Additionally, the results provide valuable insights into the trade-off between satisfying the trucking companies' preferred arrival time and the total turnaround time. Conclusions: The integration of data clustering with mathematical modeling demonstrates a notable reduction in emissions, underscoring the viability of this strategy in promoting sustainability in port-related activities. [ABSTRACT FROM AUTHOR]

An electrochemical photobioreactor with a packed bed containing transparent gel granules and immobilized photosynthetic bacterial cells is shown with a one-dimensional two-phase flow and transport model. We consider the biological/chemical events in the electrochemical photobioreactor, the intrinsically connected two-phase flow and mass transport, and other factors. This model is based on a system of nonlinear equations. This paper applies Akbari-Ganji's and Taylor series methods to find analytical solutions to nonlinear differential equations that arise in an immobilized-cell electrochemical photobioreactor. Approximate analytical expressions of the concentration of glucose and hydrogen are obtained in liquid and gas phases for different parameter values. Numerical simulations are presented to validate the theoretical investigations. [ABSTRACT FROM AUTHOR]

The paper considers the problem of cooperative control synthesis for a complex of N underwater vehicle–manipulator systems (UVMS) to perform the work of moving a cargo along a given trajectory. Here, we used the approach based on the representation of nonlinear dynamics models in the form of state space with state-dependent coefficients (SDC-form). That allowed us to apply methods of suboptimal control with feedback based on the state-dependent differential Riccati equation (SDDRE) solution at a finite time interval, providing the change in control intensity with the transient effect of the system matrices in SDC form. The paper reveals two approaches to system implementation: a general controller for the whole system and a set of N independent subcontrollers for UVMSs. The results of both approaches are similar; however, for the systems with a small number of manipulators, the common structure is recommended, and for the systems with a large number of manipulators, the approach with independent subcontrollers may be more acceptable. The proposed method of cooperative control was tested on the task of cooperative control for two UVMSs with six-link manipulators Orion 7R. The simulation results are presented in the article and show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Physically unacceptable chaotic numerical solutions of nonlinear circuits and systems are discussed in this paper. First, as an introduction, a simple example of a wrong choice of a numerical solver to deal with a second-order linear ordinary differential equation is presented. Then, the main result follows with the analysis of an ill-designed numerical approach to solve and analyze a particular nonlinear memristive circuit. The obtained trajectory of the numerical solution is unphysical (not acceptable), as it violates the presence of an invariant plane in the continuous systems. Such a poor outcome is then turned around, as we look at the unphysical numerical solution as a source of strong chaotic sequences. The 0–1 test for chaos and bifurcation diagrams are applied to prove that the unacceptable (from the continuous system point of view) numerical solutions are, in fact, useful chaotic sequences with possible applications in cryptography and the secure transmission of data. [ABSTRACT FROM AUTHOR]

Our investigation demonstrates the necessity of mathematical modeling and design methodologies for nerve signals in the creation of artificial arms. Nerve impulses vary widely in speed; for example, unmyelinated nerves transmit impulses at around one mile per hour, while myelinated nerves conduct impulses at around 200 miles per hour. The electrical signals originating from the brain, such as those measured by electroencephalography, are translated into chemical reactions in each organ to produce energy. In this paper, we describe the mechanism by which nerve signals are transferred to various organs, not just the brain or spinal cord, as these signals account for the measured amounts of physical force—i.e., energy—as nerve signals. Since these frequency signals follow no fixed pattern, we consider wavelength and amplitude over a particular time frame. Our simulation results begin with the mechanical distinction that occurs throughout the entire process of nerve signal transmission in the artificial arm as an artificial biological system, and show numerical approaches and algebraic equations as a matrix in mathematical modeling. As a result, the mathematical modeling of nerve signals accurately reflects actual human nerve signals. These chemical changes, involving K (potassium), Na (sodium), and Cl (chloride), are linked to muscle states as they are converted into electrical signals. Investigating and identifying the neurotransmitter signal transmission system through theoretical approaches, mechanical analysis, and mathematical modeling reveals a strong relationship between mathematical simulation and algebraic matrix analysis. [ABSTRACT FROM AUTHOR]

Breast cancer ranks among the most prevalent malignancies affecting the female population and is a prominent contributor to cancer-related mortality. Mathematical modeling is a significant tool that can be employed to comprehend the dynamics of breast cancer progression and dissemination and to formulate novel therapeutic approaches. This paper introduces a mathematical model of breast cancer that utilizes the Caputo–Fabrizio fractal-fractional derivative. The aim is to elucidate and comprehend the intricate dynamics governing breast cancer cells and cytotoxic T lymphocytes in the context of the fractional derivative. The derivative presented herein offers a broader perspective than the conventional derivative, as it incorporates the intricate fractal characteristics inherent in the process of tumor proliferation. The significance of this study lies in its contribution to a novel mathematical model for breast cancer, which incorporates the fractal characteristics of tumor development. The present model possesses the capability to investigate the impacts of diverse treatment strategies on the proliferation of breast cancer, as well as to formulate novel treatment strategies that exhibit enhanced efficacy. [ABSTRACT FROM AUTHOR]