Role Of Mathematical Models Research Articles

A Century of Mathematical Epidemiology: A Bibliometric Analysis and Visualization of Research Trends.

Defined as the application of mathematical models and methods for the study of disease spread and control, Mathematical epidemiology has now emerged as a very important area for understanding public health dynamics. The paper presents an overall bibliometric analysis of research in mathematical epidemiology using the Scopus database. This overview comprises 1,787 documents: journal articles, book chapters, and conference papers from 819 sources. From 1916 to 2024, it has been possible to identify key trends, influential authors, and central themes through the application of the PRISMA methodology. The results reflect that since 2000, there has been a significant growth in research production; most of it was during the period of the COVID-19 pandemic. The study also determined trends in international collaboration, leading funding sponsors, and the dynamics underlying major research topics. According to this study, the role of mathematical models in epidemiology is becoming increasingly prominent, driven by the need to address complex global health challenges and an expanding influence on public health strategies.

Stability Analysis of Diabetes Mellitus Model in Neutrosophic Fuzzy Environment

Neutrosophic differential equation (NDE) plays a vital role in mathematical modeling on uncertainty during last few years.It is established that NDE comprises a neutrosophic number whose membership function contains three parts like as truth function, indeterministic and falsity functions.In this paper, a diabetes mellitus model has been formulated in neutrosophic fuzzy environment to get more realistic mathematical model. The initial conditions of diabetes system are considered as trapezoidal neutrosophic fuzzy number. The concept of NDE via nuetrosophic generalised derivative of type-1 and type-2 has used in this article. This is the first article in which the stability analysis of diabetes model in neutrosophic environment is introduced. The existence of strong solution and weak neutrosophic solution of the proposed system are employed in the manuscript. Also, we have exposed the comparison of the suggested model between fuzzy environment and neutrosophic environment.The all results, formulas are confirmed graphically and numerically by MATLAB software.

ЕКОНОМІКО-МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ СТАЛОГО РОЗВИТКУ У ДІЯЛЬНОСТІ ПІДПРИЄМСТВ

The article examines modern aspects of the use of mathematical models in solving problems of sustainable development of enterprises. The essence of the concept of sustainable development was considered and its importance for enterprises in the modern dynamic business environment was determined. The role of mathematical modeling in the decision-making process based on the application of specific methods and tools that help to analyze and optimize the production processes of economic entities in the context of sustainable development is studied. A complex of specialized mathematical models used for modeling sustainable development is considered, including such aspects as linear and non-linear programming, simulation theory, game theory, differential equations, etc. The peculiarities of the application of these models in the activities of enterprises were analyzed and their effectiveness in ensuring the achievement of sustainable development was determined. Practical examples of the implementation of economic and mathematical models at enterprises of various industries on the basis of reducing resource consumption, optimizing production processes, waste and risk management strategies, as well as planning future investments in sustainable development were studied. The importance of the development and improvement of economic-mathematical modeling methods for achieving the goals of sustainable development of economic entities is determined. The essence of challenges and obstacles that arise in the process of implementing economic and mathematical models to achieve sustainable development of enterprises, which include the objective need for access to a large amount of data, the complexity of interaction with counterparties, as well as the instability of the modern economic environment, is considered. Strategies and recommendations for overcoming these challenges are proposed, including the development of information systems and the actualization of the needs of business entities regarding the importance of sustainable development. The necessity of integrating mathematical models in the planning and economic activities of enterprises to achieve the efficiency of their sustainable development is determined. The importance of applying economic-mathematical modeling to increase the efficiency of enterprises and stimulate their sustainable activity to achieve strategic goals is proven.

Computational Engineering Advancements: General Review of Mathematical Modeling in Computer Engineering Applications

The comprehensive review explored the advancements in computational engineering with a focus on the role of mathematical modeling in computer engineering applications. The research investigated various mathematical models that used in different computer engineering fields, including software engineering, hardware design, and networking. It also examined the importance of mathematical modeling and its impact on solving complex engineering problems. The study highlighted emerging trends in mathematical modeling, such as reduced-order modeling, multiscale modeling, and uncertainty quantification. It also explored cutting-edge computational tools and techniques, such as high-performance computing, GPU acceleration, and meshless methods, which enabled engineers to conduct more efficient and accurate simulations. Furthermore, the integration of artificial intelligence and machine learning in mathematical modeling was discussed, emphasized the growing significance of data-driven models and surrogate modeling in computer engineering applications. The research identified industries that was benefit from enhanced computational engineering approaches, including aerospace, energy, healthcare, finance, and manufacturing. Through case studies, successful implementations of mathematical models in real-world engineering projects were presented, showcasing the practical implications of these advancements. The review also addressed challenges in adopting advanced mathematical models, such as computational complexity, data limitations, and model interpretability, and proposes potential solutions to address these issues.

Editorial: Role of mathematical modeling in advanced power generation systems

Editorial: Role of mathematical modeling in advanced power generation systems

Improvement of blast furnace production using digital technology

The role of mathematical models in the improvement of the blast furnace smelting technology is shown. Examples include the new developments of the Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences in the field of digital models of blast furnace production, in particular, two-dimensional and three-dimensional mathematical models of the thermal state of various zones of the blast furnace, including analysis and forecast of phe-nomena of gas dynamics, heat exchange, recovery in blast furnace using a complex of mathematical models; monitoring of refractory lining state and hearth filling using three-dimensional mathematical model of thermal processes; forecast of silicon content and other elements in cast iron and slag based on neural network technologies; optimization of the composition and improvement of metallurgical characteristics of iron ore agglomerate and coke in order to increase the efficiency of blast furnace melting and analysis of the efficiency of blast furnaces based on the calculation of the minimum consumption of coke. These models are based on the consideration of physical, chemical and thermal phenomena occurring in the blast furnace, taking into account their two-dimensional nature implicit in the problem statement. The developed complex of models includes balance (equilibrium) model, models of gas dynamics, heat exchange, reduction, cohesion zone. New developments in the field of analysis and control of thermophysical and physicochemical phenomena occurring in different zones of the blast furnace allow to raise the technology and methods of blast furnace melting to a fundamentally new level, which saves fuel and energy resources. The possibility of using a digital model in tempo with a process using sensor readings through the blast furnace department management system of the enterprise is shown.

Values in preservice mathematics teachers’ discussions of the Body Mass Index - A critical perspective

This article explores the values that come to the fore when preservice mathematics teachers (PTs) 11In the remaining parts of the text, we will refer to preservice teachers as PTs. engage in critical discussions about the role of mathematical models in society. The specific model that was discussed was the Body Mass Index (BMI) 22From now on, the Body Mass Index will be referred to as BMI and is calculated as mass (m) divided by the square of height (h).. From the analysis of the PTs’ discussions of the BMI from a mathematical and societal point of view several mathematical and mathematics educational values were identified such as openness, rationalism, progress, reasoning, evaluating, and problematizing the instrumental understanding of mathematics. In addition, critical thinking about mathematics in society as emphasized in curricula in the three countries involved in the study, was identified with four categories of complementary pairs. Knowing the mathematical and mathematics educational values underpinning PTs’ discussions and their connection to critical thinking is important for successfully engaging with the role of mathematics in society.

The role of mathematical modelling in understanding prokaryotic predation.

With increasing levels of antimicrobial resistance impacting both human and animal health, novel means of treating resistant infections are urgently needed. Bacteriophages and predatory bacteria such as Bdellovibrio bacteriovorus have been proposed as suitable candidates for this role. Microbes also play a key environmental role as producers or recyclers of nutrients such as carbon and nitrogen, and predators have the capacity to be keystone species within microbial communities. To date, many studies have looked at the mechanisms of action of prokaryotic predators, their safety in in vivo models and their role and effectiveness under specific conditions. Mathematical models however allow researchers to investigate a wider range of scenarios, including aspects of predation that would be difficult, expensive, or time-consuming to investigate experimentally. We review here a history of modelling in prokaryote predation, from simple Lotka-Volterra models, through increasing levels of complexity, including multiple prey and predator species, and environmental and spatial factors. We consider how models have helped address questions around the mechanisms of action of predators and have allowed researchers to make predictions of the dynamics of predator-prey systems. We examine what models can tell us about qualitative and quantitative commonalities or differences between bacterial predators and bacteriophage or protists. We also highlight how models can address real-world situations such as the likely effectiveness of predators in removing prey species and their potential effects in shaping ecosystems. Finally, we look at research questions that are still to be addressed where models could be of benefit.

The role of mathematical models in designing mechanopharmacological therapies for asthma

Healthy lung function depends on a complex system of interactions which regulate the mechanical and biochemical environment of individual cells to the whole organ. Perturbations from these regulated processes give rise to significant lung dysfunction such as chronic inflammation, airway hyperresponsiveness and airway remodelling characteristic of asthma. Importantly, there is ongoing mechanobiological feedback where mechanical factors including airway stiffness and oscillatory loading have considerable influence over cell behavior. The recently proposed area of mechanopharmacology recognises these interactions and aims to highlight the need to consider mechanobiology when identifying and assessing pharmacological targets. However, these multiscale interactions can be difficult to study experimentally due to the need for measurements across a wide range of spatial and temporal scales. On the other hand, integrative multiscale mathematical models have begun to show success in simulating the interactions between different mechanobiological mechanisms or cell/tissue-types across multiple scales. When appropriately informed by experimental data, these models have the potential to serve as extremely useful predictive tools, where physical mechanisms and emergent behaviours can be probed or hypothesised and, more importantly, exploited to propose new mechanopharmacological therapies for asthma and other respiratory diseases. In this review, we first demonstrate via an exemplar, how a multiscale mathematical model of acute bronchoconstriction in an airway could be exploited to propose new mechanopharmacological therapies. We then review current mathematical modelling approaches in respiratory disease and highlight hypotheses generated by such models that could have significant implications for therapies in asthma, but that have not yet been the subject of experimental attention or investigation. Finally we highlight modelling approaches that have shown promise in other biological systems that could be brought to bear in developing mathematical models for optimisation of mechanopharmacological therapies in asthma, with discussion of how they could complement and accelerate current experimental approaches.

Feminist Perspectives on Care and Macroeconomic Modeling: Introduction to the Special Issue

ABSTRACT Macroeconomic models and associated policy analyses have long focused exclusively on market production, ignoring gender and care. Decades of feminist economic research, policy analysis, and activism around gender, care, and unpaid work have provided strong intellectual foundations for redressing this lacuna. This special issue represents the collaborative theoretical modeling work of a multidisciplinary group formed to respond to that gap. This introduction to the special issue situates this work in the wider gender and macroeconomics literature, beginning with some notes on the role of mathematical modeling in feminist economics. A key conclusion that emerges from this introductory review is that while some polices, especially greater public funding of care needs, can alleviate the inequities embedded in the gendered provision of care, more equitable and sustainable development and growth are unlikely to result without a transformation of the systems of gender stratification that underlie care provisioning. HIGHLIGHTS Macroeconomic models and policymaking should center the economic and social contributions of caregivers. Care and unpaid work are fundamental to the functioning of the market economy. A transformation of the systems of gender stratification that underlie care provisioning is needed. No single solution exists, but macroeconomic models of care provide steps toward fixing gender inequities in care provisioning.

What is the aim of models in formal epistemology?

It is certainly well accepted that formal models play a key role in scientific job. Its use goes from natural sciences like physics and even to social sciences like economics and politics. Using mathematics allows the researcher to consider more complicated scenarios involving several variables. Some models are developed to make predictions, others to describe a phenomena, or just to improve the explanation of events in the world. But what has all this to do with philosophy? The aim of the present paper is to investigate debates on the role of formal models in a specific philosophical subject, precisely, the epistemology of rationality. Are we able to explain why models are needed in epistemological work? This answer will be addressed on the assumptions that epistemological theorizing is committed with normative statements. More specifically, epistemologists are concerned with normative questions about what rationality requires from epistemic agents. The first goal is to discuss some assumptions about the role of mathematical models in formal epistemology undertaking. And secondly, I will argue for the following two claims: (i) formal models are useful tools for predicting consequences of normative assumption about what is intuitively required by rationality; and (ii) insofar rationality theory is normative in virtue of being instrumentalist and aiming at truth, formal models are means-end tools, therefore, for rationality, mathematical models are devices for maximizing truth in doxastic states.

Leveraging mathematical models of disease dynamics and machine learning to improve development of novel malaria interventions

BackgroundSubstantial research is underway to develop next-generation interventions that address current malaria control challenges. As there is limited testing in their early development, it is difficult to predefine intervention properties such as efficacy that achieve target health goals, and therefore challenging to prioritize selection of novel candidate interventions. Here, we present a quantitative approach to guide intervention development using mathematical models of malaria dynamics coupled with machine learning. Our analysis identifies requirements of efficacy, coverage, and duration of effect for five novel malaria interventions to achieve targeted reductions in malaria prevalence.MethodsA mathematical model of malaria transmission dynamics is used to simulate deployment and predict potential impact of new malaria interventions by considering operational, health-system, population, and disease characteristics. Our method relies on consultation with product development stakeholders to define the putative space of novel intervention specifications. We couple the disease model with machine learning to search this multi-dimensional space and efficiently identify optimal intervention properties that achieve specified health goals.ResultsWe apply our approach to five malaria interventions under development. Aiming for malaria prevalence reduction, we identify and quantify key determinants of intervention impact along with their minimal properties required to achieve the desired health goals. While coverage is generally identified as the largest driver of impact, higher efficacy, longer protection duration or multiple deployments per year are needed to increase prevalence reduction. We show that interventions on multiple parasite or vector targets, as well as combinations the new interventions with drug treatment, lead to significant burden reductions and lower efficacy or duration requirements.ConclusionsOur approach uses disease dynamic models and machine learning to support decision-making and resource investment, facilitating development of new malaria interventions. By evaluating the intervention capabilities in relation to the targeted health goal, our analysis allows prioritization of interventions and of their specifications from an early stage in development, and subsequent investments to be channeled cost-effectively towards impact maximization. This study highlights the role of mathematical models to support intervention development. Although we focus on five malaria interventions, the analysis is generalizable to other new malaria interventions.Graphical abstract

Exploiting Endocytosis for Non-Spherical Nanoparticle Cellular Uptake

Several challenges exist for successful nanoparticle cellular uptake—they must be able to cross many physical barriers to reach their target and overcome the cell membrane. A strategy to overcome this challenge is to exploit natural uptake mechanisms namely passive and endocytic (i.e., clathrin- and caveolin-dependent/-independent endocytosis, macropinocytosis and phagocytosis). The influence of nanoparticle material and size is well documented and understood compared to the influence of nanomaterial shape. Generally, nanoparticle shape is referred to as being either spherical or non-spherical and is known to be an important factor in many processes. Nanoparticle shape-dependent effects in areas such as immune response, cancer drug delivery, theranostics and overall implications for nanomedicines are of great interest. Studies have looked at the cellular uptake of spherical NPs, however, fewer in comparison have investigated the cellular uptake of non-spherical NPs. This review explores the exploitation of endocytic pathways for mainly inorganic non-spherical (shapes of focus include rod, triangular, star-shaped and nanospiked) nanoparticles cellular uptake. The role of mathematical modelling as predictive tools for non-spherical nanoparticle cellular uptake is also reviewed. Both quantitative structure-activity relationship (QSAR) and continuum membrane modelling have been used to gain greater insight into the cellular uptake of complex non-spherical NPs at a greater depth difficult to achieve using experimental methods.

Fault identification using a structural and functional approach for digitalization conditions

One of the fundamental components in equipment maintenance and repair systems that implement modern risk-oriented strategies is information. The effectiveness of taken decisions is determined not only by the volume, but also by the quality of information data. The article formulates and justifies the requirements for the collected information on the technical condition of equipment and data for the analysis of its failures, taking into account modern capabilities and conditions of universal digitalization. The role of mathematical modeling in the formation of data on the functional parameters of the machine is shown, the main stages of construction are outlined and a set of developed mathematical models of the refrigerator is presented. Methods of equipment fault analysis are considered, their characteristics are given, areas and application features are indicated. An algorithm for analyzing events related to the operability of equipment based on entries in the equipment maintenance log is described. The proposed approaches are demonstrated by the example of a refrigerator with walking beams and a hydraulic drive, which is an integral part of the technological line of the CCM and has the most characteristic features of metallurgical equipment, which allows to use the solution of the problem of collecting and processing information about the technical condition of the CCM refrigerator as a standard.

Investigation on Structural Analysis of Flat Head Piston

In the investigation on structural analysis of flat head piston deflection and stress equations plays major role in mathematical modeling. The same has been used in this analysis. In the part of the analysis the thickness of the flat head of the piston is considered as the same of that of simply supported circular plate and the loads are applied on it reacts with the supports held at the top of the gudgeon hole. The piston is same as one side closed cylinder and ended with flat circular plate. It is the most general that the deflections due to axial loads are neglected. Hence the deflection and stress equations of the simply supported circular plate are adopted. Aluminum is taken as material of the component throughout the analysis and grey cast iron is taken as material for the rings in the modeling of the piston. Flexural rigidity plays a major role in the calculation for the analysis. The results of the mathematical analysis have been compared with the same of that of simulation using ANSYS software.

The Role of Mathematical Models in Immuno-Oncology: Challenges and Future Perspectives.

Immuno-oncology (IO) focuses on the ability of the immune system to detect and eliminate cancer cells. Since the approval of the first immune checkpoint inhibitor, immunotherapies have become a major player in oncology treatment and, in 2021, represented the highest number of approved drugs in the field. In spite of this, there is still a fraction of patients that do not respond to these therapies and develop resistance mechanisms. In this sense, mathematical models offer an opportunity to identify predictive biomarkers, optimal dosing schedules and rational combinations to maximize clinical response. This work aims to outline the main therapeutic targets in IO and to provide a description of the different mathematical approaches (top-down, middle-out, and bottom-up) integrating the cancer immunity cycle with immunotherapeutic agents in clinical scenarios. Among the different strategies, middle-out models, which combine both theoretical and evidence-based description of tumor growth and immunological cell-type dynamics, represent an optimal framework to evaluate new IO strategies.

Pre-service mathematics teachers\u2019 professional modeling competencies: a comparative study between Germany, Mainland China, and Hong Kong

Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers’ professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions.

Role of Mathematical Model in Curbing COVID-19 in Nigeria

COVID-19 is a viral disease that is caused by Severe Acute Respiratory Syndrome coronavirus 2 (SARSCoV-2) which has no approved vaccine. Based on the available non-pharmacological interventions like wearing of face masks, observing social distancing, and lockdown, this work assesses the impact of non-pharmaceutical control measures (social distancing and use of face-masks) and mass testing on the transmission of COVID-19 in Nigeria. A mathematical model for COVID-19 is formulated with intervention measures (observing social distancing and wearing of face masks) and mass testing. The basic reproduction number, R_0, is computed using next-generation method while the disease-free equilibrium is found to be locally and globally asymptotically stable when R_0< 1. The model is parameterized using Nigeria data on COVID-19 in Nigeria. The basic reproduction number is found to be less than unity (R_0 < 1) either when the compliance with intervention measures is moderate (50% <= alpha< 70%) and the testing rate per day is moderate (0,5 <=alpha_2 < 0,7) or when the compliance with intervention measures is strict (alpha>=70%) and the testing rate per day is poor (alpha_2 = 0,3). This implies that Nigeria will be able to halt the spread of COVID-19 under these two conditions. However, it will be easier to enforce strict compliance with intervention measures in the presence of poor testing rate due to the limited availability of testing facilities and manpower in Nigeria. Hence, this study advocates that Nigerian governments (Federal and States) should aim at achieving a testing rate of at least 0.3 per day while ensuring that all the citizens strictly comply with wearing face masks and observing social distancing in public.

Analysis on Krasnoselskii’s fixed point theorem of fuzzy variable fractional differential equation for a novel coronavirus (COVID-19) model with singular operator

The fuzzy variable fractional differential equations (FVFDEs) play a very important role in mathematical modeling of COVID-19. The scientists are studying and developing several aspects of these COVID-19 models. The existence and uniqueness of the solution, stability analysis are the most common and important study aspects. There is no study in the literature to establish the existence, uniqueness, and UH stability for fuzzy variable fractional (FVF) order COVID-19 models. Due to high demand of this study, we investigate results for the existence, uniqueness, and UH stability for the considered COVID-19 model based on FVFDEs using a fixed point theory approach with the singular operator. Additionally, discuss the maximal/minimal solution for the FVFDE of the COVID-19 model.

THE ROLE OF MATHEMATICAL MODELLING OF PRODUCTION PROBLEMS IN SPECIALIZED SCHOOL

The article discusses the main directions of the development of the educational environment and the role of mathematical modeling of production problems in a specialized school. The key issue of the modernization of education is described - this is improving its quality, bringing it in line with international standards. The emphasis is not on the knowledge gained, but rather on the process of applying this knowledge. The definition of the concept of pedagogical technology is given - this is information technology, since the basis of the technological process of training is the receipt and transformation of information.