Review Of Mathematical Models Research Articles

Canada's provincial COVID-19 pandemic modelling efforts: A review of mathematical models and their impacts on the responses.

Mathematical modelling played an important role in the public health response to COVID-19 in Canada. Variability in epidemic trajectories, modelling approaches, and data infrastructure across provinces provides a unique opportunity to understand the factors that shaped modelling strategies. Provinces implemented stringent pandemic interventions to mitigate SARS-CoV-2 transmission, considering evidence from epidemic models. This study aimed to summarize provincial COVID-19 modelling efforts. We identified modelling teams working with provincial decision-makers, through referrals and membership in Canadian modelling networks. Information on models, data sources, and knowledge translation were abstracted using standardized instruments. We obtained information from six provinces. For provinces with sustained community transmission, initial modelling efforts focused on projecting epidemic trajectoriesand healthcare demands, and evaluating impacts of proposed interventions. In provinces with low community transmission, models emphasized quantifying importation risks. Most of the models were compartmental and deterministic, with projection horizons of a few weeks. Models were updated regularly or replaced by new ones, adapting to changing local epidemic dynamics, pathogen characteristics, vaccines, and requests from public health. Surveillance datasets for cases, hospitalizations and deaths, and serological studies were the main data sources for model calibration. Access to data for modelling and the structure for knowledge translation differed markedly between provinces. Provincial modelling efforts during the COVID-19 pandemic were tailored to local contexts and modulated by available resources. Strengthening Canadian modelling capacity, developing and sustaining collaborations between modellers and governments, and ensuringearlier access to linked and timely surveillance data could help improve pandemic preparedness.

A Review of Mathematical Models Used to Estimate Wheeled and Tracked Unmanned Ground Vehicle Kinematics and Dynamics

This paper presents mathematical models to estimate the kinematics and dynamics of wheeled and tracked robots. The models account for the physical–mechanical characteristics of the ground, the influence of the center of gravity displacement on the cornering moment of resistance, and the influence of the interaction of the crawler with the roadway. The results of the models are characterized by defining computational relationships for a robot’s equations of motion, longitudinal forces, transverse forces, and resistive turning moments generated via longitudinal forces and transverse forces.

Canada's Provincial Covid-19 Pandemic Modelling Efforts: A Review of Mathematical Models and Their Impacts on the Responses

Canada's Provincial Covid-19 Pandemic Modelling Efforts: A Review of Mathematical Models and Their Impacts on the Responses

Minimizing Foaming and Bulking in Activated Sludge with Bacteriophage Treatment: A Review of Mathematical Modeling

The interest in the ability of phages to control bacterial populations has extended from medical applications into the fields of agriculture, aquaculture, and the food industry. In particular, several authors have proposed using bacteriophages as an alternative method to control foaming and bulking in wastewater treatment. This strategy has shown successful results at the laboratory scale. However, this technology is still in development, and there are several challenges to overcome before bacteriophages can be widely used to control foaming and bulking in pilot or larger-scale treatment plants. Several models of the infection mechanisms in individual bacteria–phage pairs have been reported, i.e., for controlled systems with only one bacterium species in the presence of one phage species. However, activated sludge treatment systems largely differ from this situation, which opens a large horizon for future research. Mathematical models will play a key role in this development process, and this review offers an overview of the proposed models: their applications, potential, and challenges. A particular focus is placed on the model properties, such as parameter identifiability and states’ observability, which are essential for process prediction, monitoring, or dynamic optimization.

Analysis of Five Mathematical Models for Crop Yield Prediction

A review of mathematical models used for the prediction of crop yield has been presented. Though there are many other non-mathematical techniques also available for the purpose, but mathematical modeling used for any real world problem opens many perspectives and provides many possible solu-tions of the problem for the betterment of human race. Five mathematical models (remote sensing followed by mathematical modeling, fuzzy logic based model, multiple linear regression mechanistic model, linear algebra based descriptive model and growth model based on TOMGRO mechanistic model) have been extracted and analyzed critically. These models are based on different mathematical concepts and techniques (non-linear optimization, fuzzy logic, linear predictor functions, linear algebra and differential calculus) covering a wide range of mathematical modeling. The general forms of these models have been derived. Average accuracy of presented models was found to be in the range 90% - 99% that strongly favors the optimum usage of mathematical modeling for crop yield forecasting processes. The section giving gaps and future research prospects presents the comparative analysis of the models. Development of new and moderated mathematical models for more precision and better accuracy has also been suggested using new mathematical techniques and hybridization or modifying the existing models.

Возможности использования математических моделей для теплового контроля дефектов многослойных биметаллических пластин

There is an actual task of delamination detection in multilayer bimetallic materials. Various methods of nondestructive testing (NDT) are used to solve it, including the method of transient thermal NDT. This method consists in remote registration, visualization and analysis of thermal (temperature) fields, which depend on thermophysical and geometric characteristics, thermal effect capacity and internal structure features of the object. The internal structure defects cause the appearance of abnormal temperature zones on the object surface. Their analysis allows us to judge the presence of changes in the material as a whole or in individual areas. It is possible to understand whether there is a defect under the anomalous site, and what its parameters are, if there is an adequate mathematical model that theoretically describes the dependence of the measuring results on the properties of the object and the selected technological modes. This model is a significant component of thermal NDT systems. For the same object or process, a certain set of mathematical models can be compiled, differing in the number of factors taken into account, the assumptions made, the completeness and accuracy of the description of the state of the object or the conditions of the process. The set of factors is determined by the purpose of the study, and in order to unambiguously determine the model of the thermal state, it is necessary to describe the characteristics of the object (geometric shape and thermophysical characteristics of the material) and the heat exchange process (characteristics of heat sources, initial and boundary conditions). Aim. To analyze the existing mathematical models for the research object – a multilayer bimetallic plate with delaminations between the outer and inner layers, and to identify common approaches to modeling the processes of thermal NDT of multilayer objects. Materials and methods. The structure of the mathematical model of the thermal state of the object is determined. An analytical review of mathematical models of thermal NDT of multilayer objects is performed. Results. The requirements, assumptions and limitations for a mathematical model of thermal NDT of a multilayer bimetallic plate with delamination defects are formulated. Conclusion. On the basis of the considered approaches to the mathematical modeling of the thermal state of multilayer objects with ideal layers contact and delamination defects, the necessary factors for the development of a model for the transient thermal NDT processes of the studied objects are determined.

A review of mathematical modelling in educational research in Indonesia

Mathematical models are mathematical representations of real-life problems which are used to simplify the problems and also for future prediction. Mathematical modelling has been used in educational research around the world mainly to predict students’ academic performance and to identify essential factors that affect students’ learning. However, in Indonesia there are very few published researches that employ mathematical modelling for educational studies. The present study is an integrative review conducted to document these studies. The objective is to provide an overview of the usage of mathematical modelling in educational research in Indonesia. The method of the review follows Torraco’s guidelines of integrative review which consist of critical analysis and synthesis. Five open-access published articles were discovered. These articles were written either in English or in Bahasa Indonesia. 3 out of 5 articles focused on explaining several predictor variables that influence student performance. The other 2 articles focused on comparing different methods of modelling to predict student performance. These findings show that mathematical modelling has not been extensively utilized in educational research in Indonesia.

A review of mathematical modeling, artificial intelligence and datasets used in the study, prediction and management of COVID-19.

In the past few months, several works were published in regards to the dynamics and early detection of COVID-19 via mathematical modeling and Artificial intelligence (AI). The aim of this work is to provide the research community with comprehensive overview of the methods used in these studies as well as a compendium of available open source datasets in regards to COVID-19. In all, 61 journal articles, reports, fact sheets, and websites dealing with COVID-19 were studied and reviewed. It was found that most mathematical modeling done were based on the Susceptible-Exposed-Infected-Removed (SEIR) and Susceptible-infected-recovered (SIR) models while most of the AI implementations were Convolutional Neural Network (CNN) on X-ray and CT images. In terms of available datasets, they include aggregated case reports, medical images, management strategies, healthcare workforce, demography, and mobility during the outbreak. Both Mathematical modeling and AI have both shown to be reliable tools in the fight against this pandemic. Several datasets concerning the COVID-19 have also been collected and shared open source. However, much work is needed to be done in the diversification of the datasets. Other AI and modeling applications in healthcare should be explored in regards to this COVID-19.

Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

A review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unilateral contact problems with buckling, including models for plates, resting on elastic foundations, and contact models for delaminated composite plates, are formulated. Dynamic nonlinear equations for elastic plates, which possess buckling and contact effects are also presented. Most commonly used boundary and initial conditions are set up. The advantages and disadvantages of analytical, semi-analytical, and numerical techniques for the buckling and contact problems are discussed. The corresponding references are given.

A Review of mathematical models for prediction of Stress-strain and moment –curvature behaviour in concrete

In this paper, a mathematical model for predicting the stress –strain and moment curvature relations in concrete is developed. A good number of empirical equations were proposed to represent stress-strain behaviour of conventional concrete. Most of the equations can be used for the ascending portion of the curve only. In 1997 Mansur et al. have adopted Carriera and Chu (1985) model, which was based on the model proposed by Popovics (1973). As such, model proposed by Mansur et al includes both ascending and descending portions of the stress-strain curve for the confined concrete with introduction of two constants for the descending portion of the curve. Several researchers proposed various empirical equations for stress-strain behaviour as briefly reported in the previous chapter. An attempt has been made in this study to develop mathematical models for concrete in unconfined state. These analytical equations can be applied to any concrete with slight modifications. These models are developed to validate the experimental values obtained.

Review of mathematical models for calculation of gas foil bearing elastic element deformation

Review of mathematical models for calculation of gas foil bearing elastic element deformation

Forecasting the Prevalence of Diabetes Mellitus Using Econometric Models.

IntroductionThe prevalence of diabetes in Kazakhstan has reached epidemic proportions, and this disease is becoming a major financial burden. In this research, regression analysis methods were employed to build models for predicting the number of diabetic patients in Kazakhstan in 2019, as this should aid the costing and policy-making performed by medical institutions and governmental offices regarding diabetes prevention and treatment strategies.MethodsA brief review of mathematical models that are potentially useful for the task of interest was performed, and the most suitable methods for building predictive models were selected. The chosen models were applied to explore the correlation between population growth and the number of patients with diabetes as well as the correlation between the increase in gross regional product and the growth in the number of patients with diabetes. Moreover, the relationship of population growth and gross domestic product with the growth in the number of patients with diabetes in Kazakhstan was determined. Our research made use of the scikit-learn library for the Python programming language and functions for regression analysis built into the Microsoft Excel software.ResultsThe predictive models indicated that the prevalence of diabetes in Kazakhstan will increase in 2019.ConclusionMathematical models were used to find patterns in a comprehensive statistical dataset on registered diabetes patients in Kazakhstan over the last 15 years, and these patterns were then used to build models that can accurately predict the prevalence of diabetes in Kazakhstan.

Review on mathematical models for the prediction of solar radiation

Global Solar Radiation (GSR) data is important for all solar energy based applications, mainly to forecast the output power of solar PV system in case of renewable energy integration in to the existing grid. The solar radiation components are measured using pyranometer, solarimeter, pyroheliometer and so on. It is not practically possible to install this radiation measuring instruments at all the locations due to the cost and difficulty in measurements. Hence the availability of solar radiation data is limited to few meteorological stations especially in the developing country like India. Therefore, it is necessary to develop mathematical models to predict the solar radiation to eliminate the costly pyranometer. In this paper, the review of mathematical models using trigonometric functions for the prediction of global solar radiation is presented. The mathematical models are applicable wherever the radiation data is unavailable. From the review results, it is concluded that mathematical model with both sine and cosine wave equation gives good prediction accuracy with correlation coefficient of 0.95

Determination of buckling loads for wooden beams using the elastic models

This paper presents a theoretical and experimental analysis of buckling load of the square wooden beams. The buckling tests were conducted on the wooden beams with three different lengths, and the critical buckling load was determined on the basis of the measured relation between the axial displacement and axial load. Analytical solutions for the critical buckling load of the beams were derived using the Euler–Bernoulli beam theory and Timoshenko beam theory. When deriving the models, both small and large deformation theories were considered. Moreover, the effect of a grain orientation was included in the models. The results show that the selected solution was in agreement with the values measured from the experiment. The paper provides a review of mathematical models and gives us a comparison between the theories and experiments with subsequent recommendations for practice.

Noise and vibration suppression of electric power steering systems: a survey

Electric power steering (EPS) systems have become the ideal steering system for most vehicles because of the generated torque assist mechanism making steering easier for drivers. However, EPS systems generate unwanted noise and vibration that can adversely affect the comfort and health of drivers. Numerous studies have been conducted to examine the source of vibrations. Various isolation techniques including passive, active, or semi active have been proposed for achieving best noise and vibration attenuation. Discrete and distributed mathematical models have been employed to predict the dynamic response of EPS systems. This paper presents a state-of-the-art review of mathematical modelling, vibration isolation methods, and optimisation techniques used for improving the design of EPS systems.

Noise and vibration suppression of electric power steering systems: a survey

Electric power steering (EPS) systems have become the ideal steering system for most vehicles because of the generated torque assist mechanism making steering easier for drivers. However, EPS systems generate unwanted noise and vibration that can adversely affect the comfort and health of drivers. Numerous studies have been conducted to examine the source of vibrations. Various isolation techniques including passive, active, or semi active have been proposed for achieving best noise and vibration attenuation. Discrete and distributed mathematical models have been employed to predict the dynamic response of EPS systems. This paper presents a state-of-the-art review of mathematical modelling, vibration isolation methods, and optimisation techniques used for improving the design of EPS systems.

Is Management a Science or an Art? From Theory to Practice of Management

Purpose – The purpose of this article is to discuss and show that management is a science, not just an art. Decision-making in the enterprise requires talent and special skills supported by the right qualifications. According to Tatarkiewicz, management can be considered as an art, which can be interpreted as follows: “(...) man’s conscious creation is a work of art always when it recreates reality, shapes forms, or expresses experience, yet it is able either to delight, or touch, or shock” (Tatarkiewicz, 1972). On the other hand, the company management is understood as a continuous process of making decisions based on reliable knowledge, observations and experiences – it is, therefore, a science, and modern managers are not just passive consumers of research knowledge, but also its creators. Contemporary theories focus attention on constructing appropriate models, which support the decisions of managers allowing them to somehow “spy” and observe the effects of their decisions. The aim of the paper is to show that in the modern economy, design models to support the management of the enterprise is the science that uses the achievements of other sciences, creative adaptation of these achievements in modeling phenomena occurring in the world economy. The aim of this article is to show that management sciences are increasingly exploiting modern knowledge to build models for developing practical concepts of management systems. Design/Methodology/Approach – The authors present the review of mathematical models, computer models (used in situations where the analytical models cannot find the best solution), and in particular artificial intelligence algorithms and selected models of dynamic system for managing the organization and some examples of applications. Findings – The results obtained show that in the management sciences, many models are used to support managerial decisions. Of course, the achievements of other sciences are very often used, management is of an application, but also of scientific nature, because, in order to skillfully use knowledge from other fields, decision-making models should be developed to solve problems in management and allow to use the achievements of these other areas. Research limitations/implications – The limitations of this paper result from the fact that only selected models are presented in the article. The authors hope that these selected models will be the argument that management science is becoming more and more science and not an art only. Originality/Value – This paper presents the review of modern methods used in management sciences to show that modern management is more a science than an art.

The evolution of male mate choice and female ornamentation: a review of mathematical models.

The evolution of male preferences and of female ornaments in species with traditional sex roles (i.e., polygyny) have been highlighted as areas in need of more active research by an accumulation of recent findings. The theoretical literature on these topics is relatively small and has centered on the evolution of male choice. Mathematical models have emphasized that, under polygyny, the evolution of male preferences faces much greater competition costs than does the evolution of female preferences. We discuss ways in which costly male choice can nonetheless evolve, via (1) direct selection that favors preferences, primarily through mating with highly fecund females, (2) mechanisms that rely on indirect selection, which weakly counters competitive costs of male preferences, and (3) genetic constraints, primarily in the form of pleiotropy of male and female preferences and traits. We also review a variety of mathematical models that have elucidated how costs to male preferences can be avoided. Finally, we turn our attention to the relatively scant theoretical literature on the effects of male mate choice on the evolution of female traits. We emphasize the finding that the presence of male preferences cannot be assumed to lead to the evolution of female ornaments during polygyny, and point out situations where models have elucidated ways in which female ornaments can nevertheless evolve.

The Impact of Antimalarial Use on the Emergence and Transmission of Plasmodium falciparum Resistance: A Scoping Review of Mathematical Models.

The emergence and transmission of resistance to antimalarial treatments continue to hamper malaria elimination efforts. A scoping review was undertaken regarding the impact of antimalarial treatment in the human population on the emergence and transmission of Plasmodium falciparum resistance, to (i) describe the use of mathematical models used to explore this relationship; (ii) discuss model findings; and (iii) identify factors influencing the emergence and transmission of resistance. Search strategies were developed and deployed in six major databases. Thirty-seven articles met the eligibility criteria and were included in the review: nine articles modeled the emergence of resistance, 19 modeled the transmission of resistance, and nine modeled both the emergence and transmission. The proportion of antimalarial use within the population and the presence of residual drug concentrations were identified to be the main predictors of the emergence and transmission of resistance. Influencing factors pertaining to the human, parasite and mosquito populations are discussed. To ensure the prolonged therapeutic usefulness of antimalarial treatments, the effect of antimalarial drug use on the emergence and transmission of resistance must be understood, and mathematical models are a useful tool for exploring these dynamics.

Mathematical Models for Prediction of Temperature Effects on Kinetic Parameters of Microorganisms’ Inactivation: Tools for Model Comparison and Adequacy in Data Fitting

Microbial inactivation often follows a sigmoidal kinetic behaviour, with an initial lag phase, followed by a maximum inactivation rate period and tending to a final asymptotic value. Mathematically, such tendencies may be described by using primary kinetic models (Gompertz based model is one example) that describe microbial survival throughout processing time when stressing conditions are applied. The parameters of kinetic models are directly affected by temperature. Despite the number of mathematical equations used to describe the dependence of the kinetic parameters on temperature (so-called secondary models), there is a lack of studies regarding model comparison and adequacy in data fitting. This work provides a review of mathematical models that describe the temperature dependence of kinetic parameters related to microbial thermal inactivation. Regression analysis schemes and tests seeking model comparison are presented. A case study is included to provide guidance for the assessment of secondary model adequacy and regression analyses procedures. When modelling temperature effects on sigmoidal inactivation kinetics of microorganisms, one should be aware about the regression methodology applied. The most adequate models according to the two-step regression methodology may not be the best selection if a global fit is applied.