Mathematical Modeling Approach Research Articles

Emergence failure of early epidemics: A mathematical modeling approach.

Epidemic or pathogen emergence is the phenomenon by which a poorly transmissible pathogen finds its evolutionary pathway to become a mutant that can cause an epidemic. Many mathematical models of pathogen emergence rely on branching processes. Here, we discuss pathogen emergence using Markov chains, for a more tractable analysis, generalizing previous work by Kendall and Bartlett about disease invasion. We discuss the probability of emergence failure for early epidemics, when the number of infected individuals is small and the number of the susceptible individuals is virtually unlimited. Our formalism addresses both directly transmitted and vector-borne diseases, in the cases where the original pathogen is 1) one step-mutation away from the epidemic strain, and 2) undergoing a long chain of neutral mutations that do not change the epidemiology. We obtain analytic results for the probabilities of emergence failure and two features transcending the transmission mechanism. First, the reproduction number of the original pathogen is determinant for the probability of pathogen emergence, more important than the mutation rate or the transmissibility of the emerged pathogen. Second, the probability of mutation within infected individuals must be sufficiently high for the pathogen undergoing neutral mutations to start an epidemic, the mutation threshold depending again on the basic reproduction number of the original pathogen. Finally, we discuss the parameterization of models of pathogen emergence, using SARS-CoV1 as an example of zoonotic emergence and HIV as an example for the emergence of drug resistance. We also discuss assumptions of our models and implications for epidemiology.

Development of a SARS-CoV-2 viral dynamic model for patients with COVID-19 based on the amount of viral RNA and viral titer.

The target-cell limited model, which is one of the mathematical modeling approaches providing a quantitative understanding of viral dynamics, has been applied to describe viral RNA profiles of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in previous studies. However, these models have been developed mainly using patient data from the early phase of the pandemic. Furthermore, no reports focused on the profiles of the viral titer. In this study, the dynamics of both viral RNA and viral titer were characterized using data reflecting the current clinical situation in which the Omicron variant has become epidemic and vaccines for SARS-CoV-2 have become available. Consecutive data for 5212 viral RNA levels and 5216 viral titers were obtained from 720 patients with coronavirus disease 2019 (COVID-19) in a phase II/III study for ensitrelvir. Our model assumed that productively infected cells would produce only infectious viruses, which could be transformed into non-infectious viruses, and has been used to describe the dynamics of both viral RNA levels and viral titer. The time from infection to symptom onset (tinf) of unvaccinated patients was estimated to be 3.0 days, which was shorter than that of the vaccinated patients. The immune-related parameter as a power function for the vaccinated patients was 1.1 times stronger than that for the unvaccinated patients. Our model allows the prediction of the viral dynamics in patients with COVID-19 from the time of infection to symptom onset. Vaccination status was identified as a factor influencing tinf and the immune function.

Balancing parallel assembly lines with human-robot collaboration: problem definition, mathematical model and tabu search approach

Human-robot collaboration (HRC), as an emerging production mode, has garnered significant attention in the context of the growing smart manufacturing. This study aims to investigate the application of human-robot collaboration in parallel assembly lines and explore its potential for improving productivity, resource utilisation and flexibility. To the best of our knowledge, this is one of the first attempts to consider the combination of parallel assembly line balancing problem (PALBP) and human-robot collaboration. In this study, the parallel assembly line balancing problem with human-robot collaboration (PALBP-HRC) is introduced and characterised. The collaboration mode allows human workers and robots to execute tasks both in parallel and in collaboration. A mixed-integer programming model (MIP) that minimises the cycle time is formulated and a lower bound is proposed. Due to the NP-hardness, we develop an adapted tabu search (TS) algorithm specifically tailored for problem characterisation. Experimental results indicate that the proposed TS algorithm achieves competing performance compared to the MIP and other algorithms, including genetic algorithm (GA) and simulated annealing (SA) algorithm. The comparison between PALBP and PALBP-HRC demonstrates that the integration of human-robot collaboration to parallel assembly line can achieve significant improvements in efficiency and flexibility.

APPLICATION OF MATHEMATICAL MODELS IN THE DIAGNOSIS OF DISEASES OF INTERNAL ORGANS

The application of diagnostic expert systems in medical technology signifies a notable progression, as they provide a computerized framework for decision-support, assisting healthcare practitioners in the process of disease diagnosis. These systems facilitate the integration of patient data, encompassing symptoms and medical history, with a knowledge base in order to produce a comprehensive compilation of potential diagnoses. Through the utilization of knowledge-based methodologies, they enhance these potentialities in order to ascertain the most probable diagnosis. The present study examines expert systems, investigating their historical development, architectural structure, and the approaches utilized for knowledge representation. There is a significant emphasis placed on the advancement and implementation of these systems within the medical industry of Kazakhstan. This paper provides a comprehensive analysis of the benefits and drawbacks associated with diagnostic expert systems, emphasizing their potential to bring about significant advancements in medical fields. The study places significant emphasis on the necessity of developing and conducting thorough testing of these systems in order to improve the precision and effectiveness of medical diagnostics. The statement recognizes the importance of continuous research in order to enhance the design and implementation of these systems in various healthcare settings. This research makes a notable addition by examining optimization theory in the field of medical diagnosis. This study presents novel approaches for effectively addressing the intricacies and uncertainties associated with the diagnosis of complicated disorders. The work presents methodology for navigating the complex field of medical diagnostics by utilizing mathematical modeling and optimization approaches, specifically the gradient projection method. The utilization of diverse ways to tackle qualitative ambiguities in this approach signifies a significant progression inside the domain of diagnostic expert systems.

A Model Validatory Approach in Determining Solar Panel Tilting Angles and Orientations at the Brikama Environment of The Gambia

This paper determines the solar panel optimal tilt angle and orientations at the Brikama environment of The Gambia. This was achieved by comparing mathematical model results with experimental data collected using a PV module (Model AP-120) manufactured by AstroPower, USA, and a single-axis tracker technology at the same location and months of the year. The experimental tilt angles obtained range from 5.1°-28.2° with an average angle of 14.8° while the mathematical model approach obtained the tilt angle to be within the range of 9.1°-22.3° with a mean value of 15.5°. The generated power analysis revealed that the peak power produced by the solar panel was recorded at an angle of 30° due South and the mean power gain from the orientation of the PV panel ranged from 3.6-48.1W. The mean power result suggests that, in comparison to a horizontal position, solar collecting efficiency is higher at the optimal tilt angle.

Energy optimization of the smart residential electrical grid considering demand management approaches

-Many researchers have investigated the optimal energy scheduling to meet the demand regarding sustainable development issues and the economic and technical indices. This study presents the day-ahead operation of a smart residential distribution electrical grid as a bi-stage-multiple-criteria decision-making modeling. The proposed energy optimization is implemented based on optimal demand management in upper-stage and multiple-criteria decision-making in lower-stage. The multiple-criteria problem is modeled from the viewpoint of the grid's operator to optimize energy consumption costs, power losses and demand side comfort. The optimal demand management in upper-stage is coordinated considering price traffic in the upstream grid. The load shifting approach and load interruption approach are presented as optimal demand management for residential consumers. The operation of demand management by using load shifting and load interruption approaches is done via deferrable loads and clippable loads in smart residential homes, respectively. The proposed energy optimization in both stages by improved sunflower optimization (IFSO) is handled, and the TOPSIS method is proposed for the best trade-off of the multiple-criteria decision-making. The day-ahead energy operation is applied on the 33-bus distribution network to investigate the effectiveness of the residential distribution electrical grid considering obtained results from mathematical modeling and demand management approaches.

A regularization strategy for discontinuity when modelling coupled water and heat flow in freezing unsaturated soil

Freezing tightly couples the water and heat flow. In most porous media, the interface between liquid and frozen water is not sharp and a slushy zone is present. There are two distinct approaches for mathematical modelling of freezing. It is the equilibrium approach which allows an instant freezing under given conditions and non-equilibrium approach where a specific timing in the freezing process is considered. In this contribution, we specifically target the equilibrium approach.The key mathematical model for the equilibrium approach is the Clausius–Clapeyron equation, which allows the derivation of a soil freezing curve relating temperature to pressure head. Implementing freezing soil accurately is not a straight-forward. Using the Clausius–Clapeyron equation creates a discontinuity in the freezing rate and latent heat at the freezing point. Little attention has been paid to the adequate description of the numerical treatment of this phenomenon and to the computational challenges that it poses. Numerical approximation of this discontinuous system is prone to spurious oscillations. In this contribution, we show the application of regularization of the discontinuous term. This treatment successfully stabilizes the computation and can remove oscillations. To avoid over-regularization, we present here a minimax strategy to determine optimal regularization parameters. We further compare an over-regularized setup with the non-equilibrium approach, where we show that a successful regularization is equivalent to incorporating a minimal timing to the freezing process. Finally – for validating our implementation and computational approach – experimental laboratory data of the volumetric water content and temperature profiles from previously published soil freezing experiments were represented here with the optimally regulized equilibrium approach.

The effect of temperature on the boundary conditions of West Nile virus circulation in Europe.

West Nile virus (WNV) is a vector-borne flavivirus that causes an increasing number of human and equine West Nile fever cases in Europe. While the virus has been present in the Mediterranean basin and the Balkans since the 1960s, recent years have witnessed its northward expansion, with the first human cases reported in Germany in 2018 and the Netherlands in 2020. WNV transmission and amplification within mosquitoes are temperature-dependent. This study applies a mathematical modelling approach to assess the conditions under which WNV circulation occurs based on the proportion of mosquito bites on WNV-competent birds (dilution), vector-host ratios, mosquito season length and the observed daily temperature data. We modelled five distinct European regions where previous WNV circulation has been observed within the Netherlands, Germany, Spain, Italy, and Greece. We observed that the number of days in which the basic reproduction number (R0) is above one, increased over the last 40 years in all five regions. In the Netherlands, the number of days in which the R0 is above one, is 70% lower than in Spain. The temperature in Greece, Spain and Italy allowed for circulation under low vector-host ratios, and at a high dilution. On the other hand in the Netherlands and Germany, given the observed daily temperature, the thresholds for circulation requires a lower dilution and higher vector-host ratios. For the Netherlands, a short window of introductions between late May and mid-June would result in detectable outbreaks. Our findings revealed that the temperate maritime climate of the Netherlands allows WNV circulation primarily during warmer summers, and only under high vector-host ratios. This research contributes valuable insights into the dynamic relationship between temperature, vector properties, and WNV transmission, offering guidance for proactive strategies in addressing this emerging health threat in Europe.

Effect of Pulsed Electric Fields on the Shelf Stability and Sensory Acceptability of Osmotically Dehydrated Spinach: A Mathematical Modeling Approach.

This study focused on the osmotic dehydration (OD) of ready-to-eat spinach leaves combined with the pulsed electric field (PEF) pre-treatment. Untreated and PEF-treated (0.6 kV/cm, 0-200 pulses) spinach leaves were osmotically dehydrated at room temperature for up to 120 min. The application of PEF (0.6 kV/20 pulses) prior to OD (60% glycerol, 25 °C, 60 min) lowered water activity (aw = 0.891) while achieving satisfactory product acceptability (total sensory hedonic scoring of 8). During the storage of the product (at 4, 8, 12, and 20 °C for up to 30 d), a significant reduction in total microbial count evolution was observed (9.7 logCFU/g for the untreated samples vs. 5.1 logCFU/g for the PEF-OD-treated samples after 13 d of storage at 4 °C). The selection of these PEF and OD treatment conditions enabled the extension of the product shelf life by up to 33 d under chilled storage. Osmotically treated spinach could find application in ready-to-eat salad products with an extended shelf life, which is currently not possible due to the high perishability of the specific plant tissue.

A simplified mathematical modeling approach for thermal runaway of Li(Ni0.8Co0.1Mn0.1)O2 pouch cells based on thermal runaway experimental data

Currently, the numerical modeling methods used to characterize the thermal runaway and propagation mechanisms in NCM811 pouch batteries still face numerous challenges. This is primarily due to the uncertainties in thermal runaway reactions and the immense computational demands encountered when modeling begins at the granular level of the cell. To address this issue, this study designed a series of experiments for an NCM811 pouch battery. By employing experimental data, reasonable assumptions were made regarding the combined effects of solid-state thermal conduction, electrochemical heating, and fluid-solid heat transfer through gas jet streams. A simplified thermal runaway mathematical modeling method based on experimental data was proposed, effectively tackling the problem. This framework was then applied to thermal runaway experiments on a single NCM811 battery used in this study, providing essential input parameters for three-dimensional numerical modeling of modules composed of multiple batteries in multiphysics simulation software. The simulation results derived from the proposed method were in good agreement with experimental data. This study can characterize the thermal runaway and thermal propagation characteristics of battery modules using single-cell thermal runaway experiments. Moreover, the proposed modeling approach not only predicted the experimental outcomes of the NCM811 pouch battery with reasonable accuracy but also provided smoother data, elucidating the highly fluctuating trends observed in experimental data. This method also offers guidance for designing fire prevention and smoke exhaust systems for battery packs. This study presents a novel approach for the mathematical modeling of thermal runaway and thermal propagation in battery modules using NCM811 pouch batteries, contributing to the ongoing development of lithium-ion battery module design.

Optimization and sensitivity analysis of heat transfer for Powell–Eyring fluid between rotating rolls with temperature-dependent viscosity: A mathematical modeling approach

This study explores the flow of a non-Newtonian fluid between two rolls that are counter-rotating at the same speed and of equal size. The fluid's viscosity depends on temperature, and we investigate its theoretical impact on the thickness of the sheet and other engineering parameters relevant to the process. We derive non-dimensional mass and momentum balance equations using suitable transformation and the lubrication approximation theory. The expressions for velocity distribution, pressure gradient, flow rate, temperature profile, and pressure fields have been obtained by utilizing the perturbation method. After obtaining these expressions, we compute engineering quantities such as the roll separation force, streamline, Nusselt number, and the power input required to drive both cylinders based on the system's kinematical and geometrical parameters. We also obtain numerical solutions using the finite difference method and built-in (BVP method) in Maple. Further, we use response surface methodology and analysis of variance to determine what the mathematical models mean and whether they are good enough for sensitivity and optimization analysis of the heat transmission and roll separation force. Using statistical tools such as the R2, we determine that our Nusselt number and roll separation force provide the best solution for the considered model. Additionally, it has been observed that as the Weissenberg number increases, velocity tends to rise; conversely, velocity decreases with a higher velocity ratio. Also, the temperature profile is notably influenced by the Brickman number and increases with the increase in the Brickman number. It has also been noted that as the values of velocities ratio increase, the separation points shift toward the nip region, while concurrently, the coating thickness decreases. Furthermore, we also demonstrate that compression between analytical and numerical solutions for the considered problem of fluid flow, which suggests that the results presented here are reasonable. Finally, we compare our work with published studies to validate our findings. Hence, these factors help in an efficient fluid coating process and improve the substrate life.

Measuring BIM Implementation: A Mathematical Modeling and Artificial Neural Network Approach

Measuring BIM Implementation: A Mathematical Modeling and Artificial Neural Network Approach

Integrating Computational Fluid Dynamics for Maneuverability Prediction in Dual Full Rotary Propulsion Ships: A 4-DOF Mathematical Model Approach

To predict the maneuverability of a dual full rotary propulsion ship quickly and accurately, the integrated computational fluid dynamics (CFD) and mathematical model approach is performed to simulate the ship turning and zigzag tests, which are then compared and validated against a full-scale trial carried out under actual sea conditions. Initially, the RANS equations are solved, employing the Volume of Fluid (VOF) method to capture the free water surface, while a numerical simulation of the captive model test is conducted using the rigid body motion module. Secondly, hydrodynamic derivatives for the MMG model are obtained from the CFD simulations and empirical formula. Lastly, a four-degree-of-freedom mathematical model group (MMG) maneuvering model is proposed for the dual full rotary propulsion ship, incorporating full-scale simulations of turning and zigzag tests followed by a full-scale trial for comparative validation. The results indicate that the proposed method has a high accuracy in predicting the maneuverability of dual full-rotary propulsion ships, with an average error of less than 10% from the full-scale trial data (and within 5% for the tactical diameters in particular) in spite of the influence of environmental factors such as wind and waves. It provides experience in predicting the maneuverability of a full-scale ship during the ship design stage.

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

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

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

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

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

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

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

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

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

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

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

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

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

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