Mathematical Modeling Approach Research Articles

Exploring factors shaping antibiotic resistance patterns in Streptococcus pneumoniae during the 2020 COVID-19 pandemic.

Non-pharmaceutical interventions implemented to block SARS-CoV-2 transmission in early 2020 led to global reductions in the incidence of invasive pneumococcal disease (IPD). By contrast, most European countries reported an increase in antibiotic resistance among invasive Streptococcus pneumoniae isolates from 2019 to 2020, while an increasing number of studies reported stable pneumococcal carriage prevalence over the same period. To disentangle the impacts of the COVID-19 pandemic on pneumococcal epidemiology in the community setting, we propose a mathematical model formalizing simultaneous transmission of SARS-CoV-2 and antibiotic-sensitive and -resistant strains of S. pneumoniae. To test hypotheses underlying these trends five mechanisms were built into the model and examined: (1) a population-wide reduction of antibiotic prescriptions in the community, (2) lockdown effect on pneumococcal transmission, (3) a reduced risk of developing an IPD due to the absence of common respiratory viruses, (4) community azithromycin use in COVID-19 infected individuals, (5) and a longer carriage duration of antibiotic-resistant pneumococcal strains. Among 31 possible pandemic scenarios involving mechanisms individually or in combination, model simulations surprisingly identified only two scenarios that reproduced the reported trends in the general population. They included factors (1), (3), and (4). These scenarios replicated a nearly 50% reduction in annual IPD, and an increase in antibiotic resistance from 20% to 22%, all while maintaining a relatively stable pneumococcal carriage. Exploring further, higher SARS-CoV-2 R0 values and synergistic within-host virus-bacteria interaction mechanisms could have additionally contributed to the observed antibiotic resistance increase. Our work demonstrates the utility of the mathematical modeling approach in unraveling the complex effects of the COVID-19 pandemic responses on AMR dynamics.

Evaluation of Banana Sale Drying Performance Using a Tray Dryer with Mathematics Modeling

The drying process of Banana Sale involves two mathematical modeling approaches: the Newton model and the Henderson-Pabis model. The bananas are sliced and dried for 220 minutes at a temperature of 60°C with a drying rate of 4.5 m/s, and observations are made every 20 minutes. The research includes the analysis of moisture content, texture, and mass changes in banana chips. The modeling using the Newton and Henderson-Pabis models shows significant results. The drying rate coefficient (k) in both models is 0.00335, and the R2 values for both models are 0.98961 and 0.98967. These results indicate that both models are theoretically suitable for explaining the banana chips drying process, providing essential insights for understanding and optimizing this process.

Dynamic interactions of HSV-2 and HIV/AIDS: A mathematical modeling approach

To enhance my research, I would like to share my knowledge of Herpes simplex virus-2 (HSV-2) and HIV/AIDS (Acquired Immunodeficiency Syndrome) through a mathematical model. The study’s objective is to develop and examine the co-disease model for the modern era using mathematical modeling. Based on their modes of transmission, HSV-2 and HIV/AIDS are currently the leading causes of death from infectious and severe chronic diseases. Depending on the severity of HIV-2’s chronic disease, the model is divided into five phases: the first two HIV-2 stages and the remaining three HIV stages. Ordinary differential equations (ODEs) are arranged differently by each individual. Investigations into the mathematical equation model have revealed the points of equilibrium between the free and endemic models. A study of the developed model was conducted using the basic reproduction numbers [R0] of HSV-2 and HIV. The results demonstrate that if R0<1, the free equilibrium of disease is asymptotically locally stable. When R0>1, equilibrium endemic states are regarded as existing. Finally, MATLAB software was used to simulate the numerical equations of the model.

A Review of Research on Supply Chain Resilience Evaluation Indicator System and Evaluation Methods

In the context of intensifying globalization and escalating supply chain risks, the study of supply chain resilience has increasingly attracted significant scholarly attention globally. This paper provides a comprehensive review of the current research landscape on the definition of supply chain resilience, its evaluation metric systems, and assessment methodologies, with an in-depth analysis of pertinent literature from both domestic and international sources. The extant research reveals a lack of consensus on the precise definition of supply chain resilience. The predominant evaluation methodologies encompass index weighting methods, mathematical modeling approaches, and simulation techniques, each possessing distinct advantages and limitations. This paper underscores the necessity for future research to emphasize the contextual variability in supply chain complexity, bolster the inherent resilience of supply chains, and develop more objective and versatile evaluation models. Furthermore, the integration of emerging technologies such as big data, artificial intelligence, and blockchain is anticipated to play a pivotal role in enhancing supply chain resilience. The deployment of these advanced technologies not only offers novel avenues for theoretical exploration but also furnishes crucial tools and methodologies for practical supply chain management.

Mathematical Modeling Approach for Compact Objects: A New Metric Potential in the Spherically Symmetric System with Schwarzchild’s Coordinates

Mathematical Modeling Approach for Compact Objects: A New Metric Potential in the Spherically Symmetric System with Schwarzchild’s Coordinates

Integrated algorithm evaluation of a scalable digital power management innovation model

Maintaining contemporary society’s steady progress depends on the reliable functioning of the electrical grid. The complexity and nonlinearity of today’s power networks make it difficult to manage them using conventional mathematical modeling approaches. To get around these problems, researchers have started using machine learning methods, such transient stability evaluation that is based on machine learning. This research suggests a way to evaluate the transient stability of power systems by making use of the complex feature extraction capabilities of multi-layer perceptron (MLP) networks. Another approach is to suggest an ensemble learning model that uses the easy-ensemble undersampling technique to deal with power system transient stability data that is unbalanced. This method preserves unstable power system samples, performs multiple undersampling on stable samples and combines unstable and undersampling samples into multiple new balanced training sets for MLP model training. The final ensemble model is obtained through voting integration strategy. Through conducting a comparative evaluation of individual models and ensemble models, this paper discovers that the ensemble learning models exhibit superior sensitivity and accuracy in effectively addressing system instability.

The Development of a Transient Analysis Platform of Near-Critical CO2 Thermodynamic Systems via an Enthalpy-Based Implicit Continuous Eulerian Approach

This work presents the development and validation of an enthalpy-based implicit continuous Eulerian (ICE) solver, termed the near-critical ICE solver (NICES), for the analysis of near-critical CO2 thermodynamic systems. Traditional approaches relying on pressure and temperature as main inputs for the analysis have limitations in handling CO2 near the critical point, which exhibits unique characteristics and frequent phase changes. To overcome these limitations, this study proposes using enthalpy as a more suitable mathematical modeling approach. The NICES methodology employs the homogeneous equilibrium model and the Span and Wagner equations of state for CO2. This solver demonstrates improved numerical stability and computational speed compared to explicit calculation methods, as validated by frictionless heated pipe scenarios involving phase transitions near the critical point. The enthalpy-based NICES platform can predict thermohydraulics, including multiphase flows, without requiring specialized two-phase flow models.

Thiophene Stability in Photodynamic Therapy: A Mathematical Model Approach.

Thiophene-containing photosensitizers are gaining recognition for their role in photodynamic therapy (PDT). However, the inherent reactivity of the thiophene moiety toward singlet oxygen threatens the stability and efficiency of these photosensitizers. This study presents a novel mathematical model capable of predicting the reactivity of thiophene toward singlet oxygen in PDT, using Conceptual Density Functional Theory (CDFT) and genetic programming. The research combines advanced computational methods, including various DFT techniques and symbolic regression, and is validated with experimental data. The findings underscore the capacity of the model to classify photosensitizers based on their photodynamic efficiency and safety, particularly noting that photosensitizers with a constant rate 1000 times lower than that of unmodified thiophene retain their photodynamic performance without substantial singlet oxygen quenching. Additionally, the research offers insights into the impact of electronic effects on thiophene reactivity. Finally, this study significantly advances thiophene-based photosensitizer design, paving the way for therapeutic agents that achieve a desirable balance between efficiency and safety in PDT.

Mitochondria and MICOS- function and modeling.

An extensive review is presented on mitochondrial structure and function, mitochondrial proteins, the outer and inner membranes, cristae, the role of F1FO-ATP synthase, the mitochondrial contact site and cristae organizing system (MICOS), the sorting and assembly machinery morphology and function, and phospholipids, in particular cardiolipin. Aspects of mitochondrial regulation under physiological and pathological conditions are outlined, in particular the role of dysregulated MICOS protein subunit Mic60 in Parkinson's disease, the relations between mitochondrial quality control and proteins, and mitochondria assignaling organelles. A mathematical modeling approach of cristae and MICOS using mechanical beam theory is introduced and outlined. The proposed modeling is based on the premise that an optimization framework can be used for a better understanding of critical mitochondrial function and also to better map certain experiments and clinical interventions.

Wave Energy Conversion through Oscillating Water Columns: A Review

An oscillating water column (OWC) is designed for the extraction and conversion of wave energy into usable electrical power, rather than being a standalone renewable energy source. This review paper presents a comprehensive analysis of the mathematical modeling approaches employed in OWC systems, aiming to provide an in-depth understanding of the underlying principles and challenges associated with this innovative technology. A prominent classification within the realm of wave energy devices comprises OWC systems, which exhibit either fixed or floating configurations. OWC devices constitute a significant proportion of the wave energy converter prototypes currently operational offshore. Within an OWC system, a hollow structure, either permanently fixed or floating, extends below the water’s surface, creating an enclosed chamber where air is captured over the submerged inner free surface. This comprehensive study offers a thorough assessment of OWC technology in conjunction with air turbines. Additionally, the investigation delves into theoretical, computational, and experimental modeling techniques employed for analyzing OWC converters. Moreover, this review scrutinizes theoretical, computational, and experimental modeling methodologies, providing a holistic understanding of OWC converters. Ultimately, this work contributes a thorough assessment of OWC technology’s current state, accentuating its potential for efficient wave energy extraction and suggesting future research avenues.

Decoding cardiac reinnervation from cardiac autonomic markers: A mathematical model approach

BackgroundAlthough cardiac autonomic markers are commonly used to assess cardiac reinnervation in heart transplant patients (HTx), their relationship to the degree of sympathetic and vagal cardiac reinnervation is not well understood yet. To study this relationship, we applied a mathematical model of the cardiovascular system and its autonomic control. MethodsBy simulating varying levels of sympathetic and vagal efferent sinoatrial reinnervation, we analyzed the induced changes in cardiac autonomic markers including resting heart rate (HR), bradycardic and tachycardic HR response to Valsalva Maneuver, root mean square of successive differences between normal heartbeats (RMSSD), low-frequency- (LF), high-frequency- (HF), and total spectral power. ResultsThe results suggest that for assessment of vagal cardiac reinnervation levels >20%, resting HR (ρ=0.99, p<0.05), RMSSD (ρ=0.97, p<0.05), and total spectral power (ρ=0.96, p<0.05) may be equally suitable as the commonly used measure of HF-power (ρ=0.97, p<0.05). To assess sympathetic reinnervation, our results suggest that the LF/HF-ratio (ρ=0.87, p<0.05) and tachycardic response to Valsalva maneuver (ρ=0.9, p<0.05) may be more suitable than the regularly used measure of LF-power (ρ=0.77, p<0.05). ConclusionsOur model reports, for the first time, mechanistic relationships between the cardiac autonomic markers and the level of efferent autonomic sinoatrial reinnervation. The results indicate differences in the suitability of these markers to assess vagal and sympathetic reinnervation. Although our analysis is purely conceptual yet, the developed mathematical model can help to gain important insights into the genesis of cardiac autonomic markers and their relationship to efferent sinoatrial reinnervation and, thus, provide indications for clinical study evaluation.

A Model for Membrane Degradation Using a Gelatin Invadopodia Assay.

One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells. A mathematical model composed of reaction-diffusion equations describing the evolution of the tumor cells density on a gelatin substrate, MMPs enzymes concentration and the degradation of the gelatin is proposed. This is completed with a calibration strategy. We perform a sensitivity analysis and explore a parameter estimation technique both on synthetic and experimental data in order to find the optimal parameters that describe the in vitro experiments. A comparison between numerical and experimental solutions ends the work.

Working with an instructional video on mathematical modeling: upper-secondary students’ perceived advantages and challenges

Many instructional videos in mathematics education target knowledge of procedures and algorithms. To design instructional videos that support students in a non-algorithmic domain, such as mathematical modeling, we developed a framework based on research on heuristic worked examples and instructional videos. Because students’ perceptions play an important role in whether they will engage with a learning resource, our research questions focus on the advantages and challenges students perceive when they work with an instructional video on mathematical modeling and solve a subsequent related modeling problem. Using a video based on the developed framework, we conducted an interview study with 14 pairs of upper-secondary students. The results of the qualitative text analysis showed that the perceived advantages and challenges were related to certain design features and to the processes of self-regulated learning with the video. The students experienced challenges regarding the video’s duration, the transfer to a subsequent related modeling problem, the absence of a teacher, and self-discipline. Hence, further learner support is necessary to guide the transition from working with a video to autonomous modeling, such as combining the video with strategic instruments and teacher support. In addition, interactive video features may be essential, as the students enjoyed how those features involved them in the process of watching the video. Overall, the results indicate that instructional videos are promising for providing heuristic worked examples, offering an innovative approach for teaching and learning mathematical modeling.

Teaching differential equations through a mathematical modelling approach: the impact on problem-solving and the mathematical performance of engineering undergraduates

Mathematical modelling is an interlinking process between mathematics and real-world problems that can be applied as a means to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas of science, such as engineering disciplines. This study was designed to investigate the effect of applying the modelling approach on problem-solving and mathematical performance of engineering undergraduates during a differential equations (DEs) course and compare the results with those of conventional teaching. A quasi-experimental method comprising a pretest-posttest design with a control group was applied in this study. Since the antecedent knowledge of calculus directly influences the ability of students to learn DEs, a placement test was first applied to both groups. A combination of results derived from the placement test and the modelling pretest was used as the covariate in the Analysis of Covariance (ANCOVA), and the modelling and mathematical performances of both groups were eventually examined. The results of this study indicate that apart from the fact that teaching DEs based on the modelling approach can increase the ability to apply mathematical knowledge in the field of engineering, it also can significantly enhance their problem-solving and mathematical performances.

Controlling the dissemination of rumors and antirumors in social networks: a mathematical modeling and analysis approach

Controlling the dissemination of rumors and antirumors in social networks: a mathematical modeling and analysis approach

Abstract A024: Ploidy as a predictive biomarker for gemcitabine sensitivity in triple-negative breast cancers

Abstract The polyploid giant cancer cell (PGCC) state is a common response of cancer cells to various stressors including chemotherapy, irradiation, hypoxia and viral infection. Upon stress, PGCCs adopt an endoreplication in which the genome replicates, mitosis is omitted, and cells grow in size, causing drug resistance. How accessible endoreplication is to a cell, therefore, directly translates to its resistance to therapy. In this study, we hypothesized that endoreplication and PGCC state are more accessible to cancer cells that already have a higher ploidy content prior to therapy. To test this hypothesis, we developed a comprehensive three-tier framework consisting of i) computational, ii) in-vitro and iii) in silico components. First, we designed a set of ordinary differential equations (ODEs) to mathematically model how cells enter and exit the PGCC state in response to a given stressor. We engineered how this in silico approach interacts with in vitro experiments into a broadly applicable software solution called CLONEID. The software uses computer vision to monitor phenotypic changes in cell and nuclear size from standard bright-field microscopy and classify cells into PGCC and non-PGCC states. We used CLONEID to test various therapeutic agents for their ability to select for a stable near-tetraploid (4N) population in a set of near-diploid (2N) cell lines. Through spontaneous cell fusions, we also obtained tetraploid breast cancer cells matched with their parental lines. Altogether, this framework enabled us to i) monitor the PGCC state experimentally in ii) two sets of matched isogenic cell lines with 2N and 4N DNA content to iii) model the successful entry and exit rates to and from the endoreplication state, respectively. As the first application of this framework, we tested the ability of our 2N and 4N TNBC lines (SUM159 and MDA-MB-231) to access the PGCC state upon treatment with 18 chemotherapy agents. Among those drugs, we observed that only gemcitabine caused continued cell growth without cell division in both tetraploid SUM159 and MDA-MB-231 cells whereas near-diploid parental lines were hypersensitive to the treatment. Consequently, tetraploid cancer cells continued to safely grow in the presence of gemcitabine. Furthermore, these PGCCs re-entered the proliferative cell cycle and grew in cell number when treatment is terminated. Gemcitabine-based chemotherapy is a standard treatment for patients with TNBC although its efficacy is limited mainly due to drug resistance. We expect our findings and three-component framework strategy to help stratify the TNBC patient population by their response to gemcitabine. In addition, our mathematical modelling approach has the promising potential to inform personalized dose optimization and to effectively decrease administered gemcitabine dose for a subset of patients, which would alleviate severe therapy-associated side effects and co-morbidities. Citation Format: Vural Tagal, Jackson Cole, Daria Miroshnychenko, Andriy Marusyk, Noemi Andor. Ploidy as a predictive biomarker for gemcitabine sensitivity in triple-negative breast cancers [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr A024.

Dynamic Optimization for Petrophysical Property Estimation in Unsteady-State Coreflooding Using Pyomo

Summary This paper deals with a mathematical modeling and optimization-based approach for estimating relative permeability and capillary pressure from average water saturation data collected during unsteady-state waterflooding experiments. Assuming the Lomeland-Ebeltoft-Thomas (LET) model for the variation of the relative permeability with saturation, the appropriate governing equations, boundary, and initial conditions were solved within the Pyomo framework. Using interior point optimization (IPOPT) with a least-squares objective function, the six parameters of the LET model that ensure the history matching between the measured and calculated average saturation are determined. Additionally, we inferred the capillary pressure function and performed a Sobol sensitivity analysis on the LET model parameters. The results showcase the reliability and robustness of our proposed approach, as it estimates the crucial parameters driving the variation of oil-water flow relative permeability across several cases and effectively predicts the capillary pressure trend. The proposed approach can be seen as an alternative to experimental and numerical simulation-based techniques for predicting relative permeability and capillary pressure curves.

Applications of Factor Analysis and Response Surface Methodology in Chemical Process Optimization Problems

Purpose: This work aims to show two applications of Design of Experiments to optimize processes in chemical industries. Theoretical Framework: Among the various mathematical modeling approaches, Design of Experiments (DoE) is widely used for the for the implementation of Quality by Design (QbD) in both research and industry. In QbD, understanding the product and the process is the key factor in ensuring the quality of the end product (Politis et al., 2017). Method: An assessment was made of the best method for creating mathematical models using Pareto graphs, factor graphs, contour graphs, response surface graphs and analysis of variance. Results and Conclusion: In both case studies, the statistical tools proved to be suitable for analyzing the processes and were able to find the optimum process factors to guarantee the best possible response variable. Originality/Value: Design of Experiments (DoE) is the main component of the statistical toolbox to deploy Quality by Design in both research and industrial settings.

Mathematical Modeling for Non-Linear Behaviorial Analysis of Job Embeddedness on Organization with Improved Statistical Tools

This research endeavors to enhance our understanding of job embeddedness within organizations by employing advanced mathematical modeling and statistical tools to analyze its non-linear behavioral dynamics. Job embeddedness refers to the extent to which an individual feels deeply connected to their job, colleagues, and the organization, which has significant implications for employee retention, performance, and organizational success. Our study applies cutting-edge statistical techniques, such as nonlinear regression models, machine learning algorithms, and network analysis, to decipher the complex interplay of factors that contribute to job embeddedness. By examining various intrinsic and extrinsic factors, including job satisfaction, organizational culture, social networks, and employee engagement, our mathematical models aim to provide a comprehensive perspective on the phenomenon. Through a rigorous analysis of large-scale organizational datasets, we uncover hidden patterns, nonlinear relationships, and critical tipping points that influence job embeddedness. This research not only contributes to a deeper theoretical understanding of job embeddedness but also offers practical insights for organizational leaders and human resource professionals to design targeted strategies for fostering employee commitment and reducing turnover. Ultimately, our mathematical modeling approach improves the accuracy of predicting and managing job embeddedness within organizations, thereby assisting businesses in creating more engaged, satisfied, and embedded workforces.

Facilitation and competition deconstructed: a mechanistic modelling approach to the stress gradient hypothesis applied to drylands

Facilitative interactions among species are key in plant communities. While experimental tests support the Stress Gradient Hypothesis (SGH) as an association between facilitation and stress, whether the shape of net effects along stress gradients can be predicted is controversial, with no available mathematical modelling approaches. We proposed a novel test, using a modification of the R* model to study how negative and positive partial effects of plant interactions in drylands combine along two common stress gradients. We modelled different interactions: competition for water and light, amelioration of soil infiltration and/or grazing protection, obtaining that intensity and importance of facilitation did not generally increase along stress gradients, being dependent on the interaction type. While along the water stress gradient net interactions became more positive, reaching a maximum and then waning again, various outcomes were observed along the grazing gradient. Shape variety was mainly driven by the various shapes of the partial positive effects. Under resource stress, additive interaction effects can be expected, whereas when including grazing, the effects were non-additive. In the context of the SGH, deconstructing the effect of positive and negative interaction in a pairwise mechanistic models of drylands does not show a unique shape along stress gradients.