Mathematical Modeling Perspective Research Articles

The use of an imperfect vaccination and awareness campaign in the control of antibiotic resistant gonorrhoea infection: A mathematical modelling perspective

The multi drug-resistant Neisseria gonorrhoeae has been classified by the World Health Organisation (WHO) as a high-priority global public health problem. This underlines the need for better understanding of the transmission dynamics and proposing an optimal intervention strategy to control the disease. In this article, a deterministic mathematical model for the transmission dynamics of gonorrhoea as an antibiotic resistant disease in a population with an imperfect vaccination is proposed and analysed. The model incorporates the classes of vaccinated individuals and individuals equipped with self protection interventions to reduce antibiotic resistant cases. The threshold parameter R0, the basic reproduction number, for the analysis of the model is calculated. In the given setting, the model exhibits a backward bifurcation for R0<1. However, if the efficacy of the vaccine is 100% without a waning effect, the model is shown to be without a backward bifurcation and the disease-free equilibrium is globally asymptotically stable whenever R0<1. The global sensitivity analysis of the model to variations in parameter values is also performed to determine the most influential parameters on the disease transmission. Moreover, the optimal control analysis of the full model is presented and the optimal intervention strategies are proposed. The proposed intervention strategies are shown to be able to control the disease within a relatively shorter period of time. Finally, numerical experiments are presented to support the theoretical analysis of the model.

Real-Time Anomaly Detection in Video Surveillance: A Mathematical Modeling and Nonlinear Analysis Perspective with MobileNet and Bi-LSTM

Real-Time Anomaly Detection in Video Surveillance: A Mathematical Modeling and Nonlinear Analysis Perspective with MobileNet and Bi-LSTM

Optimal Control Strategy for SLBRS with Two Control Inputs

Computer virus attacks result in significant losses each year, drawing considerable attention from enterprises, governments, academic institutions, and various other sectors. Researchers have proposed various approaches to fight against computer viruses, including antivirus software and internet firewalls. In this paper, we focus on investigating computer virus transmission from the perspective of mathematical modeling. Our main contributions in this paper are threefold: (1) we improve the classical SLBRS model by incorporating cure rates, effectively capturing the dynamics of computer network maintenance; (2) we introduce an optimal control system within the SLBRS framework, with the dual objectives of minimizing network detoxification costs and reducing the proportion of broken-out nodes; and (3) by employing Pontryagin’s Maximum Principle, we establish the existence and uniqueness of an optimal control strategy for the proposed control system. Furthermore, we perform numerical simulations to demonstrate the effectiveness of our theoretical analyses.

A Survey of Information Dissemination Model, Datasets, and Insight

Information dissemination refers to how information spreads among users on social networks. With the widespread application of mobile communication and internet technologies, people increasingly rely on information on the internet, and the mode of information dissemination is constantly changing. Researchers have performed various studies from mathematical modeling and cascade prediction perspectives to explore the previous problem. However, lacking a comprehensive review of the latest information dissemination models hinders scientific development. As a result, it is essential to review the latest models or methods. In this paper, we review information dissemination models from the past three years and conduct a detailed analysis, such as explanatory and predictive models. Moreover, we provide public datasets, evaluation metrics, and interface tools for researchers focusing more on algorithm design and modeling. Finally, we discuss the model application and future research directions. This paper aims to understand better the research progress and development trends for beginners and guide future research endeavors. We believe this article will attract more researchers’ interest and attention to the information dissemination field on social networks.

Investigating the Dynamics of Single and Dual Infection of Schistosoma Species: A Mathematical Modeling Perspective

Schistosomiasis is a prevalent parasitic disease that poses significant challenges to effective control measures, particularly in the presence of dual infections. This paper presents a study that aims to investigate the underlying mechanisms of schistosomiasis transmission through mathematical modeling, focusing on the dynamics of both single and dual infections, as well as the interaction between different species or strains of Schistosoma parasites. Sensitivity analysis of the basic reproduction number, , reveals the substantial influence of parameters such as and on disease transmission. The findings highlight the crucial need for comprehensive management strategies that address the complexities of dual infections and target influential parameters to effectively reduce disease transmission and mitigate the impact of schistosomiasis in endemic areas.

수학적 모델링 관점에서 바라본 고등학교 &lt;정보&gt; 교과서의 모델링 과제 분석

Objectives The purpose of this study was to analyze high school information textbooks from the perspective of mathematical modeling, with the goal of gaining insights for designing mathematical modeling tasks using digital resources.&#x0D; Methods To achieve this objective, the study selected the ‘modeling’ unit and ‘project unit’ tasks from eight high school information textbooks for analysis, and conducted a literature review. The study examined whether the modeling tasks were related to mathematics or real-life scenarios, and analyzed them through the lens of the mathematical modeling cycle and computational thinking skills, which are increasingly recognized as crucial competencies for the future workforce, including digital literacy.&#x0D; Results The material in the ‘Modeling’ unit of the high school &lt;information&gt; textbook was heavily based on ‘mathematics’. &lt;Information&gt; ‘Modeling’ is treated as a method of abstraction in the textbook, and when analyzed as a process of ‘mathematical modeling cycle’, it consists of constructing, simplifying, and mathematizing. The results of the analysis showed that the treatment of ‘modeling’ in the information textbooks was distinct from ‘mathematical modeling,’ as it was seen primarily as a method of abstraction. However, the project tasks in the information textbooks included most of the components of the mathematical modeling cycle and the computational thinking process, and were organized as independent units for a systematic experience of the modeling process.&#x0D; Conclusions Based on these findings, the study concludes that a systematic discussion is needed to teach ‘mathematical modeling’ in connection with modeling tasks in the information textbooks in order to foster digital literacy, which is a crucial competency for future societies. Additionally, the modeling and project tasks in the information textbooks can be modified and supplemented to be incorporated into mathematics courses. Finally, the study recommends organizing project tasks related to mathematical modeling into independent units to better structure mathematics textbooks.

An efficient methodology for modeling to predict wine aroma expression based on quantitative data of volatile compounds: A case study of oak barrel-aged red wines

Correlating aroma expression with volatile compounds has long been an ambition in researches of flavor chemistry. To propose a reliable methodology to depict wine aroma, 76 oak barrel-aged dry red wines were investigated through the combination of machine learning algorithm and multivariate analysis. Aromatic characteristic was evaluated by quantitative descriptive analysis (QDA), while non– or oak derived volatiles were detected by HS-SPME-GC–MS and targeted SPE-GC-QqQ-MS/MS, respectively. Results showed that variable importance for projection values (VIPs) from partial least-squares regression (PLSR) and mean decrease accuracy (MDA) from random forest were efficient parameters for feature selection. The correlating accuracy of the optimal PLSR model to predict intensities of different aroma characteristics through selected volatile compounds could achieve 0.754 to 0.943, representing potential application to manage wine aroma by chemical assay in winemaking. From the perspective of mathematical modeling in the real wine matrix, the network analysis between aroma characteristics and key volatile compounds indicated that the expression of oak aroma was not only directly contributed by volatiles derived from oak wood, but also influenced by ethyl esters, including ethyl acetate, ethyl butanoate, ethyl hexanoate, ethyl decanoate, and ethyl nonanoate.

The Management of the Corruption Phenomenon and its Approaches

Abstract Corruption is one of the plagues of the modern world that is characteristic especially of the economic, administrative, and political areas. The history of civilization shows us that this phenomenon has existed in the world since the beginning. Still, depending on the era and the measures taken against it, it was more or less developed. From an economic perspective, it is considered to be particularly harmful because it constitutes an obstacle to the healthy, prosperous, and fair development of a nation. In our era, the phenomenon of globalization has acquired very strong valences, unfortunately, and corruption has acquired an impressive development, ripping the fruits of global deepening, especially now that we are also talking about corruption manifested across borders when it affects or is promoted by multinational companies. Of course, the phenomenon of corruption cannot be completely eradicated and there is no country in the world that can boast of such a performance, but firm measures are needed to limit and stop it. Romania has been dealing with this phenomenon for a long time, and the legislative measures, the political will and the pressures of the European institutions should aim, in the medium term, to reduce it. The present article evokes the terminological aspects of the phenomenon of corruption, analyzing its causes and possible solutions, but also a perspective of mathematical modeling of its progression. The study’s novelty is given by the deepening of the corruption phenomenon in light of the opportunities offered by the new paradigm of the globalization phenomenon.

13C metabolic flux analysis: Classification and characterization from the perspective of mathematical modeling and application in physiological research of neural cell.

13C metabolic flux analysis (13C-MFA) has emerged as a forceful tool for quantifying in vivo metabolic pathway activity of different biological systems. This technology plays an important role in understanding intracellular metabolism and revealing patho-physiology mechanism. Recently, it has evolved into a method family with great diversity in experiments, analytics, and mathematics. In this review, we classify and characterize the various branch of 13C-MFA from a unified perspective of mathematical modeling. By linking different parts in the model to each step of its workflow, the specific technologies of 13C-MFA are put into discussion, including the isotope labeling model (ILM), isotope pattern measuring technique, optimization algorithm and statistical method. Its application in physiological research in neural cell has also been reviewed.

Cluster Expansion Method for Critical Node Problem Based on Contraction Mechanism in Sparse Graphs

The objective of critical nodes problem is to minimize pair-wise connectivity as a result of removing a specific number of nodes in the residual graph. From a mathematical modeling perspective, it comes the truth that the more the number of fragmented components and the evenly distributed of disconnected sub-graphs, the better the quality of the solution. Basing on this conclusion, we proposed a new Cluster Expansion Method for Critical Node Problem (CEMCNP), which on the one hand exploits a contraction mechanism to greedy simplify the complexity of sparse graph model, and on the other hand adopts an incremental cluster expansion approach in order to maintain the size of formed component within reasonable limitation. The proposed algorithm also relies heavily on the idea of multi-start iterative local search algorithm, whereas brings in a diversified late acceptance local search strategy to keep the balance between interleaving diversification and intensification in the process of neighborhood search. Extensive evaluations show that CEMCNP running on 35 of total 42 benchmark instances are superior to the outcome of KBV, while holding 3 previous best results out of the challenging instances. In addition, CEMCNP also demonstrates equivalent performance in comparison with the existing MANCNP and VPMS algorithms over 22 of total 42 graph models with fewer number of node exchange operations.

Modelling the effect of vascular status on tumour evolution and outcome after thermal therapy

Microscale oxygenation plays a prominent role in tumour progression. Spatiotemporal variability of oxygen distribution in the tumour microenvironment contributes to cellular heterogeneity and to the emergence of normoxic and hypoxic populations. Local levels of oxygen strongly affect the response of tumours to the administration of different therapeutic modalities and, more generally, to the phenomenon of resistance to treatments. Several interventions have been proposed to improve tumour oxygenation, being the elevation of the local temperature (hyperthermia) an important one. While other factors such as the metabolic activity have to be considered, the proficiency of the tumour vascular system is a key factor both for the tissue oxygenation and for its temperature maps. Consequently, the interplay of these factors has attracted considerable attention from the mathematical modelling perspective. Here we put forward a transport-based system of partial differential equations aimed at describing the dynamics of healthy and tumour cell subpopulations at the microscale in a region placed between two blood vessels. By using this model with diverse flow conditions, we analyse the oxygen and temperature profiles that arise in different scenarios of vascular status, both during free progression and under thermal therapy. We find that low oxygen levels are associated to elevations of temperature in locations preferentially populated by hypoxic cells, and hyperthermia-induced cell death, being strongly dependent on blood flow, would only appear under highly disrupted conditions of the local vasculature. This results in a noticeable effect of heat on hypoxic cells. Additionally, when pronounced cell death occurs, it is followed by a significant increase in the oxygen levels. Our results provide quantitative insight to the physiological and biological processes taking place at sub-voxel sizes, currently not accessible to standard functional imaging due to spatial resolution limitations.

Unboxing mathematics: creating a culture of modeling as critic.

From the socio-critical perspective of mathematical modeling, reflexive discussions about the nature, criteria, and consequences of mathematical models are not a natural consequence of modeling in school. This report is part of a larger study focused on stimulating reflexive discussions in practice employing constructivist grounded theory as a research method. Twenty-seven college algebra students engaged in a 3-week modeling project at a community college in the USA. Audio-recorded group discussions and written reflections were collected to determine how reflexive discussions were taking place. Analysis of students’ actions and reflexive discussions during the modeling project produced four concepts: voicing mathematics, personalizing mathematics, challenging mathematics, and negotiating mathematics. These concepts are integrated into an overall process for stimulating reflexive discussions and are conceptualized as unboxing mathematics. The overarching concept of unboxing mathematics represents one interpretation of how reflexive discussions may be constituted during modeling activities and identifies classroom mathematical practices specific to the socio-critical modeling context of this study.

The Students–Professors Problem—The Reversal Error and Beyond

Abstract This paper first introduces and reviews the existing research on the well-known “students–professors (S/P) problem”, which was first formulated in 1979. Next, it presents an empirical study of Danish upper secondary students’ answers to two mathematical modeling versions of the S/P-problem; a mathematization version (296 students), and a de-mathematization version (658 students). Besides reproducing several previously reported findings, e.g., the so-called reversal error, the study identifies new error types not previously reported in the literature. The mathematical modeling perspective adopted, along with a mixed-methods design, give rise to new potential explanations of the reversal error as well as explanations of the new error types. Our study shows that interpreting the linguistic formulation of the S/P-problem statement is not only related to language but is intrinsically of a mathematical – and cognitive – nature as well. Altogether, there is still more to be said about the S/P-problem forty years after its emergence. The impact sheet to this article can be accessed at 10.6084/m9.figshare.16610104.

The dynamics of psittacosis in human and poultry populations: a mathematical modelling perspective

Psittacosis is a disease in human beings that is commonly associated with pet birds such as cockatiels and parrots, and among poultry such as ducks and turkeys. This paper proposed and developed a deterministic epidemiological model that explains the transmission dynamics of Psittacosis infection in humans and poultry. The Psittacosis deterministic model was analyzed to determine positivity of the solution set, the invariant feasible region, the basic reproduction number, the disease free equilibrium points, the endemic equilibrium points and the corresponding stability of each of the equilibrium points. The basic reproduction number is calculated using the next generation matrix and it was found to be entirely dependent on the poultry population parameters. The study established that whenever R0 1, Psittacosis keeps persisting in the population. Sensitivity analysis was conducted to determine the contribution of each parameter to the basic reproduction number. The more sensitive parameters were found to be responsible for the further propagation of Psittacosis while the less sensitive parameters rarely contributed to the spread. Stability analysis of both the disease free equilibrium and the Endemic equilibrium were conducted. Lastly, numerical simulation was conducted to justify quantitative analysis of the dynamics of the transmission of Psittacosis.

수학적 모델링 관점에 따른 한국과 싱가포르의 통계영역 과제 분석

This study aims to analyze statistical tasks in Korean and Singaporean textbooks with the mathematical modeling perspective and compare the learning contents and experiences of students from both countries. I analyzed mathematical modeling tasks in the textbooks based on five aspects: (1) the mathematical modeling process, (2) the data type, (3) the expression type, (4) the context, and (5) the mathematical activity. The results of this study show that Korean and Singaporean textbooks provide the highest percentage of the “working-with-mathematics” task, the highest percentage of the “matching task,” and the highest percentage of the “picture” task. The real-world context and mathematical activities used in Korean and Singaporean textbooks differed in percentage. This study provides implications for the development of textbook tasks to support future mathematical modeling activities. This includes providing a balanced experience in mathematical modeling processes and presenting tasks in various forms of expression to raise students’ cognitive level and expand the opportunity to experience meaningful mathematizing. In addition, it is necessary to present a contextually realistic task for students’ interest in mathematical modeling activities or motivation for learning.

Enhancing reservoir control in the co-dynamics of HIV-VL: from mathematical modeling perspective

HIV patients are vulnerable to developing active visceral leishmaniasis (VL). To understand this complication, we studied a mathematical model for HIV and visceral leishmaniasis coinfection. In this approach, we reckoned two distinct equilibria: the disease-free and the endemic equilibria. The local and global stability of the disease-free equilibrium were thoroughly investigated. To further support the qualitative findings, we performed simulations to quantify the changes of the dynamical behavior of the full model for variation of relevant parameters. Increasing the rate of VL recovery (phi _{1}), the recovery rate for VL–HIV Co-infection (phi _{2}), removing reservoirs (c_{1}), minimizing the contact rate (beta _{h}) are important in controlling the transmission of individual and co-infection disease of VL and HIV. In conclusion, possible measures should be implemented to reduce the number of infected individuals. Therefore, we recommend that policy makers and stakeholders incorporate these measures during planing and implementation phases to control the transmission of VL–HIV co-infection.

Research on the optimal strategy of desert crossing game under known weather conditions

The “Crossing the Desert” mini-game needs to consider a variety of mutually restrictive factors. Players must coordinate funding and path issues to find the optimal strategy to reach the end within the specified time. Based on the study of crossing the desert when the weather conditions are known, this paper establishes a topology model, and uses priority search and game theory to solve the player’s optimal strategy for passing through the barriers. First, the entire map is digitized and represented by a general topological map; then, given the map and weather distribution, the highest profit of each path is calculated. Specific calculation details require further analysis to arrive at a more practical and efficient route planning plan. The model proposed in this paper only provides a more effective solution for this problem from the perspective of mathematical modeling.

Qfold: a new modeling paradigm for the RNA folding problem

Ribonucleic acid (RNA) molecules play informational, structural, and metabolic roles in all living cells. RNAs are chains of nucleotides containing bases {A, C, G, U} that interact via base pairings to determine higher order structure and functionality. The RNA folding problem is to predict one or more secondary RNA structures from a given primary sequence of bases. From a mathematical modeling perspective, solutions to the RNA folding problem come from minimizing the thermodynamic free energy of a structure by selecting which bases will be paired, subject to a set of constraints. Here we report on a Quadratic Unconstrained Binary Optimization (QUBO) modeling paradigm that fits naturally with the parameters and constraints required for RNA folding prediction. Three QUBO models are presented along with a hybrid metaheuristic algorithm. Extensive testing results show a strong positive correlation with benchmark results.

Not Taken for Granted: Configuring Scalable Live Video Streaming Under Throughput Fluctuations in Mobile Edge Networks

We consider end-to-end live video streaming in mobile edge networks with fluctuating but predictable throughput. We employ scalable video coding (SVC) to adapt the bitrate of each frame to the throughput evolution in a timely manner. When streaming SVC-encoded live video, the video source should dynamically derive and configure a set of coding parameters for each upcoming chunk, which consists of a number of consecutive frames. The coding parameters quantify the throughput evolution of an upcoming chunk by providing a few bitrate options for the frames within this chunk to encode with. Unlike the majority of existing works that simply treat the coding parameters as given (i.e., taking them for granted), in this paper, we derive the coding parameters from a comprehensive mathematical modeling and optimization perspective. Our approach consists of an optimization problem that captures the fundamental trade-off in determining the coding parameters and a customized search algorithm based on the analysis of the optimization problem's solution structure. Numerical results produced by the NS-3 network simulator show that our approach outperforms the state-of-the-art benchmarks.

Fuzzy Integrated Cell Formation and Production Scheduling Considering Automated Guided Vehicles and Human Factors

In today's competitive environment, it is essential to design a flexible-responsive manufacturing system with automatic material handling systems. In this article, a fuzzy mixed integer linear programming model is designed for cell formation problems including the scheduling of parts within cells in a cellular manufacturing system (CMS) where several automated guided vehicles (AGVs) are in charge of transferring the exceptional parts. Notably, using these AGVs in CMS can be challenging from the perspective of mathematical modeling due to consideration of AGVs’ collision as well as parts pickup/delivery. This article investigates the role of AGVs and human factors as indispensable components of automation systems in the cell formation and scheduling of parts under fuzzy processing time. The proposed objective function includes minimizing the makespan and intercellular movements of parts. Due to the NP-hardness of the problem, a hybrid genetic algorithm (GA/heuristic) and a whale optimization algorithm (WOA) are developed. The experimental results reveal that our proposed algorithms have a high performance compared to CPLEX and the other two well-known algorithms, i.e., particle swarm optimization and ant colony optimization, in terms of computational efficiency and accuracy. Finally, WOA stands out as the best algorithm to solve the problem.