Mathematical Modeling Approach Research Articles

Control of schistosomiasis by the selective competitive and predatory intervention of intermediate hosts: A mathematical modeling approach

Schistosomiasis, a freshwater-borne neglected tropical disease, disproportionately affects impoverished communities mainly in the tropical regions. Transmission involves humans and intermediate host (IH) snails. This manuscript introduces a mathematical model to probe schistosomiasis dynamics and the role of non-host snail competitors and predators as biological control agents for IH snails. The numerical analyses include investigations into steady-state conditions and reproduction numbers associated with uncontrolled scenarios, as well as scenarios involving non-host snail competitors and/or predators. Sensitivity analysis reveals that increasing snail mortality rates is a key to reducing the IH snail population and control of the transmission. Results show that specific snail competitors and/or predators with strong competition/predation abilities reduce IH snails and the subsequent infectious cercaria populations, reduce the transmission, and possibly eradicate the disease, while those with weaker abilities allow disease persistence. Hence our findings advocate for the effectiveness of snail competitors with suitable competitive pressures and/or predators with appropriate predatory abilities as nature-based solutions for combating schistosomiasis, all while preserving IH snail biodiversity. However, if these strategies are implemented at insignificant levels, IH snails can dominate, and disease persistence may pose challenges. Thus, experimental screening of potential (native) snail competitors and/or predators is crucial to assess the likely behavior of biological agents and determine the optimal biological control measures for IH snails.

The characteristics of medical technical task working out as a factor of successful implementation of project of public-private partnership in health care

The application of mathematical modeling approaches based on factual demand of the population of territories in setting of medical and technical tasks makes it possible to significantly optimize costs of construction and equipping primary health care objects. This is confirmed by both corresponding calculations and results of analysis. This operation is oriented both on structural divisions of regional executive authorities responsible for setting of medical and technical tasks, and on investment companies implementing projects in health care.

Using relational learning in exploring the effectiveness of using hashtags in future topics and user relations in X

This research has a research object, namely relational learning with a mathematical modeling approach from graph queries for exploring future topics and user relationships. The problem in this research is the large and varied number of tweets that are produced every day, where each use of hashtags always increases, which has an impact on the accumulation of data that needs to be processed to obtain information because users on social media X can interact to influence trends so as to solve the problem. This requires the application of relational learning by utilizing graph query mathematical models. The results obtained from this research are in the form of a model that can produce predictions of future topics and see user relationships based on interactions on social media with relationships between entities at interconnected nodes. In applying relational learning with mathematical models utilizing graph queries there will be a process of examining the relationships between entities, content and communication interactions in accordance with the definitions and theorems that have been described to observe each node. In relational learning, there will be each node according to the entity used, then the mathematical model with graph queries will connect all the entities to form a graph that can be used as a model for predicting future topics and relationships between users. This research is research with a level of novelty in applying graphical queries to mathematical models to predict future topics and applying relational learning to user relationships so that it can add information related to future communication. Graph queries aim to model a node between relations in the data so that it can represent a relationship between variables

Cost-effectiveness analysis of optimal control strategies on the transmission dynamics of HIV and Varicella-Zoster co-infection

HIV and Varicella-Zoster co-infection has been threatens the lives and livelihood of millions of individuals all over the world. In various nations of the world the co-infection disease is presently a major health problem. Although, various researchers carried out studies related with HIV and Zoster single infections, no one has carried out a study on the co-infection disease. Therefore, investigating the HIV and Varicella-Zoster co-infection transmission dynamics using mathematical modeling approach is relatively necessary. The main objective of this study is to investigate the cost-effective analysis of the proposed optimal control strategies on the transmission dynamics of HIV and Varicella-Zoster co-infection in the community using compartmental modeling approach. Qualitatively, we have computed the model equilibrium points and analyze their local stabilities using Routh-Hurwitz stability criteria, the effective reproduction numbers by using the next generator matrix operator method, we re-formulated the optimal control problem of the complete co-infection model by implementing five time dependent optimal control strategies, analyzed the optimal control problem by applying the Pontryagin's Maximum/Minimum principle. Sensitivity analysis and numerical simulations have been carried out using the forward sensitivity index formula and the fourth order Runge-Kutta numerical methods respectively and verified the analytic results. Finally, we have performed the cost effective analysis for the proposed controlling strategies and from the result we have observed that implementing strategy four (treatment of Varicella-Zoster infected individuals to increase their recovery rate and recovery period) is the most cost effective-strategy as compared with other alternatives.

A new mathematical model approach on the oncolytic virotherapy potency

A new mathematical model approach on the oncolytic virotherapy potency

Computational Model Predicts Patient Outcomes in Luminal B Breast Cancer Treated with Endocrine Therapy and CDK4/6 Inhibition.

Development of a computational biomarker to predict, prior to treatment, the response to CDK4/6 inhibition (CDK4/6i) in combination with endocrine therapy in patients with breast cancer. A mechanistic mathematical model that accounts for protein signaling and drug mechanisms of action was developed and trained on extensive, publicly available data from breast cancer cell lines. The model was built to provide a patient-specific response score based on the expression of six genes (CCND1, CCNE1, ESR1, RB1, MYC, and CDKN1A). The model was validated in five independent cohorts of 148 patients in total with early-stage or advanced breast cancer treated with endocrine therapy and CDK4/6i. Response was measured either by evaluating Ki67 levels and PAM50 risk of relapse (ROR) after neoadjuvant treatment or by evaluating progression-free survival (PFS). The model showed significant association with patient's outcomes in all five cohorts. The model predicted high Ki67 [area under the curve; AUC (95% confidence interval, CI) of 0.80 (0.64-0.92), 0.81 (0.60-1.00) and 0.80 (0.65-0.93)] and high PAM50 ROR [AUC of 0.78 (0.64-0.89)]. This observation was not obtained in patients treated with chemotherapy. In the other cohorts, patient stratification based on the model prediction was significantly associated with PFS [hazard ratio (HR) = 2.92 (95% CI, 1.08-7.86), P = 0.034 and HR = 2.16 (1.02 4.55), P = 0.043]. A mathematical modeling approach accurately predicts patient outcome following CDK4/6i plus endocrine therapy that marks a step toward more personalized treatments in patients with Luminal B breast cancer.

Triple-diode solar cell current optimization – An analytical solution based on the Lambert W function

A novel mathematical modeling approach for the Triple-Diode Model (TDM) and its parameter estimation is introduced in this paper. For the first time in the literature, this paper presents two analytical solutions for calculating the current in TDM solar cells using the Lambert W function. Additionally, a new metaheuristic algorithm, the Adaptive Evaporation Rate Water Cycle Algorithm (Adaptive ERWCA), is proposed for estimating TDM solar cell parameters. The proposed algorithm is tested using both the new analytical solutions and a well-known iterative approach for the current-voltage characteristics of the TDM solar cells model. Extensive testing is conducted on three well-known solar cells/modules and a panel under various weather conditions. The results demonstrate that the proposed analytical expressions for the current-voltage characteristics are accurate and highly effective for representing TDM solar cell current. The accuracy of the parameter estimates obtained with the application of the proposed algorithm, considering both analytical solutions and the iterative approach, is compared with existing literature results. It is shown that the proposed algorithm outperforms existing algorithms in solar cell parameter estimation across both the analytical and iterative approaches for current-voltage characteristics. Remarkably, for the RTC France solar cell, the SOLAREX MSX 60 solar module, and the PHOTOWATT-PWP 201 solar module, the obtained Root Mean Square Errors (RMSE) are 0.00075141, 0.01157153, and 0.0010578, respectively. These results are currently the best reported in the literature.

Mathematical Assessment of the Role of Human Behavior Changes on SARS-CoV-2 Transmission Dynamics in the United States.

The COVID-19 pandemic has not only presented a major global public health and socio-economic crisis, but has also significantly impacted human behavior towards adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities worldwide. This study is based on the use of mathematical modeling approaches to assess the extent to which SARS-CoV-2 transmission dynamics is impacted by population-level changes of human behavior due to factors such as (a) the severity of transmission (such as disease-induced mortality and level of symptomatic transmission), (b) fatigue due to the implementation of mitigation interventions measures (e.g., lockdowns) over a long (extended) period of time, (c) social peer-pressure, among others. A novel behavior-epidemiology model, which takes the form of a deterministic system of nonlinear differential equations, is developed and fitted using observed cumulative SARS-CoV-2 mortality data during the first wave in the United States. The model fits the observed data, as well as makes a more accurate prediction of the observed daily SARS-CoV-2 mortality during the first wave (March 2020-June 2020), in comparison to the equivalent model which does not explicitly account for changes in human behavior. This study suggests that, as more newly-infected individuals become asymptomatically-infectious, the overall level of positive behavior change can be expected to significantly decrease (while new cases may rise, particularly if asymptomatic individuals have higher contact rate, in comparison to symptomatic individuals).

Thickness optimization of semi-structural CIPP pressure pipe liners: A mathematical modeling approach

This paper introduces a novel mathematical model to optimize the thickness of semi-structural liners in Cured-In-Place-Pipe (CIPP) rehabilitation based on the host pipe holes criterion defined in current standards. The model considers the residual structural mechanical properties of the damaged host pipe, and holes are defined considering the direction, the area, and the perimeter of the host pipe hole, providing a more accurate estimation of the liner behavior. Results indicate potential thickness reductions of 20%–40% for circular holes, while non-circular holes offer even greater optimization possibilities ranging from 40 to 80%. Moreover, a full-scale test was conducted on a reinforced concrete host pipe of DN 400, damaged with three holes 150 mm in diameter. The full-scale test results were used to refine the numerical model employed in developing the mathematical model, ensuring its accuracy and reliability.

New Solutions for Assessing Corporate Social Responsibility in Pharmaceutical Companies: A Mathematical Modelling Approach

New Solutions for Assessing Corporate Social Responsibility in Pharmaceutical Companies: A Mathematical Modelling Approach

Mathematical Modelling and Response Surface Methodology Approach of Electrocoagulation Hybrid Activated Sludge Process for an Efficient Removal of Selenium from Mining Wastewater

Mathematical Modelling and Response Surface Methodology Approach of Electrocoagulation Hybrid Activated Sludge Process for an Efficient Removal of Selenium from Mining Wastewater

A Model Based on Fuzzy Neural Networks for Sharing Digital Educational Resources in English

The ineffective digitization of core English course resources, due to limited autonomy, fragmentation, and inadequate management, has prompted the development of digital teacher libraries using multimedia and Internet technologies. Fuzzy neural networks (FNNs), combining fuzzy and neural network controls, have emerged as a promising approach for mathematical modeling. This paper presents an FNN-based model for sharing digital English educational resources and proposes an effective guidance mechanism for sharing digital science education resources. Experimental results show that the FNN outperforms the Apriori algorithm in training sample error by 0.02069 and reduces running time by 0.0034 seconds on average. This indicates the FNN's superior approximation capabilities with appropriate initial fuzzy rules. Consequently, the FNN-based model enhances the value and quality of educational resources, expands the capacity of information resource libraries, and effectively mitigates the creation of low-quality resources.

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.