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23 pages, 676 KiB

Open AccessArticle

Numerical and Theoretical Treatments of the Optimal Control Model for the Interaction Between Diabetes and Tuberculosis

by Saburi Rasheed, Olaniyi S. Iyiola, Segun I. Oke and Bruce A. Wade

Algorithms 2025, 18(6), 348; https://doi.org/10.3390/a18060348 - 5 Jun 2025

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We primarily focus on the formulation, theoretical, and numerical analyses of a non-autonomous model for tuberculosis (TB) prevention and control programs in a population where individuals suffering from the double trouble of tuberculosis and diabetes are present. The model incorporates four time-dependent control [...] Read more.

We primarily focus on the formulation, theoretical, and numerical analyses of a non-autonomous model for tuberculosis (TB) prevention and control programs in a population where individuals suffering from the double trouble of tuberculosis and diabetes are present. The model incorporates four time-dependent control functions, saturated treatment of non-infectious individuals harboring tuberculosis, and saturated incidence rate. Furthermore, the basic reproduction number of the autonomous form of the proposed optimal control mathematical model is calculated. Sensitivity indexes regarding the constant control parameters reveal that the proposed control and preventive measures will reduce the tuberculosis burden in the population. This study establishes that the combination of campaigns that teach people how the development of tuberculosis and diabetes can be prevented, a treatment strategy that provides saturated treatment to non-infectious individuals exposed to tuberculosis infections, and prompt effective treatment of individuals infected with tuberculosis disease is the optimal strategy to achieve zero TB by 2035. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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14 pages, 698 KiB

Open AccessArticle

Inferring the Timing of Antiretroviral Therapy by Zero-Inflated Random Change Point Models Using Longitudinal Data Subject to Left-Censoring

by Hongbin Zhang, McKaylee Robertson, Sarah L. Braunstein, David B. Hanna, Uriel R. Felsen, Levi Waldron and Denis Nash

Algorithms 2025, 18(6), 346; https://doi.org/10.3390/a18060346 - 5 Jun 2025

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Abstract

We propose a new random change point model that utilizes routinely recorded individual-level HIV viral load data to estimate the timing of antiretroviral therapy (ART) initiation in people living with HIV. The change point distribution is assumed to follow a zero-inflated exponential distribution [...] Read more.

We propose a new random change point model that utilizes routinely recorded individual-level HIV viral load data to estimate the timing of antiretroviral therapy (ART) initiation in people living with HIV. The change point distribution is assumed to follow a zero-inflated exponential distribution for the longitudinal data, which is also subject to left-censoring, and the underlying data-generating mechanism is a nonlinear mixed-effects model. We extend the Stochastic EM (StEM) algorithm by combining a Gibbs sampler with a Metropolis–Hastings sampling. We apply the method to real HIV data to infer the timing of ART initiation since diagnosis. Additionally, we conduct simulation studies to assess the performance of our proposed method. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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18 pages, 934 KiB

Open AccessArticle

Optimization of PFMEA Team Composition in the Automotive Industry Using the IPF-RADAR Approach

by Nikola Komatina and Dragan Marinković

Algorithms 2025, 18(6), 342; https://doi.org/10.3390/a18060342 - 4 Jun 2025

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Abstract

In the automotive industry, the implementation of Process Failure Mode and Effect Analysis (PFMEA) is conducted by a PFMEA team comprising employees who are connected to the production process or a specific product. Core PFMEA team members are actively engaged in PFMEA execution [...] Read more.

In the automotive industry, the implementation of Process Failure Mode and Effect Analysis (PFMEA) is conducted by a PFMEA team comprising employees who are connected to the production process or a specific product. Core PFMEA team members are actively engaged in PFMEA execution through meetings, analysis, and the implementation of corrective actions. Although the current handbook provides guidelines on the potential composition of the PFMEA team, it does not strictly define its members, allowing companies the flexibility to determine the team structure independently. This study aims to identify the core PFMEA team members by adhering to criteria based on the recommended knowledge and competencies outlined in the current handbook. By applying the RAnking based on the Distances and Range (RADAR) approach, extended with Interval-Valued Pythagorean Fuzzy Numbers (IVPFNs), a ranking of potential candidates was conducted. A case study was performed in a Tier-1 supplier company within the automotive supply chain. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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22 pages, 8623 KiB

Open AccessArticle

Polarization in Political Rallies: A Markovian Agent-Based Model for Opinion Dynamics

by Marco Scarpa, Marco Garofalo, Francesco Longo and Salvatore Serrano

Algorithms 2025, 18(6), 308; https://doi.org/10.3390/a18060308 - 23 May 2025

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Abstract

One of the most studied problems among researchers in recent years is how individuals form their opinions. This problem has become more urgent with the advent of social networks, which can easily influence a huge number of followers and have become increasingly pervasive [...] Read more.

One of the most studied problems among researchers in recent years is how individuals form their opinions. This problem has become more urgent with the advent of social networks, which can easily influence a huge number of followers and have become increasingly pervasive over time. The produced effect is the rise of polarized opinions among different groups of people. Understanding polarization is of great relevance across various application domains, such as economics and politics. Opinion dynamics has often been studied by exploiting the popular Friedkin–Johnsen model. In this paper, we propose a different modeling approach based on the Markovian agents paradigm for deriving metrics characterizing polarized opinions. The main goal of this work is to demonstrate the potential of the Markovian agent modeling paradigm for the analysis of opinion dynamics. The main advantages of Markovian agents are the ease of setting a large number of behavioral parameters, spatial distribution of agents, scalability, and numerical tractability. We extend our previous work, in which we analyzed a peer assembly and validated it against other commonly used modeling approaches. In our opinion, the Markovian agent approach offers an effective modeling framework due to its scalability and flexibility in handling parameters that describe the behavior of individuals in the opinion formation process. The context we will discuss is inspired by election rallies, where an assembly attends a speech by a political candidate. The crowd consists of individuals with diverse initial political opinions, and the candidate seeks to polarize them toward his/her own political stance. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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22 pages, 1552 KiB

Open AccessArticle

A Regret-Enhanced DEA Approach to Mapping Renewable Energy Efficiency in Asia’s Growth Economies

by Chia-Nan Wang, Nhat-Luong Nhieu and Yu-Cin Ye

Algorithms 2025, 18(5), 297; https://doi.org/10.3390/a18050297 - 20 May 2025

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Abstract

Renewable energy (RE) is pivotal to achieving both environmental sustainability and long-term energy security, yet systematic evidence on the efficiency of RE investment across South and Southeast Asia remains sparse. This study introduces a rejoice–regret utility cross-efficiency DEA (RRUCE-DEA) framework that fuses conventional [...] Read more.

Renewable energy (RE) is pivotal to achieving both environmental sustainability and long-term energy security, yet systematic evidence on the efficiency of RE investment across South and Southeast Asia remains sparse. This study introduces a rejoice–regret utility cross-efficiency DEA (RRUCE-DEA) framework that fuses conventional quantitative efficiency measurement with the behavioral insights of regret theory. Applying the model to 16 countries shows India as the benchmark for efficient RE investment allocation, followed closely by Pakistan and Indonesia. The Philippines, Malaysia, and Vietnam also post strong results, whereas Sri Lanka and Thailand reveal moderate performance with clear room for improvement. At the lower end of the spectrum, Cambodia, Myanmar, and Afghanistan encounter significant hurdles that must be overcome to achieve a successful clean energy transition. A sensitivity analysis further explores how variations in the regret aversion and rejoice–regret coefficients affect the RRUCE-DEA outcomes. The findings provide actionable guidance for policymakers and investors seeking to channel resources toward a cleaner, more sustainable regional energy portfolio. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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25 pages, 339 KiB

Open AccessArticle

Existence and Mittag–Leffler Stability for the Solution of a Fuzzy Fractional System with Application of Laplace Transforms to Solve Fractional Differential Systems

by Mohammad Saeid Abolhassanifar, Reza Saadati, Mohammad Bagher Ghaemi and Donal O’Regan

Algorithms 2025, 18(5), 264; https://doi.org/10.3390/a18050264 - 3 May 2025

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Abstract

This study explores the existence and Mittag–Leffler stability of solutions for fuzzy fractional systems that include Caputo derivatives and ordinary derivatives with non-local conditions using the Schauder fixed-point theorem. Following this, we employ the Laplace transform method and numerical techniques to create iterative [...] Read more.

This study explores the existence and Mittag–Leffler stability of solutions for fuzzy fractional systems that include Caputo derivatives and ordinary derivatives with non-local conditions using the Schauder fixed-point theorem. Following this, we employ the Laplace transform method and numerical techniques to create iterative methods for obtaining exact and approximate solutions. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

31 pages, 9472 KiB

Open AccessArticle

Mathematics-Driven Analysis of Offshore Green Hydrogen Stations

by Álvaro García-Ruiz, Pablo Fernández-Arias and Diego Vergara

Algorithms 2025, 18(4), 237; https://doi.org/10.3390/a18040237 - 21 Apr 2025

Viewed by 366

Abstract

Renewable energy technologies have become an increasingly important component of the global energy supply. In recent years, photovoltaic and wind energy have been the fastest-growing renewable sources. Although oceans present harsh environments, their estimated energy generation potential is among the highest. Ocean-based solutions [...] Read more.

Renewable energy technologies have become an increasingly important component of the global energy supply. In recent years, photovoltaic and wind energy have been the fastest-growing renewable sources. Although oceans present harsh environments, their estimated energy generation potential is among the highest. Ocean-based solutions are gaining significant momentum, driven by the advancement of offshore wind, floating solar, tidal, and wave energy, among others. The integration of various marine energy sources with green hydrogen production can facilitate the exploitation and transportation of renewable energy. This paper presents a mathematics-driven analysis for the simulation of a technical model designed as a generic framework applicable to any location worldwide and developed to analyze the integration of solar energy generation and green hydrogen production. It evaluates the impact of key factors such as solar irradiance, atmospheric conditions, water surface flatness, as well as the parameters of photovoltaic panels, electrolyzers, and adiabatic compressors, on both energy generation and hydrogen production capacity. The proposed mathematics-based framework serves as an innovative tool for conducting multivariable parametric analyses, selecting optimal design configurations based on specific solar energy and/or hydrogen production requirements, and performing a range of additional assessments including, but not limited to, risk evaluations, cause–effect analyses, and/or degradation studies. Enhancing the efficiency of solar energy generation and hydrogen production processes can reduce the required photovoltaic surface area, thereby simplifying structural and anchoring requirements and lowering associated costs. Simpler, more reliable, and cost-effective designs will foster the expansion of floating solar energy and green hydrogen production in marine environments. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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18 pages, 974 KiB

Open AccessArticle

On the Q-Convergence and Dynamics of a Modified Weierstrass Method for the Simultaneous Extraction of Polynomial Zeros

by Plamena I. Marcheva, Ivan K. Ivanov and Stoil I. Ivanov

Algorithms 2025, 18(4), 205; https://doi.org/10.3390/a18040205 - 5 Apr 2025

Viewed by 238

Abstract

In the present paper, we prove a new local convergence theorem with initial conditions and error estimates that ensure the Q-quadratic convergence of a modification of the famous Weierstrass method. Afterward, we prove a semilocal convergence theorem that is of great practical importance [...] Read more.

In the present paper, we prove a new local convergence theorem with initial conditions and error estimates that ensure the Q-quadratic convergence of a modification of the famous Weierstrass method. Afterward, we prove a semilocal convergence theorem that is of great practical importance owing to its computable initial condition. The obtained theorems improve and complement all existing such kind of convergence results about this method. At the end of the paper, we provide three numerical examples to show the applicability of our semilocal theorem to some physics problems. Within the examples, we propose a new algorithm for the experimental study of the dynamics of the simultaneous methods and compare the convergence and dynamical behaviors of the modified and the classical Weierstrass methods. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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