Pub Date : 2026-03-01Epub Date: 2025-12-11DOI: 10.1016/j.rico.2025.100637
Somaye Jafari
This paper presents a new solution concept for interval-valued equilibrium problems using an appropriate interval ordering that considers both the central value and the uncertainty inherent in the data. The aim is to define solutions in a way that represents the imprecision frequently encountered in real-world situations. The proposed solution concept is then explained through a motivating example, demonstrating its advantages in handling interval-valued data. Furthermore, the study shows that the introduced interval-valued equilibrium problem can be reduced to a mixed equilibrium problem, for which existence results are established using a proof technique based on a KKM-type argument. A projection-based algorithm is also presented by adapting classical splitting methods for equilibrium problems to the proposed interval-valued equilibrium model. This work provides a rigorous and verifiable framework for addressing interval-valued equilibrium problems.
{"title":"Midpoint-width lexicographic equilibria: Existence results for interval-valued equilibrium problems","authors":"Somaye Jafari","doi":"10.1016/j.rico.2025.100637","DOIUrl":"10.1016/j.rico.2025.100637","url":null,"abstract":"<div><div>This paper presents a new solution concept for interval-valued equilibrium problems using an appropriate interval ordering that considers both the central value and the uncertainty inherent in the data. The aim is to define solutions in a way that represents the imprecision frequently encountered in real-world situations. The proposed solution concept is then explained through a motivating example, demonstrating its advantages in handling interval-valued data. Furthermore, the study shows that the introduced interval-valued equilibrium problem can be reduced to a mixed equilibrium problem, for which existence results are established using a proof technique based on a KKM-type argument. A projection-based algorithm is also presented by adapting classical splitting methods for equilibrium problems to the proposed interval-valued equilibrium model. This work provides a rigorous and verifiable framework for addressing interval-valued equilibrium problems.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100637"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-02-06DOI: 10.1016/j.rico.2026.100669
Safa Jameel Al-Kamil , Edit Laufer , Róbert Szabolcsi
Autonomous mobile robot navigation in dynamic and uncertain environments demands control architectures that are simultaneously robust, adaptive, and provably stable. This work introduces a hierarchical predictive navigation framework that combines adaptive fuzzy decision-making with forward-looking motion optimization and explicit stability constraints.
Simulation studies conducted in static, mixed, and dynamic environments demonstrate that the proposed framework achieves approximately 30–40% higher average velocity, a 25–35 % reduction in traversal time, and 5–10 % lower energy consumption per unit distance compared with conventional fuzzy–potential field and optimization-tuned fuzzy navigation baselines. Across all evaluated scenarios, the robot maintained collision-free navigation and bounded control behavior. Selective human supervision was required in fewer than 10 % of operating intervals, reducing operator involvement while preserving safety.
These results indicate that the proposed framework provides a quantitatively validated and interpretable alternative to existing fuzzy-based and predictive navigation approaches for autonomous mobile robots.
{"title":"Deep–adaptive fuzzy predictive navigation framework for stable and intelligent mobile robot control","authors":"Safa Jameel Al-Kamil , Edit Laufer , Róbert Szabolcsi","doi":"10.1016/j.rico.2026.100669","DOIUrl":"10.1016/j.rico.2026.100669","url":null,"abstract":"<div><div>Autonomous mobile robot navigation in dynamic and uncertain environments demands control architectures that are simultaneously robust, adaptive, and provably stable. This work introduces a hierarchical predictive navigation framework that combines adaptive fuzzy decision-making with forward-looking motion optimization and explicit stability constraints.</div><div>Simulation studies conducted in static, mixed, and dynamic environments demonstrate that the proposed framework achieves approximately 30–40% higher average velocity, a 25–35 % reduction in traversal time, and 5–10 % lower energy consumption per unit distance compared with conventional fuzzy–potential field and optimization-tuned fuzzy navigation baselines. Across all evaluated scenarios, the robot maintained collision-free navigation and bounded control behavior. Selective human supervision was required in fewer than 10 % of operating intervals, reducing operator involvement while preserving safety.</div><div>These results indicate that the proposed framework provides a quantitatively validated and interpretable alternative to existing fuzzy-based and predictive navigation approaches for autonomous mobile robots.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100669"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146173470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-02-06DOI: 10.1016/j.rico.2026.100670
Kalim Ullah , Zou Ran , Muhammad Ishfaq Khan , Homan Emadifar , Aseel Smerat , Karim K. Ahmed
This work investigates the dispersion limit of the fractional complex Ginzburg–Landau (FCGL) equation in the energy-critical defocusing regime. Using an energy-method framework, we prove that, as the phase parameter , solutions of the FCGL equation with initial data in , , converge to solutions of the energy-critical fractional nonlinear heat (FNLH) equation, for which the limiting dynamics are well posed under the stronger regularity assumption . The analysis highlights the additional analytical challenges introduced by the nonlocal fractional Laplacian in the energy-critical setting. Numerical simulations are performed using a Fourier spectral discretization in space, which exactly resolves the fractional Laplacian through its Fourier symbol, combined with a fourth-order Runge–Kutta (RK4) scheme in time. Numerical errors between the FCGL and FNLH solutions are computed for different values of , and a temporal convergence study is carried out for fixed , confirming the consistency and accuracy of the numerical scheme. As decreases, the solutions transition from dispersive, oscillatory dynamics to smoother profiles that closely approximate the FNLH solution. Quantitative measures, including the evolution of the -norm and representative spatial profiles, provide clear numerical confirmation of the theoretical dispersion limit. These results elucidate the interplay between dispersion and dissipation in energy-critical fractional PDEs and contribute to the understanding of nonlocal dynamics in complex media.
{"title":"The zero-dispersion regime of energy-critical fractional nonlinear equations","authors":"Kalim Ullah , Zou Ran , Muhammad Ishfaq Khan , Homan Emadifar , Aseel Smerat , Karim K. Ahmed","doi":"10.1016/j.rico.2026.100670","DOIUrl":"10.1016/j.rico.2026.100670","url":null,"abstract":"<div><div>This work investigates the dispersion limit of the fractional complex Ginzburg–Landau (FCGL) equation in the energy-critical defocusing regime. Using an energy-method framework, we prove that, as the phase parameter <span><math><mrow><mi>θ</mi><mo>→</mo><mn>0</mn></mrow></math></span>, solutions of the FCGL equation with initial data in <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>α</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>N</mi><mo>=</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></math></span>, converge to solutions of the energy-critical fractional nonlinear heat (FNLH) equation, for which the limiting dynamics are well posed under the stronger regularity assumption <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn><mi>α</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. The analysis highlights the additional analytical challenges introduced by the nonlocal fractional Laplacian in the energy-critical setting. Numerical simulations are performed using a Fourier spectral discretization in space, which exactly resolves the fractional Laplacian through its Fourier symbol, combined with a fourth-order Runge–Kutta (RK4) scheme in time. Numerical errors between the FCGL and FNLH solutions are computed for different values of <span><math><mi>θ</mi></math></span>, and a temporal convergence study is carried out for fixed <span><math><mi>θ</mi></math></span>, confirming the consistency and accuracy of the numerical scheme. As <span><math><mi>θ</mi></math></span> decreases, the solutions transition from dispersive, oscillatory dynamics to smoother profiles that closely approximate the FNLH solution. Quantitative measures, including the evolution of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm and representative spatial profiles, provide clear numerical confirmation of the theoretical dispersion limit. These results elucidate the interplay between dispersion and dissipation in energy-critical fractional PDEs and contribute to the understanding of nonlocal dynamics in complex media.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100670"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146173473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-13DOI: 10.1016/j.rico.2025.100644
G. Arthi , M. Vaanmathi , R. Sivasangari , Yong-Ki Ma
This study investigates the damping behavior of impulsive fractional-order stochastic systems with state delays, which are essential for modeling dynamical processes exhibiting both memory and stochastic effects. The system is formulated using Caputo fractional derivatives and Mittag-Leffler functions, allowing for analytical expressions that accurately capture the hereditary properties of fractional dynamics. The main contribution of this work is the establishment of sufficient conditions for the controllability of both linear and nonlinear systems, achieved through a combination of stochastic analysis and fixed-point techniques, explicitly accounting for the influences of delays, damping, and impulses. The proposed methodology extends existing controllability results to a broader class of fractional stochastic systems and provides a systematic approach for analyzing their damping mechanisms. The theoretical findings are illustrated through a numerical example, confirming the accuracy and effectiveness of the developed methodology.
{"title":"Controllability of stochastic multi-term fractional-order impulsive systems involving state delay","authors":"G. Arthi , M. Vaanmathi , R. Sivasangari , Yong-Ki Ma","doi":"10.1016/j.rico.2025.100644","DOIUrl":"10.1016/j.rico.2025.100644","url":null,"abstract":"<div><div>This study investigates the damping behavior of impulsive fractional-order stochastic systems with state delays, which are essential for modeling dynamical processes exhibiting both memory and stochastic effects. The system is formulated using Caputo fractional derivatives and Mittag-Leffler functions, allowing for analytical expressions that accurately capture the hereditary properties of fractional dynamics. The main contribution of this work is the establishment of sufficient conditions for the controllability of both linear and nonlinear systems, achieved through a combination of stochastic analysis and fixed-point techniques, explicitly accounting for the influences of delays, damping, and impulses. The proposed methodology extends existing controllability results to a broader class of fractional stochastic systems and provides a systematic approach for analyzing their damping mechanisms. The theoretical findings are illustrated through a numerical example, confirming the accuracy and effectiveness of the developed methodology.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100644"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-15DOI: 10.1016/j.rico.2025.100647
Khandaker Mohammad Mohi Uddin , Abir Chowdhury , Md. Mahbubur Rahman Druvo , Mehreen Tabassum Jaima , Md. Tofael Ahmed Bhuiyan , Md. Manowarul Islam
Polycystic Ovary Syndrome (PCOS), which affects 5–10 % of women worldwide who are of reproductive age, is often misdiagnosed (∼70 %) despite the rising risks of metabolic disorders and infertility. Current machine learning diagnostics frequently struggle with unbalanced data and are not interpretable. This research improves PCOS diagnosis by introducing a new, interpretable hybrid architecture. We used mutual information and extra trees to improve feature selection and extensive preprocessing, including SMOTE for class imbalance, on a dataset of 541 patient records. A Soft Voting Ensemble that included Multilayer Perceptron (MLP) with CatBoost, optimized using GridSearchCV, and verified with 5-fold cross-validation, outperformed each individual model with previous research with a state-of-the-art accuracy of 96.88 %. Additionally, deep learning models performed well, most notably DANet (94.50 % accuracy). Importantly, SHAP and LIME improved model interpretability, offering clear insights into diagnostic judgments. The architecture was put into practice in an intuitive Flask web application for explainable, real-time forecasts. This study offers a therapeutically applicable method that strikes a balance between interpretability and high accuracy, enabling early PCOS identification and better patient outcomes. Multimodal integration and dataset extension are potential avenues for future study.
{"title":"Improving diagnostic accuracy for PCOS: A hybrid machine learning architecture with feature selection, data balancing, and explainable AI techniques","authors":"Khandaker Mohammad Mohi Uddin , Abir Chowdhury , Md. Mahbubur Rahman Druvo , Mehreen Tabassum Jaima , Md. Tofael Ahmed Bhuiyan , Md. Manowarul Islam","doi":"10.1016/j.rico.2025.100647","DOIUrl":"10.1016/j.rico.2025.100647","url":null,"abstract":"<div><div>Polycystic Ovary Syndrome (PCOS), which affects 5–10 % of women worldwide who are of reproductive age, is often misdiagnosed (∼70 %) despite the rising risks of metabolic disorders and infertility. Current machine learning diagnostics frequently struggle with unbalanced data and are not interpretable. This research improves PCOS diagnosis by introducing a new, interpretable hybrid architecture. We used mutual information and extra trees to improve feature selection and extensive preprocessing, including SMOTE for class imbalance, on a dataset of 541 patient records. A Soft Voting Ensemble that included Multilayer Perceptron (MLP) with CatBoost, optimized using GridSearchCV, and verified with 5-fold cross-validation, outperformed each individual model with previous research with a state-of-the-art accuracy of 96.88 %. Additionally, deep learning models performed well, most notably DANet (94.50 % accuracy). Importantly, SHAP and LIME improved model interpretability, offering clear insights into diagnostic judgments. The architecture was put into practice in an intuitive Flask web application for explainable, real-time forecasts. This study offers a therapeutically applicable method that strikes a balance between interpretability and high accuracy, enabling early PCOS identification and better patient outcomes. Multimodal integration and dataset extension are potential avenues for future study.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100647"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-26DOI: 10.1016/j.rico.2025.100650
Muhammad Farman , David Amilo , Manal Ghannam , Kottakkaran Sooppy Nisar , Mohamed Hafez
According to World Health Organization data, tuberculosis (TB) affects nearly one-third of the world’s population and causes several million deaths and new cases each year. Recent advances in fractal–fractional differential operators have proven effective in simulating complex real-world problems. In this study, we present a TB model with an emphasis on hospital treatment and public health education, using a fractal–fractional operator under the Mittag-Leffler function. The study focuses on biological feasibility elements such as unique solutions, existence, positivity, and feasible domains. The Lipschitz and growth conditions are used to demonstrate the existence and uniqueness of solutions to the proposed TB system. A next-generation matrix technique is used to calculate the effective reproductive number of tuberculosis to determine its spread. Suitable Lyapunov functionals are developed to demonstrate the global stability of both TB-free and endemic equilibria. Each model parameter’s impact on the effective reproductive number is assessed using a normalized sensitivity index calculation. A numerical iterative method with Newton polynomial interpolation is utilized to demonstrate the usefulness of the proposed model, and numerical simulations show that it is more efficient at various fractional orders. We looked at numerical data from a variety of factors and fractional order values, concentrating on their impact on disease eradication. The simulation results are compared between the Newton polynomial interpolation approach and the fractional Adams–Bashforth–Moulton predictor–corrector method for the model compartments. The fractal–fractional approach essentially combines the complex real-world dynamics of infectious diseases with theoretical mathematics. This approach offers deep insights that help improve public health decision-making and guide successful control measures.
{"title":"Stability and optimizing the treatment control of tuberculosis model via numerical approach","authors":"Muhammad Farman , David Amilo , Manal Ghannam , Kottakkaran Sooppy Nisar , Mohamed Hafez","doi":"10.1016/j.rico.2025.100650","DOIUrl":"10.1016/j.rico.2025.100650","url":null,"abstract":"<div><div>According to World Health Organization data, tuberculosis (TB) affects nearly one-third of the world’s population and causes several million deaths and new cases each year. Recent advances in fractal–fractional differential operators have proven effective in simulating complex real-world problems. In this study, we present a TB model with an emphasis on hospital treatment and public health education, using a fractal–fractional operator under the Mittag-Leffler function. The study focuses on biological feasibility elements such as unique solutions, existence, positivity, and feasible domains. The Lipschitz and growth conditions are used to demonstrate the existence and uniqueness of solutions to the proposed TB system. A next-generation matrix technique is used to calculate the effective reproductive number of tuberculosis to determine its spread. Suitable Lyapunov functionals are developed to demonstrate the global stability of both TB-free and endemic equilibria. Each model parameter’s impact on the effective reproductive number is assessed using a normalized sensitivity index calculation. A numerical iterative method with Newton polynomial interpolation is utilized to demonstrate the usefulness of the proposed model, and numerical simulations show that it is more efficient at various fractional orders. We looked at numerical data from a variety of factors and fractional order values, concentrating on their impact on disease eradication. The simulation results are compared between the Newton polynomial interpolation approach and the fractional Adams–Bashforth–Moulton predictor–corrector method for the model compartments. The fractal–fractional approach essentially combines the complex real-world dynamics of infectious diseases with theoretical mathematics. This approach offers deep insights that help improve public health decision-making and guide successful control measures.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100650"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-01-05DOI: 10.1016/j.rico.2026.100655
Qiang Yu, Lijuan Mao
The paper introduces the admissible-edge-dependent weighted average dwell time switching strategy that not only considers the differences and compensation between subsystems, but also takes into account the switching order of subsystems. The global uniform asymptotic stability and weighted -gain of a class of discrete-time switched nonlinear systems and its related switched T–S (Takagi–Sugeno) model are studied under the new strategy and the multiple discontinuous Lyapunov function approach. The obtained results present a larger feasible range of switching signals than the existing results. Finally, a numerical example is given to illustrate the validity and superiority of the results.
{"title":"Stability and weighted l2-gain analysis of discrete-time switched T–S fuzzy systems based on admissible-edge-dependent weighted average dwell time strategy","authors":"Qiang Yu, Lijuan Mao","doi":"10.1016/j.rico.2026.100655","DOIUrl":"10.1016/j.rico.2026.100655","url":null,"abstract":"<div><div>The paper introduces the admissible-edge-dependent weighted average dwell time switching strategy that not only considers the differences and compensation between subsystems, but also takes into account the switching order of subsystems. The global uniform asymptotic stability and weighted <span><math><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-gain of a class of discrete-time switched nonlinear systems and its related switched T–S (Takagi–Sugeno) model are studied under the new strategy and the multiple discontinuous Lyapunov function approach. The obtained results present a larger feasible range of switching signals than the existing results. Finally, a numerical example is given to illustrate the validity and superiority of the results.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100655"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-02-20DOI: 10.1016/j.rico.2026.100676
Nadeem Abbas , Syeda Alishwa Zanib , Sehrish Ramzan , Syed Ibn E Ali Zulqarnain , Wasfi Shatanawi
Corruption can be defined as the misuse of power, of public office, or of authority entrusted to the state for one’s benefit, thus bringing to light the lack of transparency, accountability, and fairness in public and private sectors. In this context, we introduce a fresh compartmental model for corruption dynamics which fully aligns theoretical assumptions to empirical realities. The different individuals are divided into the five compartments, namely, susceptible , corrupt , under investigation , jailed , and honest . To introduce memory and lineage effects in the corruption dynamics, the Atangana–Baleanu–Caputo fractional derivative is utilized. Applying the next-generation matrix method, we determine the basic reproduction number , which acts as a threshold parameter for the survival of corruption in the system. The case of corresponds to the situation where the corruption-free equilibrium enjoys both local and global asymptotic stability, while results in the endemic equilibrium (corruption-present) being asymptotically stable. Additionally, the bifurcation analysis is used to expound the parameter-induced transitions in the level of corruption and to pinpoint the main intervention mechanisms. The model now achieves improved predictive accuracy through the implementation of an artificial neural network (ANN) method which operates three distinct scenarios that researchers define as , , and . The ANN accurately models the system behavior and encompasses complex nonlinear traits. The ANN-derived predictions match the numerical simulations conducted with Maple 19 and the Lagrange interpolation technique almost perfectly. The results indicate that anti-corruption measures carefully chosen according to the model can lead to a substantial decrease in corruption thus proving the usefulness of the proposed model for political evaluation and strategy-making.
{"title":"A hybrid fractional-order and neural network model for corruption dynamics using the ABC derivative","authors":"Nadeem Abbas , Syeda Alishwa Zanib , Sehrish Ramzan , Syed Ibn E Ali Zulqarnain , Wasfi Shatanawi","doi":"10.1016/j.rico.2026.100676","DOIUrl":"10.1016/j.rico.2026.100676","url":null,"abstract":"<div><div>Corruption can be defined as the misuse of power, of public office, or of authority entrusted to the state for one’s benefit, thus bringing to light the lack of transparency, accountability, and fairness in public and private sectors. In this context, we introduce a fresh compartmental model for corruption dynamics which fully aligns theoretical assumptions to empirical realities. The different individuals are divided into the five compartments, namely, susceptible <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>ϱ</mi></mrow></msup></math></span>, corrupt <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>ϱ</mi></mrow></msup></math></span>, under investigation <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>ϱ</mi></mrow></msup></math></span>, jailed <span><math><msup><mrow><mi>J</mi></mrow><mrow><mi>ϱ</mi></mrow></msup></math></span>, and honest <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>ϱ</mi></mrow></msup></math></span>. To introduce memory and lineage effects in the corruption dynamics, the Atangana–Baleanu–Caputo fractional derivative is utilized. Applying the next-generation matrix method, we determine the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, which acts as a threshold parameter for the survival of corruption in the system. The case of <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span> corresponds to the situation where the corruption-free equilibrium enjoys both local and global asymptotic stability, while <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span> results in the endemic equilibrium (corruption-present) being asymptotically stable. Additionally, the bifurcation analysis is used to expound the parameter-induced transitions in the level of corruption and to pinpoint the main intervention mechanisms. The model now achieves improved predictive accuracy through the implementation of an artificial neural network (ANN) method which operates three distinct scenarios that researchers define as <span><math><mtext>Case 1</mtext></math></span>, <span><math><mtext>Case 2</mtext></math></span>, and <span><math><mtext>Case 3</mtext></math></span>. The ANN accurately models the system behavior and encompasses complex nonlinear traits. The ANN-derived predictions match the numerical simulations conducted with Maple 19 and the Lagrange interpolation technique almost perfectly. The results indicate that anti-corruption measures carefully chosen according to the model can lead to a substantial decrease in corruption thus proving the usefulness of the proposed model for political evaluation and strategy-making.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100676"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147396203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-02-16DOI: 10.1016/j.rico.2026.100674
Muhammad Farman , Noreen Asghar , Muhammad Umer Saleem , Soheil Salahshour , Aseel Smerat , Mohamed Hafez
Smoking has numerous impacts on the human body, including damage to the lungs. Throughout global history, respiratory diseases have presented serious health challenges, with asthma emerging as one of the most prevalent chronic disorders worldwide for health risk control. Addressing the growing impact of asthma requires comprehensive modeling techniques to better understand its spread and to support effective disease management. This study presents a deterministic mathematical model that investigates the dynamics of asthma disease influenced by active smoking. To capture the transmission and progression of the disease, a smoking-induced asthma model is formulated in which the total population is divided into six compartments. Fundamental properties of the model, including positivity, boundedness, invariant regions, and equilibrium points, are rigorously analyzed to ensure biological feasibility. The basic reproductive number is derived and investigated to determine its role in disease persistence or eradication, while sensitivity analysis identifies the most influential factors governing asthma spread. This investigation further explores local stability of the smoking-induced asthma model, with special focus on a small number of observations. To obtain numerical solutions, the well-established Non-standard finite difference (NSFD) scheme is employed to illustrate the systems behavior and validate analytical findings. Additionally, to achieve the fundamental goal of this research, an optimal control approach is introduced by incorporating two control factors: awareness campaigns through social media and treatment protocols aimed at reducing the abundance of infected individuals. Simulations demonstrate the predictive effect of smoking on asthma prevalence and highlight the dynamics under different parameter variations. The findings emphasize that smoking significantly accelerates asthma transmission and severity, underscoring the importance of medical services and public health interventions. This work provides valuable insights into asthma dynamics and establishes a mathematical foundation for developing future strategies to reduce the disease burden.
{"title":"Optimal control and dynamical transmission of asthma due to smoking populations: Incorporating medical and public health measures","authors":"Muhammad Farman , Noreen Asghar , Muhammad Umer Saleem , Soheil Salahshour , Aseel Smerat , Mohamed Hafez","doi":"10.1016/j.rico.2026.100674","DOIUrl":"10.1016/j.rico.2026.100674","url":null,"abstract":"<div><div>Smoking has numerous impacts on the human body, including damage to the lungs. Throughout global history, respiratory diseases have presented serious health challenges, with asthma emerging as one of the most prevalent chronic disorders worldwide for health risk control. Addressing the growing impact of asthma requires comprehensive modeling techniques to better understand its spread and to support effective disease management. This study presents a deterministic mathematical model that investigates the dynamics of asthma disease influenced by active smoking. To capture the transmission and progression of the disease, a smoking-induced asthma model is formulated in which the total population is divided into six compartments. Fundamental properties of the model, including positivity, boundedness, invariant regions, and equilibrium points, are rigorously analyzed to ensure biological feasibility. The basic reproductive number <span><math><mrow><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow></math></span> is derived and investigated to determine its role in disease persistence or eradication, while sensitivity analysis identifies the most influential factors governing asthma spread. This investigation further explores local stability of the smoking-induced asthma model, with special focus on a small number of observations. To obtain numerical solutions, the well-established Non-standard finite difference (NSFD) scheme is employed to illustrate the systems behavior and validate analytical findings. Additionally, to achieve the fundamental goal of this research, an optimal control approach is introduced by incorporating two control factors: awareness campaigns through social media and treatment protocols aimed at reducing the abundance of infected individuals. Simulations demonstrate the predictive effect of smoking on asthma prevalence and highlight the dynamics under different parameter variations. The findings emphasize that smoking significantly accelerates asthma transmission and severity, underscoring the importance of medical services and public health interventions. This work provides valuable insights into asthma dynamics and establishes a mathematical foundation for developing future strategies to reduce the disease burden.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100674"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147396393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-10DOI: 10.1016/j.rico.2025.100640
Md. Abdullah Bin Masud , Tanjina Tasnim , Mostak Ahmed , Md. Khalilur Rahman
Mpox, as a re-emerging infectious disease, poses considerable challenges due to uncertain transmission dynamics and sudden outbreak shocks, which cannot be adequately addressed by classical deterministic control models. To overcome these limitations, we develop a dynamic Nash game framework based on linear stochastic control with Markov jump disturbances. The framework integrates a controlled SEIR system in which regional decision-makers adopt strategies involving vaccination, social distancing, and awareness campaigns, interacting both competitively and cooperatively. By applying Pontryagin’s maximum principle, we derive the Hamiltonians and costate equations and obtain explicit formulations for both Nash equilibrium controls and team optimal controls. The stochastic SEIR model with Markov jumps is solved numerically using the Euler–Maruyama method. Simulation results indicate that Nash strategies significantly reduce infection prevalence compared to uncontrolled dynamics, yet they may produce unequal benefits across regions. Numerical simulations show that Nash controls reduce exposure and infection compared with uncontrolled dynamics, while coordinated team-optimal controls provide substantially greater reductions in outbreak magnitude and duration. This stochastic game-theoretic framework offers a robust extension of existing Mpox models by integrating Markov-jump uncertainty, multi-agent control, and analytically derived equilibrium strategies, providing practical insights for coordinated epidemic interventions.
{"title":"Dynamic Nash game for linear stochastic control with Markov Jump in Mpox","authors":"Md. Abdullah Bin Masud , Tanjina Tasnim , Mostak Ahmed , Md. Khalilur Rahman","doi":"10.1016/j.rico.2025.100640","DOIUrl":"10.1016/j.rico.2025.100640","url":null,"abstract":"<div><div>Mpox, as a re-emerging infectious disease, poses considerable challenges due to uncertain transmission dynamics and sudden outbreak shocks, which cannot be adequately addressed by classical deterministic control models. To overcome these limitations, we develop a dynamic Nash game framework based on linear stochastic control with Markov jump disturbances. The framework integrates a controlled SEIR system in which regional decision-makers adopt strategies involving vaccination, social distancing, and awareness campaigns, interacting both competitively and cooperatively. By applying Pontryagin’s maximum principle, we derive the Hamiltonians and costate equations and obtain explicit formulations for both Nash equilibrium controls and team optimal controls. The stochastic SEIR model with Markov jumps is solved numerically using the Euler–Maruyama method. Simulation results indicate that Nash strategies significantly reduce infection prevalence compared to uncontrolled dynamics, yet they may produce unequal benefits across regions. Numerical simulations show that Nash controls reduce exposure and infection compared with uncontrolled dynamics, while coordinated team-optimal controls provide substantially greater reductions in outbreak magnitude and duration. This stochastic game-theoretic framework offers a robust extension of existing Mpox models by integrating Markov-jump uncertainty, multi-agent control, and analytically derived equilibrium strategies, providing practical insights for coordinated epidemic interventions.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100640"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145711874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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