This study introduces a dual-hybrid COVID-19 forecasting modeling approach that integrates an eight-compartment SEAIQHRD model with Gaussian Process Regression (GPR) and ARIMA-based residual learning to enhance predictive performance. A central methodological contribution is the incorporation of convergence and stability diagnostics, demonstrating reliable parameter estimation through multi-start optimization and bootstrap analysis. Although the SEAIQHRD model captures core disease progression, it is limited in representing nonlinear multi-wave patterns and reporting inconsistencies. The SEAIQHRD–ARIMA hybrid improves short-term linear adjustments, while the SEAIQHRD–GPR hybrid effectively models nonlinear residual structure and provides uncertainty-aware forecasts. Using COVID-19 data from India, both hybrids outperform the standalone model, with the GPR variant yielding the greatest accuracy. Forecast superiority, confirmed by DM, CW, GW, Wilcoxon, and Friedman tests, underscores the robustness and applicability of the proposed modeling approach for public-health. Clinical trial Not applicable.

This study develops an age–stratified SEIR framework with dose–dependent recovery to explore how therapeutic allocation across age groups can mitigate epidemic spread. The susceptible and exposed classes are modeled as a single homogeneous pool, while infectious and recovered individuals are partitioned into four age groups (infants, children, adolescents, adults) with distinct recovery rates. Recovery in each age class is governed by a sigmoid dose–response relationship, representing age–specific pharmacodynamic efficacy as a function of administered dose. We derive an explicit expression for the basic reproduction number ℛ_0 , identify the corresponding transmission threshold β_c , and characterize the forward threshold at ℛ_0=1 separating disease-free extinction from transient epidemic waves with age-stratified quasi-steady plateaus. Numerical simulations, including time series and low–dimensional phase portraits, illustrate how improving recovery in high–contribution age groups (particularly infants and children) can reduce ℛ_0 and suppress epidemic peaks under a range of initial conditions. The results provide a conceptual quantitative framework for assessing age–specific dosing strategies and highlight the need for disease – and setting–specific calibration before drawing operational policy conclusions. Not applicable.

Chronic kidney disease (CKD), affecting approximately 843 million individuals globally, substantially increases susceptibility to severe COVID-19 outcomes, while SARS-CoV-2 infection independently accelerates renal deterioration through cytokine storms and microvascular injury. Despite this clinically significant bidirectional interaction, rigorous mathematical characterization of their co-dynamics within a unified framework integrating stability theory, bifurcation analysis, and optimal control remains limited. We formulated a seven-compartment deterministic model incorporating CKD'S irreversibility, the enhanced blue susceptibility of CKD patients, and vaccine imperfection, calibrated against Indian epidemiological data. The basic reproduction number R0 was derived using the next-generation matrix method, and stability and bifurcation analysis were performed. Sensitivity analysis identified transmission and immunity waning as dominant drivers, while optimal control strategies significantly reduced co-infections and hospitalizations, demonstrating the effectiveness of coordinated intervention policies.

In this manuscript, sufficient conditions for the existence and uniqueness of solutions to the Hilfer-Katugampola Fractional Differential Equations, characterized by two parameters, ϰ and ς ( ς≤ 1 and ϰ > 1 ), which generalize classical fractional differential equations are established. By a fixed point technique and the results of fractional calculus, the local asymptotic stability of the attractive solution is analyzed. Two numerical examples are provided in order to illustrate the attractivity results.

The Banach fixed-point theorem, along with a fuzzy number characterized by normality, convexity, upper semicontinuity, and a compactly supported interval to look into the possibility of a solution equation to the fuzzy nonlinear neutral integrodifferential equation of the Sobolev-type within a fuzzy vector space of n dimensions, is employed in this research. At the end, to demonstrate the practical application of the findings, an example is also presented.

In this article, we explore the existence and uniqueness of mild solutions to fractional stochastic differential equations involving the ABC derivative with the Lipschitz coefficients. To do so, we extract a stochastic version of the variation of constants formula for fractional ABC differential system with the coefficients satisfying the standard Lipschitz condition. Our main goal is to establish the relationship between the integral equation and the mild solution by employing Ito's isometry, martingale representation, and weighted maximum norm. Furthermore, we verify the systems Hyer-Ulam stability. We successfully illustrate the practical relevance of our theoretical results with an example.

Severe cases of COVID-19 can progress to pneumonia and, in some patients, to COVID-19-associated pulmonary aspergillosis (CAPA), a fungal co-infection linked to high mortality. Most existing models address COVID-19 transmission alone, without explicitly capturing the sequential progression to pneumonia and CAPA. To address this gap, we develop a novel compartmental model (SIIcpIcaHR) that integrates the co-dynamics of COVID-19 pneumonia and CAPA, incorporating both disease progression pathways and hospitalisation processes. The model is calibrated using cumulative COVID-19 case data from India, and analysed through stability theory, sensitivity analysis, and an optimal control framework. Sensitivity indices and Partial Rank Correlation Coefficients identify key parameters influencing transmission and severity. We evaluate time-dependent intervention strategies—vaccination, early hospitalisation, and enhanced treatment—individually and in combination, using Pontryagin’s Maximum Principle and numerical simulation. Results show that while each single measure reduces disease burden, combined application of all three significantly minimises pneumonia and CAPA prevalence, lowers hospitalisation needs, and is cost-effective within realistic constraints. These findings emphasise the importance of integrated public health strategies that couple pharmaceutical and clinical interventions to curb severe COVID-19 outcomes and associated fungal complications.

Epidemic modeling plays a crucial role in understanding disease transmission and informing public health strategies. This study presents a fractional Susceptible-Exposed-Infected-Quarantined-Recovered (SEIQR) model incorporating Atangana–Baleanu-Caputo (ABC) fractional derivatives to capture memory effects in disease dynamics. The model extends classical ordinary differential equation-based frameworks by integrating a fractional approach, enhancing its applicability to real-world epidemic scenarios. A key feature of our model is the inclusion of mortality rates across all disease compartments, providing a refined representation of influenza-like infections with pandemic potential. We conduct a detailed stability analysis to assess equilibrium states and derive conditions for disease control. Numerical simulations further validate the theoretical findings, offering insights into epidemic progression and intervention strategies. Our results highlight the significance of fractional calculus in epidemiological modeling and its potential to improve predictive accuracy for infectious disease outbreaks.

The efficiency of various control measures to stop the spread of monkeypox disease is examined in this paper by analyzing a compartmental model for the disease using the Caputo-Fabrizio fractional derivative approach. The methodology of maximum likelihood estimation is used to fully parametrize the model. By conducting a thorough mathematical analysis of the model, we look into the existence and uniqueness of solutions as well as the establishment of requirements guaranteeing the rigidity and continuation of these solutions. We then analyze the fundamental reproduction number in terms of sensitivity. To provide numerical answers, the Adams-Bashforth predictor-corrector approach is utilized, which is specifically designed for the fractional derivatives of Caputo-Fabrizio. The model is numerically simulated over a range of fractional-order numbers to illustrate our results. Our study contributes significantly to the area of epidemiology by emphasizing the vital roles that effective treatment, infection awareness, and immunization programs have in significantly lowering the spread of disease.

In this research article, we propose a fuzzy fractional-order SEIRiUiHR model to describe the transmission dynamics of COVID-19, comprising susceptible, exposed, infected, reported, unreported, hospitalized, and recovered compartments. The uncertainty in initial conditions is represented using fuzzy numbers, and the fuzzy Laplace transform combined with the Adomian decomposition method is employed to solve nonlinear differential equations and also to derive approximate analytical series of solutions. In addition to fuzzy lower and upper bound solutions, a model is introduced to provide a representative trajectory under uncertainty. A key feature of the proposed model is its inherent symmetry in compartmental transitions and structural formulation, which show the difference in reported and unreported cases. Numerical experiments are conducted to compare fuzzy and normal (non-fuzzy) solutions, supported by 3D visualizations. The results reveal the influence of fractional-order and fuzzy parameters on epidemic progression, demonstrating the model’s capability to capture realistic variability and to provide a flexible framework for analyzing infectious disease dynamics.

The emergence of alpha, beta, gamma, and delta COVID-19 variants has posed important challenges to global health. Understanding the transmission dynamics and evaluating the impact of vaccination strategies are critical for effective pandemic management. The present study develops a novel mathematical model that incorporates time-dependent vaccination rates to analyze the spread of these four COVID-19 variants, utilizing India as a case study. We assess the model’s positivity, boundedness, and disease-free equilibrium, as well as we calculate basic reproduction numbers. A sensitivity analysis is conducted to evaluate the impact of key parameters on transmission dynamics. Using optimal control theory, we evaluate three strategies: continuous vaccination of susceptible individuals, public awareness campaigns to reduce contact rates, and quarantine/hospitalization of infected individuals. Numerical simulations over a 300-day period demonstrate that the combined strategy — continuous vaccination, public awareness campaigns, and quarantine/hospitalization — leads to the greatest reduction in infections across all four variants. This is confirmed by the incremental cost-effectiveness ratio and provides practical insights for optimizing pandemic response. The model extends prior research by integrating real-world vaccination data with multi-strain COVID-19 dynamics, offering a comprehensive framework that can guide policymakers in managing future outbreaks. Our study emphasizes the necessity of synergistic public health strategies, and highlights their practical relevance for epidemic management in regions with high population density and limited healthcare resources.

In this study, we introduce a bipolar interval-valued intuitionistic fuzzy (BIVIF) norm, projection, and bidirectional projection measure within the framework of BIVIF topological spaces. These tools enable us to handle ambiguity with greater accuracy, calculate relationships between sets more effectively, and make rational decisions in uncertain situations. Our approach combines practical calculation procedures with carefully established axioms, ensuring both mathematical soundness and real-world applicability. The effectiveness of the proposed BIVIF framework is demonstrated in the context of agricultural decision-making, where the bidirectional projection measure is applied to identify the most profitable crops for farmers. The results show that BIVIF sets provide a stronger and more reliable framework than bipolar intuitionistic fuzzy (BIF) sets, thereby supporting well-informed decisions that optimize crop yield and profitability.

Bipolar fuzzy sets (BPFs) provide a suitable framework for knowledge representation if some data contains imprecise and ambiguous information. In this manuscript, the lower and upper bounds of the Seidel Laplacian energy of a bipolar fuzzy graph were examined with suitable illustrative examples. Moreover, the energy of a bipolar fuzzy graph, the Laplacian energy of a bipolar fuzzy graph, and the Seidel Laplacian energy of a bipolar fuzzy graph were examined. Furthermore, to address complex multi-criteria decision-making (MCDM) problems involving uncertainty and bipolar information, we proposed novel score functions: The score function, improved score function, and double improved score function. These functions were demonstrated through examples to effectively handle ambiguity and duality in decision-makers' inputs represented via bipolar fuzzy sets.

Every manufacturing industry strives to always provide impeccable goods. Due to machine failures, labor issues, etc., this is practically unachievable in real-world situations during the manufacturing run time. As a result, things of subpar quality are produced by the equipment systems. The inferior-quality products are improved at a cost to make them better, and then they are prepared for sale. The nonlinear programming Lagrangian method is used to determine the best solution, which affects the average monthly cost. In the suggested model, the graded mean integration representation method is used to describe defuzzification while trapezoidal and pentagonal fuzzy numbers are used to calculate the optimal cost though there are different types of fuzzy numbers available that are used to test the optimality. The main aim of the paper is to compare the trapezoidal and pentagonal fuzzy numbers to test the optimal total cost. As a result, the trapezoidal fuzzy number gives an accurate result in all cases, while in the pentagonal fuzzy number, there is a slight deviation in the fuzzy case. So when we go with a higher-order fuzzy number, the accuracy of the optimal total cost changes. Finally, a graphic comparison using MATLAB is carried out for the two fuzzy numbers and the best out of them is found.

The article demonstrates the novel solutions available for several QDEs and offers incredible promise for the investigation of quaternion differential equations (QDEs). This result is likely due to the matrix representation strategy and the use of the Picard–Lindelöf theorem, which is an important consequence of traditional ordinary differential equations (ODE) formulations. Using this numerical calculation aid research, the authors rightly point out that there is a feasible QDE solution. Furthermore, this article goes beyond the direct proof of its existence and digs into the analysis of the stability of the solution, which was obtained. In particular, the authors use the appropriate Lyapunov equations to determine the asymptotic stability of the QDE. This study adds depth to the understanding of QDE solutions and provides fundamental insights into their absorbed dynamics. Furthermore, this particular manuscript examines the symmetry and asymmetry aspects of QDEs, possibly investigating how these properties manifest themselves in solving implicit situations Through examples, architects describe methods that through the behaviours exhibited by QDEs, revealing insights into the elegant mathematical architecture inherent in these situations. By Homotopy Pertubation method and Li–He modified Homotopy Perturbation method, the numerical solutions are provided. In general, this article fully contributes to the conceptual framework associated with QDEs, providing new insights into their unique existence, stability, and symmetry properties

This paper explores the realm of dynamical control systems through fuzzy modelling, where the dynamics are shaped by a fuzzy stochastic process (FSP) propelled by fuzzy Brownian motion (FBM). Specifically, the paper introduces a new fractional stochastic differential equation (FSDE) featuring variable fuzzy delays and non-instantaneous impulses driven by FBM. The study attempts to ascertain whether global and local solutions for the suggested system exist and are unique by applying fuzzy metrics and Banach contraction mapping principle. The efficacy of the analytical findings is demonstrated through a pertinent example.

The global crisis of the COVID-19 pandemic has highlighted the need for mathematical models to inform public health strategies. The present study introduces a novel six-compartment epidemiological model that uniquely incorporates a higher isolation rate for unreported symptomatic cases of COVID-19 compared to reported cases, aiming to enhance prediction accuracy and address the challenge of initial underreporting. Additionally, we employ optimal control theory to assess the cost-effectiveness of interventions and adapt these strategies to specific epidemiological scenarios, such as varying transmission rates and the presence of asymptomatic carriers. By applying this model to COVID-19 data from India (30 January 2020 to 24 November 2020), chosen to capture the initial outbreak and subsequent waves, we calculate a basic reproduction number of 2.147, indicating the high transmissibility of the virus during this period in India. A sensitivity analysis reveals the critical impact of detection rates and isolation measures on disease progression, showing the robustness of our model in estimating the basic reproduction number. Through optimal control simulations, we demonstrate that increasing isolation rates for unreported cases and enhancing detection reduces the spread of COVID-19. Furthermore, our cost-effectiveness analysis establishes that a combined strategy of isolation and treatment is both more effective and economically viable. This research offers novel insights into the efficacy of non-pharmaceutical interventions, providing a tool for strategizing public health interventions and advancing our understanding of infectious disease dynamics.

In this article, we present a novel methodology for inventory management in the pharmaceutical industry, considering the nature of its supply chain. Traditional inventory models often fail to capture the particularities of the pharmaceutical sector, characterized by limited storage space, product degradation, and trade credits. To address these particularities, using fuzzy logic, we propose models that are adaptable to real-world scenarios. The proposed models are designed to reduce total costs for both vendors and clients, a gap not explored in the existing literature. Our methodology employs pentagonal fuzzy number (PFN) arithmetic and Kuhn–Tucker optimization. Additionally, the integration of the naive Bayes (NB) classifier and the use of the Weka artificial intelligence suite increase the effectiveness of our model in complex decision-making environments. A key finding is the high classification accuracy of the model, with the NB classifier correctly categorizing approximately 95.9% of the scenarios, indicating an operational efficiency. This finding is complemented by the model capability to determine the optimal production quantity, considering cost factors related to manufacturing and transportation, which is essential in minimizing overall inventory costs. Our methodology, based on machine learning and fuzzy logic, enhances the inventory management in dynamic sectors like the pharmaceutical industry. While our focus is on a single-product scenario between suppliers and buyers, future research hopes to extend this focus to wider contexts, as epidemic conditions and other applications.

In this work, we introduce a new SEVIR epidemic model to analyze the dynamics of infectious diseases by incorporating the key compartments such as susceptible, exposed, vaccinated, infected, and recovered populations. We add the vaccination compartment in the current model and calculate the consequences concerning the disease spreading; it is significantly relevant at the present day considering the general policies of worldwide vaccinations. For a stringent assessment of stability, it should involve derivation of a basic reproduction number, as this parameter characterizes whether an infection will be spread at all. Our results demonstrate that when we have R-0 < 1, the disease-free equilibrium is locally asymptotically stable, which implies that an infection will eventually die out. We also identify two distinguished disease-dependent equilibrium points for the first time, giving much deeper insight into long term behavior of the disease. Numerical simulations show the efficacy of vaccination toward reducing the newly infected individuals and suggest the model can predict stabilization for all compartments over time. The exposed and recovered population increases and stabilizes as the susceptible, infected, and vaccinated populations decline. In this regard, these are valuable insights into the progression of epidemics and put emphasis on vaccination programs. Our model provides a perspective on disease control by taking into account the interplay between vaccination and infection dynamics. It can be very useful for predicting future outbreaks and can guide public health policy. Future work will extend the model by adding quarantine measures to further hone our understanding of disease transmission.

The Fermatean fuzzy set, in contrast to other generalizations of fuzzy sets like PFS and IFS, has a wide range of acceptance for both MF and NMF. In light of this, the Fermatean fuzzy set performs as an efficient, flexible, and comprehensive representation in situations that lack certainty. Here, the weaker forms of Fermatean fuzzy sets are introduced, and their traits are analyzed. Decomposition and continuity of the Fermatean fuzzy α-open set are also accustomed. With the goal of safeguarding our green environment, hiring the best supplier is of the utmost significance in the construction industry. Using outranking techniques, Visual PROMETHEE Academic Edition 1.4 is a live multi-criteria decision aid software program. It runs virtual analysis through GAIA and applies selected criteria to contrast parameters. It also saves them for possible export and editing. In this article, the PROMETHEE II method is applied for Fermatean fuzzy numbers with FF(α,β)-level for selecting the optimal green supplier for a construction company. Because of its ability to handle vagueness, the FF PROMETHEE II method emerges as a valuable tool in Multi-criteria decision making. Furthermore, this study assesses the efficacy of the proposed technique by comparing its results with those obtained through other established methods.