In this research, we have derived a mathematical model to study the impact of health center-based awareness campaigns on the spread of human papillomavirus (HPV) infection to cervical cancer. In the model, the human population is divided into susceptible, vaccinated, permanently immune, infected with HPV, and recovered. Moreover,awareness level is assumed as a model compartment. The awareness level affects the rates of infection, vaccination, recovery, and disease progression. The basic reproduction number (R₀) is calculated using the next-generation matrix method. The equilibrium points are determined, and their stability analysis is conducted. Disease-free equilibrium (DFE) is globally asymptotically stable for R₀ < 1. Forward transcritical bifurcation occurs at R₀ = 1. Furthermore, optimal control theory is employed using Pontryagin’s maximum principle, with the objective of minimizing infection rates through optimal vaccination at the minimum cost of control. These results are validated by numerical simulations. The results show that effective HPV awareness campaigns can help control the spread of HPV infections, making it easier to manage cervical cancer. This study confirms the importance of awareness-induced behavioral dynamics in modeling spread of HPV for efficient disease management. Awareness campaigns with optimal vaccination can significantly lower HPV transmission and reduce the incidence of cervical cancer.

Printed circuit boards (PCBs) are an indispensable part of electronic products. As the consumer electronics market continues to expand, the PCB assembly rate has become a key factor limiting production line efficiency. PCB placement scheduling is a highly complex, multivariable combinatorial optimization problem characterized by nonlinearity and high coupling. From a system perspective, this scheduling problem is modeled as a complex network optimization, wherein the intricate coupling of resources, time, and processes parallels the node interdependencies and information propagation mechanisms inherent in complex system architectures. Given its nondeterministic polynomial-time (NP)-hard nature and the dynamic constraints of the production environment, this study develops a rigorous mathematical model based on motion trajectory analysis and proposes a three-stage hierarchical decoupling framework. This decomposition transforms the high-dimensional network complexity into manageable subtasks while preserving essential variable interdependencies. To solve this complex network optimization, the framework integrates a hybrid adaptive genetic algorithm (HAGA) implemented through a three-level strategy.Initially, an improved adaptive genetic algorithm (IAGA) handles global load balancing; subsequently, an improved spectral clustering algorithm groups components to minimize tool-changing overhead; finally, a hybrid genetic algorithm and ant colony optimization (GA-ACO) optimizes synchronized intramachine paths. Unlike partial-stage methods, this holistic approach ensures synergistic optimization from global network equilibrium to local machine precision. Numerical experiments using real-world data from Dalian Rijia Co., Ltd. demonstrate that HAGA achieves at least a 10% reduction in the production cycle. This research proves that the hierarchical strategy effectively balances computational efficiency with global optimization performance.

This article investigates the truncated M-fractional Shynaray-IIA equation, which has important applications in many fields, such as fiber optic communication, magnetodynamics of ferromagnetic materials, and fluid dynamics. First, the truncated M-fractional Shynaray-IIA equation is transformed into a nonlinear ordinary differential equation through a fractional-order derivative and the traveling wave transformation. Then, the generalized (G^′/G)-expansion method is adopted to get multiple groups of coefficient solutions based on the auxiliary equation. The conditions satisfied by the coefficients of the auxiliary equation are classified, and all novel wave solutions of the TMF-SIIAE are obtained, including bright solitons, dark solitons, and breathers. Finally, in order to better understand the behavior of the solutions, a 3D graph, cartesian and polar graph, contour graph and density graph of the solutions are drawn using Python software. Specifically, we also conducted a comparative analysis between the newly obtained solution and the existing solution, and quantitatively discussed the parameters of fractional-order derivatives and analyzed their physical applications.

Periodic capillary-gravitational perturbations propagating along the free surface of a heterogeneous liquid were investigated by methods of united perturbation theory. A reduced system of heterogeneous fluid mechanics equations, which takes into account the non-uniformity of the liquid density distribution without considering the physical nature of stratification, was analyzed. The methods of the united theory of regular and singular perturbations in linear approximation were employed to obtain complete dispersion relations that describe the large-scale dynamics and fine structure of periodic flows. Analysis of solution showed that calculated regular functions characterize wave components that determine the large-scale geometry and flow dynamics. Singular functions describe ligament components that determine the fine structure of flows. Moreover, the basic properties of large-scale wave components and ligament fine-structured components were calculated for a liquid with water parameters and different values of the buoyancy frequency in an exponentially stratified liquid. When performing the limiting transition to simpler models, the relations obtained uniformly converged to known expressions for capillary-gravity and internal waves. Singular solutions were lost when the effects of viscosity were neglected in a stratified and homogeneous liquid. A substantial difference of the first constructed complete dispersion relation for periodic gravity–capillary flows from that previously obtained using the Boussinesq approximation is shown.

In this study, we formulated and analyzed a within-host co-infection model of Dengue virus (DENV) and Zika virus (ZIKV) that incorporated CTL-mediated immunity, and four types of distributed time delays. The model described the dynamics of uninfected cells, latently, and productively infected cells for each virus, along with free DENV and ZIKV particles and virus-targeted CTL responses. We first proved that all model solutions remained nonnegative and bounded. We computed the basic reproduction numbers $R_{D}^{L}$ for DENV and $R_{Z}^{L}$ for ZIKV, together with the invasion reproduction numbers $R_{D}^{L, i n v}$ and $R_{Z}^{L, i n v}$, which determined invasion capability under pre-existing infection. These numbers governed the existence and the global asymptotic stability of model equilibria. Global stability was established using the Lyapunov method, and numerical simulations were performed to validate the analytical results. In addition, sensitivity analysis identified the most influential parameters affecting viral clearance. The effects of antiviral therapy, time delays, and latent infection stages on the DENV–ZIKV co-dynamics were investigated. The results showed that treatment intervention, prolonged delays, and the inclusion of latent infection stages led to a reduction in $R_{D}^{L}$ and $R_{Z}^{L}$. Furthermore, neglecting intracellular delays or latent infection stages leads to an overestimation of $R_{D}^{L}$ and $R_{Z}^{L}$ and the antiviral efficacy required for infection control. This suggests that therapeutic strategies aimed at prolonging intracellular delay phases and accounting for latent-stage dynamics may decrease these reproduction numbers below unity, thereby promoting viral elimination within the host.

The growing role of artificial intelligence (AI) in information dissemination has made algorithmic recommendation a significant pathway for rumor spread. To address this, we developed a dual-path rumor propagation model that integrates interpersonal communication with AI-driven algorithmic diffusion. The model employs Caputo fractional derivatives to capture memory effects and historical dependencies in the spreading process. For intervention, we proposed a coordinated control framework combining traditional measures (e.g., legal regulation and science education) with dynamic AI algorithmic control. A key innovation was the design of a time-varying cost function and the introduction of a time-sensitive factor to model the realistic constraint of rising AI control costs over time, forming a novel fractional-order optimal control problem. The trade-off between control cost and governance effectiveness was analyzed via Pareto frontier optimization. Theoretical analysis confirmed that the equilibrium and its global stability are governed by the basic reproduction number. Numerical simulations revealed the existence of a critical regime for the time-sensitive factor (ρ = 0.8), in which the optimal strategy exhibits a distinct staged control behavior: intensive AI-based intervention is emphasized during the early phase, followed by a gradual transition toward traditional measures for sustained long-term governance. This strategy effectively reduces the peak and overall scale of rumor propagation, demonstrates robustness across parameters, and achieves a balanced trade-off between control cost and social benefit. The study provides a dynamic modeling framework for rumor governance in the AI era, highlighting the importance of integrating algorithmic and traditional controls while accounting for time-varying costs.

Synchronization in multilayer networks plays a fundamental role in many real-world systems; yet, understanding how interlayer structures influence synchronizability remains a major challenge. In this paper, we investigated the synchronizability of multilayer networks with undirected and directed interlayer couplings. By deriving the exact spectral properties of the corresponding supra-Laplacian matrices, explicit synchronizability criteria were established for bounded and unbounded synchronization regions. The results revealed that interlayer coupling patterns strongly affected synchronization behavior. In undirected multilayer networks, increasing the number of layers weakened synchronizability, whereas stronger intra- and interlayer coupling strengths could enhance synchronization performance. In contrast, multilayer networks with directed interlayer couplings exhibited different behavior: Synchronizability became independent of the number of layers, demonstrating the significant impact of coupling asymmetry on collective dynamics. Moreover, simulations on Erdös–Rényi multilayer networks validated the theoretical predictions. These findings provide analytical insights into how multilayer architectures and coupling asymmetry shape synchronization dynamics and may offer guidance for the design and optimization of complex interconnected systems.

We introduce a lacunary bivariate q-Laguerre–Sheffer family generated by the product of a Sheffer factor, a first q-exponential, and a q-Tricomi–Bessel kernel. The construction has three independent controls: the lacunarity index fixes which powers enter the finite sums, the kernel order changes the Bessel-type shifts, and the Sheffer factor supplies an additional deformation of the sequence. We derive explicit coefficient and convolution formulas, lowering relations, a quasi-monomial operator structure, a q-difference equation, and a q-translation identity. We then evaluate the polynomials at a mass-weighted graph Laplacian associated with heterogeneous network diffusion. This gives polynomial spectral filters whose vertex-domain support is limited to a prescribed graph-hop radius. Numerical examples illustrate the locality bound, spectral response tuning, comparison with a Chebyshev polynomial filter, kernel truncation accuracy, and a one-parameter calibration problem.

The event-triggered non-synchronous stabilization problem for Markov jump systems was investigated via state-feedback control. The possible mismatch between the plant and controller modes was modeled by a hidden Markov model. Both memoryless and memory-based switched event-triggered mechanisms were proposed to reduce the frequency of controller updates. Two sufficient conditions were established to guarantee the stochastic stability of the closed-loop system by employing Lyapunov–Krasovskii functionals, free-weighting matrices, and stochastic analysis. Computationally tractable schemes were then developed to obtain the state-feedback controller gains via congruence transformations. A numerical example is presented to illustrate the efficiency of the switched event-triggered non-synchronous state-feedback control schemes.

This study presents a reaction-diffusion framework that integrates boundary outflow mechanisms with logistic population dynamics to investigate epidemic evolution in spatially non-uniform environments. By incorporating non-linear, density-dependent regulation and boundary leakage, the model builds on the constraints of population conservation or closed habitats found in classical studies, thus offering a more objective representation of open population dynamics under resource limitations. We provide a rigorous analysis of the system’s foundational mathematical properties, establishing the invariant non-negativity of state variables and uniform upper bounds for all global solutions, thereby ensuring the reliability of the subsequent dynamical analysis. Based on the spectral radius characterizations, the fundamental parameter R₀ acts as the definitive threshold for disease control: the infection is destined for extinction when R₀ < 1, whereas the system exhibits spatial persistence and the emergence of at least one non-trivial endemic equilibrium when R₀ > 1. The findings reveal that the boundary outflow mechanism remains an effective mitigation strategy in resource-constrained environments, thereby significantly mitigating the infection pressure and suppressing the spatial dissemination of the disease.

This paper addresses the problem of constructing and analyzing a new four-variable family of hybrid special polynomials that unifies several classical polynomial systems within the Sheffer sequence framework. Specifically, we introduce the Legendre-Laguerre-Gould-Hopper-based Sheffer polynomials (LeLGHSP) by embedding the Legendre-Laguerre–Gould–Hopper hybrid structure defined via Bessel-Tricomi functions and higher-order exponential terms into the Sheffer generating function governed by the pair (µ(τ), σ(τ)). Using operational calculus, inverse derivative operators, and Riordan array methods, we derive explicit series representations, determinantal forms via Cramer’s rule, four operational identities expressing the new family in terms of known Sheffer and Gould–Hopper polynomials, and shift relations of binomial type. The quasi-monomial structure of the family is established by constructing multiplicative and derivative operators satisfying the Weyl algebra commutation relation, from which differential equations governing the polynomials are obtained directly. Three important special cases (generalized Legendre-Laguerre-Gould-Hopper-Hermite, Laguerre, and Pidduck-type Sheffer polynomials) are investigated in a unified manner. Surface plots illustrate the geometric behavior of the family. The framework generalizes numerous classical polynomial families and has potential applications in quantum mechanics, heat-type equations, approximation theory, and combinatorics.

In this paper, we introduce a new class of generalized Bernoulli polynomials and numbers by making use of the generalized Bessel–Struve kernel function as a generating mechanism. This combination enriches the structural and analytical characteristics of the resulting polynomial family and provides a broader extension of classical Bernoulli-type sequences. By choosing specific values of the free parameters, the classical Bernoulli polynomials appear as special cases, which confirms that the proposed framework has a unifying nature. We carry out a detailed investigation of the basic structural properties, which includes generating function representations, recurrence and differential relations, and implicit summation formulas. In addition, we extend the Stirling numbers of the second kind in connection with the new polynomial families, which adds a combinatorial dimension to the study. Explicit expressions for the higher-order generalized sequence $X_{n, \mu}^{b, c,(\alpha)}(x)$ are provided for n = 0, 1, 2, 3. Numerical experiments include the verification of the addition formula to machine-precision accuracy across positive, negative, and complex inputs, systematic tracking of the real zeros as the kernel parameters vary, and a graphical analysis of the root locus and complex root distribution for degrees up to n = 20. We hope that the results obtained here will open new directions of research in mathematical analyses and related areas of applied mathematics and theoretical physics.

The primary objective of this study is to develop and analyze a numerical scheme to solve nonlinear fractional reaction-convection-diffusion equations, where the fractional derivative is interpreted in the Caputo sense. First, the nonlinear system is linearized using a direct linearization strategy, after which a barycentric rational interpolation method is employed to construct a fully discrete numerical scheme. A rigorous theoretical framework is established to demonstrate the stability and convergence of the proposed method. To corroborate the theoretical findings, several numerical experiments are conducted, illustrating the method’s accuracy, robustness, and computational efficiency. This work advances the numerical analysis of nonlinear systems characterized by fractional- order dynamics and provides effective computational tools to model complex processes in various scientific and engineering contexts.

This paper presents an integrated methodological framework for analyzing the structure and operational performance of intercity public transportation systems by combining complex network theory with discrete event simulation. The road network is modeled as a directed multigraph, enabling the identification of critical nodes and corridors through centrality metrics and percolation analysis, while the simulation operates directly on the network’s topology by incorporating travel speed variability, passengers’ boarding and alighting times, and service frequencies. A case study of the intercity public transportation network of the Department of Quindío (Colombia) demonstrates the applicability of the methodology. The results show that network vulnerability is concentrated in a limited number of strategic corridors, with betweenness centrality providing the most effective criterion for identifying structurally critical nodes. Furthermore, although alternative routes exist, they do not necessarily guarantee operational resilience. The proposed framework provides a quantitative decision support tool for transportation planning and infrastructure management and, owing to its modular and scalable design, can be readily adapted to other intercity transportation systems.

This paper proposes a semi-analytical valuation framework for a European call option on the maximum of two assets under a two-factor stochastic volatility model that incorporates both stochastic long-term means and stochastic liquidity risk. By applying the Feynman–Kac theorem, the joint characteristic function of the two liquidity-adjusted log-prices is explicitly derived. Using this joint characteristic function, a semi-analytical pricing formula for the option is obtained through measure changes and bivariate Fourier inversion techniques. The formula is validated against Monte Carlo simulation, and comparisons with nested benchmark models quantify the incremental pricing effects of stochastic liquidity and the stochastic long-term mean. Finally, through various numerical examples, a sensitivity analysis is conducted to illustrate how changes in significant parameters affect the option’s price.