Search Results (322)

Avian influenza (AI) remains a serious threat to poultry and public health worldwide due to its zoonotic nature and pandemic potential. This paper develops and analyzes a coupled system of nonlinear ordinary differential equations and an SEIR-SEIR model that describes the transmission dynamics of avian influenza in both human and bird populations. The model incorporates multiple transmission routes (bird-to-bird, bird-to-human, human-to-human), exposed/latent compartments in both hosts, disease-induced mortality, and demographic processes. From a mathematical perspective, we present a rigorous analysis of this eight-dimensional dynamical system. We prove positivity and boundedness of solutions in ${\mathbb{R}}_{+}^8$, characterize the equilibrium points, and derive the basic reproduction numbers $R_0^b$ and $R_0^h$ using the next-generation matrix method. Local asymptotic stability of the disease-free equilibrium is established via the Routh–Hurwitz criterion. A composite Lyapunov function is constructed to prove global asymptotic stability when both reproduction numbers are less than unity—a result that exploits the cascade structure of the system and provides a template for analyzing similar multi-host models. Sensitivity analysis using normalized forward sensitivity indices identifies critical parameters. In addition, we use neural network models to validate both models and provide error analysis. These results emphasize the crucial role of controlling cross-species transmission and improving recovery efforts, which have significant implications for the design of effective intervention and surveillance programs in the context of the One Health framework. Full article

A within-host HIV dynamics model incorporating latent reservoirs, distributed time delays, and a B-cell-mediated humoral immune response is developed and analyzed mathematically. The model includes five compartments: uninfected CD4⁺ T cells, latently infected cells, actively infected cells, free virions, and B cells. Four distinct distributed delays are introduced to account for the periods between viral entry and the emergence of latently or actively infected cells, reactivation of latently infected cells, and intracellular virion production. For the non-delayed system, the basic reproduction number ${\mathcal{R}}_0$ is derived using the next-generation matrix method. Using Lyapunov functions and LaSalle’s Invariance Principle, a sharp threshold dynamic is proven: the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0\le 1$, whereas a unique endemic equilibrium is GAS when ${\mathcal{R}}_0>1$. For the full distributed-delay system, a delay-dependent reproduction number ${\mathcal{R}}_0^d$ is defined. The global asymptotic stability of the infection-free equilibrium is established for ${\mathcal{R}}_0^d\le 1$, and the global asymptotic stability of the endemic equilibrium is established for ${\mathcal{R}}_0^d>1$, using suitably constructed Lyapunov functionals that account for the delay history. Numerical simulations validate the analytical threshold behavior. A sensitivity analysis of ${\mathcal{R}}_0^d$ identifies the most influential parameters for potential intervention. A treatment-dependent reproduction number is derived, and the critical drug efficacy required for viral eradication is determined. The intracellular production delay is shown to act as a critical threshold for infection clearance. Full article

Thisarticle develops and analyzes a fractional-order Leslie–Gower prey–predator–parasite system incorporating two discrete delays and nonlocal spatial diffusion. The model’s central novelty lies in the simultaneous integration of three biologically realistic features that have not previously been combined: (i) fractional-order memory effects via a Caputo derivative of order $\alpha \in (0,1]$, (ii) two distinct biological delays—an infection transmission delay ${\tau }_1$ and a predator handling delay ${\tau }_2$—and (iii) nonlocal spatial dispersal modeled through fractional Laplacian operators ${(-\Delta )}^{\gamma /2}$. This triple integration enables the model to capture long-range temporal memory, delayed biological responses, and nonlocal spatial interactions simultaneously, offering insights into dynamics that are challenging to capture with classical integer-order or single-delay formulations. The fractional Laplacian generalizes classical diffusion by allowing long-range dispersal events (Lévy flights), where individuals can occasionally move over large distances with heavy-tailed step-size distributions—a phenomenon observed in many animal movement patterns but absent from standard diffusion models. We provide rigorous proofs of solution existence, uniqueness, non-negativity, and boundedness in both temporal and spatiotemporal settings. Local asymptotic stability conditions are derived for all feasible equilibrium states via characteristic equation analysis. The coexistence equilibrium undergoes a Hopf bifurcation when either delay crosses a critical threshold, with fractional order $\alpha$ modulating the bifurcation point and post-bifurcation oscillation frequency. A Lyapunov functional demonstrates global asymptotic stability of the infection-free equilibrium under biologically interpretable conditions. Turing instability analysis reveals conditions for spontaneous pattern formation, with the fractional exponent $\gamma$ controlling pattern wavelength and correlation length. Numerical simulations validate theoretical predictions, including spatial patterns, traveling waves, and chaos. To bridge theory with potential applications, we outline a statistical framework for parameter estimation and uncertainty quantification, suggesting that $\beta$, $\alpha$, and ${\tau }_1$ may be priority targets for parameter estimation. Full article

This paper presents a unified analytical and computational framework for the study of typhoid fever transmission dynamics governed by a Caputo fractional-order compartmental model of order $\kappa \in (0,1]$. The population is stratified into five epidemiological classes, namely susceptible $\left(\mathcal{S}\right)$, asymptomatic $\left(\mathcal{A}\right)$, symptomatic $\left(\mathcal{I}\right)$, hospitalised $\left(\mathcal{H}\right)$, and recovered $\left(\mathcal{R}\right)$, and the governing system explicitly incorporates asymptomatic transmission, treatment dynamics, and temporary immunity with waning. The use of the Caputo fractional derivative is motivated by the well-documented existence of chronic asymptomatic Salmonella Typhi carriers, whose heavy-tailed sojourn times in the carrier state are naturally encoded by the Mittag–Leffler waiting-time distribution arising from the fractional operator. A complete qualitative analysis of the fractional system is carried out: the basic reproduction number ${\mathcal{R}}_0$ is derived via the next-generation matrix method; local and global asymptotic stability of both the disease-free equilibrium ${\mathcal{E}}_0$ (when ${\mathcal{R}}_0\le 1$) and the endemic equilibrium ${\mathcal{E}}^{*}$ (when ${\mathcal{R}}_0>1$) are established using fractional Lyapunov theory and the LaSalle invariance principle; and the normalised sensitivity indices of ${\mathcal{R}}_0$ are computed to identify transmission-amplifying and transmission-suppressing parameters. Existence, uniqueness, and Ulam–Hyers stability of solutions are established via Banach and Leray–Schauder fixed-point arguments. To complement the analytical results, a fractional physics-informed neural network ($\mathcal{PINN}$) framework is developed to simultaneously reconstruct compartmental trajectories and identify unknown biological parameters from sparse synthetic observations. $\mathcal{PINN}$ embeds the L1-Caputo discretisation directly into the training residuals and employs a four-stage Adam–L-BFGS optimisation strategy to recover five trainable parameters $\mathbf{\Theta }$ = $\{\varphi ,\mu ,\sigma ,\psi ,\beta \}$ across three fractional orders $\kappa \in \{1.0,0.95,0.9\}$. The estimated parameters show strong agreement with the true values at the classical limit $\kappa =1.0$ ($\mathrm{MAPE}=2.27\%$), with the natural mortality rate $\mu$ recovered with $\mathrm{APE}\le 0.51\%$ and the transmission rate $\beta$ with $\mathrm{APE}\le 3.63\%$ across all fractional orders, confirming the structural identifiability of the model. Pairwise correlation analysis of the learned parameters establishes the absence of equifinality, validating that $\beta$ can be reliably included in the trainable set. Noise robustness experiments under Gaussian perturbations of $1\%$, $3\%$, and $5\%$ demonstrate graceful degradation ($\mathrm{MAPE}$: $0.82\%\to 3.10\%\to 7.31\%$), confirming the reliability of the proposed framework under realistic observational conditions. Full article

Minimizing the impacts of coupling, randomness, time variation and uncertain nonlinearity to enhance real-time performance is critical for controlling complex industrial systems. This paper proposes an optimized adaptive filtering method (LAF-MTNF) for time-varying uncertain nonlinear systems with multiple-input multiple-output (MIMO) measurement noise, which integrates the multi-dimensional Taylor network (MTN) with Lyapunov stability theory (LST). Leveraging MTN’s inherent advantages—simple structure, linear parameterization, and low computational complexity—LAF-MTNF achieves efficient real-time filtering while avoiding the exponential computation burden of neural networks. The contributions of this work are threefold: (1) A novel integration of LST and MTN is proposed for MIMO filtering, in which an energy space is constructed with a unique global minimum to eliminate local optimization traps, addressing the stability deficit of traditional MTN filters using LMS/RLS algorithms. (2) Convergence performance is systematically quantified by deriving explicit expressions for the error convergence rate (regulated by a positive constant) and convergence region (a sphere centered at the origin) while modifying adaptive gain to avoid singularity, filling the gap of incomplete performance analysis in existing Lyapunov-based filters. (3) The design is disturbance-independent, relying only on input/output measurements and requiring no prior knowledge of noise statistics, thus enhancing robustness to unknown industrial disturbances. We systematically analyze the Lyapunov stability of LAF-MTNF, and simulations on a complex MIMO system verify that it outperforms existing methods in filtering precision (mean error 0.0227 vs. 0.0674 of RBFNN) and dynamic response speed, while ensuring asymptotic stability and real-time applicability. The proposed LAF-MTNF method achieves significant advantages over traditional adaptive filtering methods in filtering accuracy, convergence speed and anti-cross-coupling capability. This method has broad application prospects in high-precision industrial servo motion control, power system state monitoring and other multi-variable nonlinear industrial scenarios with complex noise environments. Full article

Monkeypox (Mpox), caused by the monkeypox virus (MPXV), has re-emerged as a significant global public health concern, particularly following the 2022 outbreaks. Understanding its transmission dynamics is essential for designing effective control strategies. In this study, we develop and analyze a deterministic compartmental model that captures both human-to-human and rodent-to-human transmission pathways in order to better reflect the zoonotic nature of the disease. The model is investigated using qualitative and quantitative analytical techniques, including stability analysis, bifurcation theory, and sensitivity analysis. The basic reproduction number, $R_0$, is derived and used to determine threshold conditions for disease persistence or eradication. We show that the disease-free equilibrium is globally asymptotically stable when $R_0<1$, while an endemic equilibrium exists and is stable when $R_0>1$. Furthermore, the model exhibits backward bifurcation, indicating that reducing $R_0$ below unity may not be sufficient for disease elimination. Sensitivity analysis identifies key parameters driving transmission, particularly the rodent-to-human and human-to-human contact rates. Numerical simulations further demonstrate that reducing cross-species transmission and improving isolation of infected individuals significantly decrease disease burden. These findings highlight the complexity of Mpox transmission and emphasize that effective control requires not only lowering $R_0$, but also targeting critical transmission pathways. This study provides useful insights for public health planning by identifying priority intervention strategies such as minimizing rodent–human interactions and strengthening isolation measures. Full article

In recent years, fractional HIV models have received increasing attention. This study derives a fractional HIV model using the continuous-time random walk (CTRW) method, endowing the mathematical model with physical significance. Based on the transmission characteristics of HIV, the proposed model considers extrinsic infectivity, intrinsic infectivity, and drug control, specifically as follows: the extrinsic infectivity is a constant independent of the infection time; the intrinsic infectivity is a power-law function that depends on drug efficacy and infection time; the drug efficacy rate follows a Mittag–Leffler distribution with a long-term effect. Based on these considerations, a fractional HIV model with drug control is established in this paper. In addition, the global asymptotic stability of the equilibrium and the sensitivity analysis of the basic reproduction number $R_0$ are studied, and the theoretical results are verified by numerical simulations. The results show that reducing extrinsic infectivity, controlling intrinsic infectivity, and the drug efficacy rate are crucial in controlling the spread of HIV. Full article

This paper investigates the stability of nonlinear systems with truncated $\mathcal{V}$-fractional-order derivatives. Initially, based on the fundamental properties of $\mathcal{V}$-fractional calculus, the Bellman–Gronwall inequality for $\mathcal{V}$-fractional $\alpha$-differentiable functions is derived. Subsequently, several sufficient conditions for the stability of the considered systems are established via the Lyapunov direct method. For practical applications, multiple synchronization criteria for drive-response systems are further deduced by leveraging the aforementioned stability results. Finally, numerical examples are presented to verify the effectiveness and feasibility of the main theoretical findings. Full article

Underwater micro-bubble detection entails multiple challenges, including diminutive target sizes, sparse pixel information, pronounced specular highlights and water scattering, indistinct bubble boundaries, and adhesion or overlap between instances. To address these issues, we propose HSMD-YOLO, an improved detector tailored for high-resolution micro-bubble detection and built upon YOLOv11. The model incorporates three novel components: the Scale Switch Block (SSB), a scale-transformation module that suppresses artifacts and background noise, thereby stabilizing edges in thin-walled bubble regions and enhancing sensitivity to geometric contours; the Global Local Refine Block (GLRB), which achieves efficient global relationship modeling with an asymptotic linear complexity ($O\left(N\right)$) in spatial dimensions while further refining local features, thereby strengthening boundary perception and improving bubble–background separability; and the Bidirectional Exponential Moving Attention Fusion (BEMAF), which accommodates the multi-scale nature of bubbles by employing a parallel multi-kernel architecture to extract spatial features across scales, coupled with a multi-stage EMA based attention mechanism to enhance detection robustness under weak boundaries and complex backgrounds. Experiments conducted on an Side-Illuminated Light Field Bubble Database (SILB-DB) and a public gas–liquid two-phase flow dataset (GTFD) demonstrate that HSMD-YOLO achieves mAP@50 scores of 0.911 and 0.854, respectively, surpassing mainstream detection methods. Ablation studies indicate that SSB, GLRB, and BEMAF contribute performance gains of 1.3%, 2.0%, and 0.4%, respectively, thereby corroborating the effectiveness of each module for micro-scale object detection. Full article

This paper proposes an impulsive SIRQ model for the analysis of computer network resilience against malware propagation and distributed denial-of-service (DDoS) attacks. The model extends classical epidemic frameworks by combining the continuous-time dynamics of malicious object spreading with discrete control actions corresponding to mass updates, node isolation, and access control policies. A qualitative analysis of the resulting system of impulsive differential equations is performed. The basic reproduction number ${\mathcal{R}}_0$, identified as a threshold parameter characterizing the intensity of attack propagation, and sufficient conditions for the global asymptotic stability of the infection-free state are established. It is shown that, under periodic impulsive control, the infection-free state can be stabilized with respect to the target population coordinates even when ${\mathcal{R}}_0>1$. An exponential decay estimate for the total active threat is derived, guaranteeing the asymptotic extinction of the infected and quarantined node populations. The proposed approach provides quantitative criteria for the effectiveness of impulsive cyber defense strategies and offers a theoretical foundation for the design of adaptive multi-layer protection systems for critical information infrastructures. Practical interpretation of the results illustrates the dependence of the critical impulsive control period on the model parameters and demonstrates the applicability of the approach to cybersecurity strategy design. Full article

This paper investigates the consensus problem for a class of uncertain nonlinear multi-agent systems (MASs) subject to external disturbances with unknown control directions (UCDs). A novel control scheme integrating Nussbaum-type gain is proposed to actively compensate for UCDs, while fuzzy logic systems (FLSs) are embedded in a feed-forward compensator to approximate unknown nonlinear dynamics, thereby achieving global stability. The proposed distributed control laws ensure global asymptotic convergence for both first- and second-order MASs through Lyapunov stability analysis. By implementing a strategic reparameterization technique, this scheme systematically reduces computational complexity, requiring each agent to adapt only a minimal parameter set. Moreover, the framework is extended to address complex formation control tasks. Comprehensive simulations validate the efficacy of the theoretical findings. Full article

The primal-dual hybrid gradient (PDHG) method is widely used for convex–concave saddle-point problems, yet its extrapolated variants are typically asymmetric because only one side is extrapolated. We propose a symmetry-preserving refinement, E-PDHG, which performs dual-side extrapolation followed by an explicit correction step. Under standard step-size conditions, we establish global convergence for all $\eta \in (-1,1)$ and derive a pointwise (non-ergodic) $O(1/\sqrt{t})$ rate for the last iterate. The method does not improve the asymptotic complexity order of PDHG; instead, it enlarges the practically stable parameter region while retaining the same per-iteration cost. Numerical experiments on image deblurring/inpainting and additional machine learning benchmarks (logistic regression and LASSO) demonstrate improved finite-iteration stability and efficiency. Full article

In this study, we propose a compartmental mathematical model that considers two interacting populations (citrus plants and insect vectors) and investigate the transmission dynamics of Huanglongbing in citrus crops. This disease is caused by the bacterium Candidatus Liberibacter asiaticus and is vectored by the psyllid Diaphorina citri. The disease is modeled under the following three main assumptions: there is vital dynamics with constant recruitment rates of citrus plants, the force of infection in both populations is a spatially dependent function varying with geographic location, and there is a spatial displacement of the vectors. In the main results of the paper, we formulate a coupled ordinary and partial differential equation system with initial and zero flux boundary conditions, establish the existence and uniqueness of solutions to the proposed model by applying semigroup theory, and introduce a numerical approximation of the system. Moreover, we develop a stability and persistence analysis. From the analytical point of view, we calculate the basic reproduction number $R_0$ and prove three facts: the disease-free equilibrium is globally asymptotically stable when $R_0<1$; the disease-free equilibrium is globally asymptotically stable when $R_0>1$; and the hybrid system exhibits uniform persistence of infection when $R_0>1$. In addition, we present some numerical examples. Full article

High-precision trajectory tracking of robotic manipulators is fundamentally challenged by strong nonlinear dynamics, unmodeled uncertainties, and external disturbances. This paper proposes a Reciprocal Neural State–Disturbance Observer (RNSDO) featuring a neural activation mechanism for adaptive gain modulation and a reciprocally coupled state–disturbance estimation architecture. By reshaping the observer error dynamics through mutual feedback between state and disturbance estimation, the proposed structure alleviates the conflict between fast transient disturbance reconstruction and steady-state noise suppression, while requiring only position measurements. A decentralized position controller is designed based on RNSDO. The global asymptotic stability of the resulting closed-loop system is rigorously established via Lyapunov analysis. Extensive simulations on a PUMA 560 and experiments on a 7-DOF Franka FR3 robotic manipulator demonstrate highly consistent performance trends. The proposed method achieves improved state and disturbance estimation accuracy and enhanced robustness against unmodeled dynamics and payload variations compared with a linear Improved Extended State Observer (IESO), a classical Nonlinear Extended State Observer (NLESO), and a model-based Nonlinear Disturbance Observer-based Adaptive Robust Controller (NDO-ARC). Furthermore, the algorithm exhibits excellent real-time feasibility with a minimal computational footprint. Full article

This article deals with the global existence and uniqueness of solutions to a fractional-order SIQR epidemic model, alongside its intricate chaotic and complex dynamics as functions of the fractional order. The well-posedness of the model solutions, including global existence, uniqueness, and positivity, is established by constructing appropriate Lyapunov functions. The local and global stability analyses are conducted for both the disease-free and endemic equilibria of the model. An asymptotic solution of the system in the form of series is derived by the Laplace–Adomian decomposition method (L–ADM), and its convergence is rigorously proved. Subsequently, numerical analysis determines and interprets the optimal truncation order of this asymptotic solution. Numerical simulations are performed based on the asymptotic solution, and the dynamics and chaos of the dynamic system with respect to the fractional order are analyzed and illustrated in terms of the maximum Lyapunov exponent and structural complexity. Finally, a local sensitivity analysis is conducted for each state variable with respect to the model parameters. Full article