We develop and analyze an SIRSD epidemic model, which extends the classical SIR framework by incorporating waning immunity and disease-induced mortality. A rigorous well-posedness analysis ensures the existence, uniqueness, positivity, and boundedness of solutions, guaranteeing the model's epidemiological feasibility. To facilitate theoretical investigations and data-driven modeling, we reformulated the system in normalized variables. To capture and predict complex nonlinear epidemic dynamics, we use the Koopman operator framework with extended dynamic mode decomposition (EDMD) and an epidemiologically informed dictionary of observables. We compare two Koopman approximations: one based on a minimal epidemiological dictionary and another enriched with nonlinear and cross terms. We generate synthetic data using a nonstandard finite difference (NSFD) scheme for four representative epidemics: SARS-CoV-2, seasonal influenza, Ebola, and measles. Numerical experiments demonstrate that the Koopman-based approach effectively identifies dominant epidemic modes and accurately predicts key outbreak characteristics, including peak infection dynamics.

This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2) learning key parts of those models directly from data; (3) methods that can generate realistic synthetic data in continuous time; and (4) numerical techniques that keep simulations stable, accurate, and faithful over long runs. The objective is practical: help researchers quickly see what is new, how the pieces fit together, and where important gaps remain. We summarize tools for estimating changing infection or reaction rates under noisy and incomplete observations, modeling spatial spread, accounting for sudden jumps and heavy tails, and reporting uncertainty in a way that is useful for decisions. We also highlight open problems that deserve near-term attention: separating true dynamics from noise when data are irregular; learning spatial dynamics under random influences with guarantees of stability; aligning training with the numerical method used in applications; preserving positivity and conservation in all simulations; reducing cost while controlling error for large studies; estimating rare but important events; and adopting clear, comparable reporting standards. By organizing the field around these aims, the review offers a concise guide to current methods, their practical use, and the most promising directions for future work in biology and epidemiology.s.

The purpose of this paper is to establish the well-posedness of martingale (probabilistic weak) solutions to stochastic degenerate aggregation--diffusion equations arising in biological and public health contexts. The studied equation is of a stochastic degenerate parabolic type, featuring a nonlinear two-sidedly degenerate diffusion term accounting for repulsion, a locally Lipschitz reaction term representing competitive interactions, and a stochastic perturbation term capturing environmental noise and uncertainty in biological systems. The existence of martingale solutions is proved via an auxiliary nondegenerate stochastic system combined with the Faedo--Galerkin method. Convergence of approximate solutions is established through Prokhorov's compactness and Skorokhod's representation theorems, and uniqueness is obtained using a duality approach. Finally, numerical simulations are given to illustrate the impact of environmental noise on aggregation dynamics and the long-term behavior of the system, offering insights that may inspire medical innovation and predictive modeling in public health.

In the 21st century, the industry of drones, also known as Unmanned Aerial Vehicles (UAVs), has witnessed a rapid increase with its large number of airspace users. The tremendous benefits of this technology in civilian applications such as hostage rescue and parcel delivery will integrate smart cities in the future. Nowadays, the affordability of commercial drones expands its usage at a large scale. However, the development of drone technology is associated with vulnerabilities and threats due to the lack of efficient security implementations. Moreover, the complexity of UAVs in software and hardware triggers potential security and privacy issues. Thus, posing significant challenges for the industry, academia, and governments. In this paper, we extensively survey the security and privacy issues of UAVs by providing a systematic classification at four levels: Hardware-level, Software-level, Communication-level, and Sensor-level. In particular, for each level, we thoroughly investigate (1) common vulnerabilities affecting UAVs for potential attacks from malicious actors, (2) existing threats that are jeopardizing the civilian application of UAVs, (3) active and passive attacks performed by the adversaries to compromise the security and privacy of UAVs, (4) possible countermeasures and mitigation techniques to protect UAVs from such malicious activities. In addition, we summarize the takeaways that highlight lessons learned about UAVs' security and privacy issues. Finally, we conclude our survey by presenting the critical pitfalls and suggesting promising future research directions for security and privacy of UAVs.

We develop a physics-informed neural network (PINN) framework for parameter estimation in fractional-order SEIRD epidemic models. By embedding the Caputo fractional derivative into the network residuals via the L1 discretization scheme, our method simultaneously reconstructs epidemic trajectories and infers both epidemiological parameters and the fractional memory order $\alpha$. The fractional formulation extends classical integer-order models by capturing long-range memory effects in disease progression, incubation, and recovery. Our framework learns the fractional memory order $\alpha$ as a trainable parameter while simultaneously estimating the epidemiological rates $(\beta, \sigma, \gamma, \mu)$. A composite loss combining data misfit, physics residuals, and initial conditions, with constraints on positivity and population conservation, ensures both accuracy and biological consistency. Tests on synthetic Mpox data confirm reliable recovery of $\alpha$ and parameters under noise, while applications to COVID-19 show that optimal $\alpha \in (0, 1]$ captures memory effects and improves predictive performance over the classical SEIRD model. This work establishes PINNs as a robust tool for learning memory effects in epidemic dynamics, with implications for forecasting, control strategies, and the analysis of non-Markovian epidemic processes.

We classify, up to automorphism, left invariant Riemannian metrics on 4-dimensional simply connected nonunimodular Lie groups. This is equivalent to classifying, up to automorphism, inner products on 4-dimensional nonunimodular Lie algebras.

We describe the full group of isometries of each left invariant Riemannian metric on the simply connected unimodular nilpotent or solvable $(R)$-type Lie groups of dimension four.

Recent advances have extended the Dunkl transform to the setting of Clifford algebras. In particular, the two-sided quaternionic Dunkl transform has been introduced as a Dunkl analogue of the two-dimensional quaternionic Fourier transform. In this paper, we develop the two-sided Clifford Dunkl transform, defined using two square roots of -1 in Cl_{p,q}. We establish its fundamental properties, including the inversion and Plancherel formulas, and provide two explicit expressions for the associated translation operator. Moreover, we prove an analogue of Miyachi's theorem for this transform, thereby extending a classical result in harmonic analysis to the Clifford-Dunkl framework.

This report investigates the main definitions and fundamental properties of the fractional two-sided quaternionic Dunkl transform in two dimensions. We present key results concerning its structure and emphasize its connections to classical harmonic analysis. Special attention is given to inversion, boundedness, spectral behavior, and explicit formulas for structured functions such as radial or harmonic functions. Within this framework, we establish a generalized form of the classical Heisenberg-type uncertainty principle. Building on this foundation, we further extend the result by proving a higher-order Heisenberg-type inequality valid for arbitrary moments $p \geq 1$, with sharp constants characterized through generalized Hermite functions. Finally, by analyzing the interplay between the two-sided fractional quaternionic Dunkl transform and the two-sided fractional quaternionic Fourier transform, we derive a corresponding uncertainty principle for the latter.

In 1990 Kantor introduced the conservative algebra $\mathcal{W}(n)$ of all algebras (i.e. bilinear maps) on the $n$-dimensional vector space. In case $n >1$the algebra$\mathcal{W}(n)$ does not belong to well known classes of algebras (such as associative, Lie, Jordan, Leibniz algebras). We describe $\frac{1}{2}$derivations, local (resp. $2$-local) $\frac{1}{2}$-derivations and biderivations of $\mathcal{W}(2)$. We also study similar problems for the algebra $\mathcal{W}_2$ of all commutative algebras on the two-dimensional vector space and the algebra $\mathcal{S}_2$ of all commutative algebras with trace zero multiplication on the two-dimensional space.

The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with delayed and non-delayed dampings. The class in question consists of two strongly coupled wave equations featuring a delayed and non-delayed damping terms on the first wave equation. Through a standard change of variables and semi-group theory, we address the well-posedness of the considered coupled system. Thereon, based on some observability inequalities, we derive sufficient conditions guaranteeing the exponential decay of a suitable energy. On the other hand, from the numerical point of view, we validate the theoretical results in $1D$ domains based on a suitable numerical approximation obtained through the Finite Difference Method. More precisely, we construct a discrete numerical scheme which preserves the energy decay property of its continuous counterpart. Our theoretical analysis and implementation of our developed numerical scheme assert the effect of the time-delayed damping on the exponential stability of strongly coupled wave equations.

Convolutional Neural Networks (CNNs) models are one of the most frequently used deep learning networks, and extensively used in both academia and industry. Recent studies demonstrated that adversarial attacks against such models can maintain their effectiveness even when used on models other than the one targeted by the attacker. This major property is known as transferability, and makes CNNs ill-suited for security applications. In this paper, we provide the first comprehensive study which assesses the robustness of CNN-based models for computer networks against adversarial transferability. Furthermore, we investigate whether the transferability property issue holds in computer networks applications. In our experiments, we first consider five different attacks: the Iterative Fast Gradient Method (I-FGSM), the Jacobian-based Saliency Map (JSMA), the Limited-memory Broyden Fletcher Goldfarb Shanno BFGS (L- BFGS), the Projected Gradient Descent (PGD), and the DeepFool attack. Then, we perform these attacks against three well- known datasets: the Network-based Detection of IoT (N-BaIoT) dataset, the Domain Generating Algorithms (DGA) dataset, and the RIPE Atlas dataset. Our experimental results show clearly that the transferability happens in specific use cases for the I- FGSM, the JSMA, and the LBFGS attack. In such scenarios, the attack success rate on the target network range from 63.00% to 100%. Finally, we suggest two shielding strategies to hinder the attack transferability, by considering the Most Powerful Attacks (MPAs), and the mismatch LSTM architecture.

Sink mobility is seen as a successful strategy to resolve the hotspot problem in Wireless Sensor Network (WSN). Mobile sinks roam in the network and collect data from special nodes such as Cluster Heads (CH) by means of short-range communications which improves the energy efficiency. Numerous mobile sink based routing protocols have been proposed, however, they incur high delays especially in large scale networks where the mobile sink has to travel for a long distance to collect data from CHs and consequently they failed to ensure a tradeoff between energy efficiency and delay. To resolve this issue, we propose in this paper an Effective Hybrid Routing Protocol termed as EHRP. The main aim of this protocol is to combine between single-hop and multi-hop routing. Indeed, when the mobile sink arrives at a cluster it collects its data while the other distant CHs continue to send their data using our proposed improved Ant Colony Optimization (ACO) algorithm to avoid the waiting-time. The existing ACO algorithms use in the distance heuristic which is not practical in real world and fail to consider relevant statistic information of energy (e.g., minimum energy, average energy) in path selection which leads to unbalanced energy consumption in the network. To address these issues, the proposed routing algorithm employs the Received Signal Strength Indicator (RSSI) and statistic information of energy to consume energy efficiently and decrease the probability of sending failure. The performance of the proposed routing protocol is tested and compared with those of the relevant routing protocols. The simulation results show that, in comparison with its counterparts, EHRP succeeds to minimize energy consumption and delay as well as enhancing the packet delivery ratio.

The main aim of this study is to analyze a fractional parabolic SIR epidemic model of a reaction-diffusion, by using the nonlocal Caputo fractional time-fractional derivative and employing the $p$-Laplacian operator. The immunity is imposed through the vaccination program, which is regarded as a control variable. Finding the optimal control pair that reduces the number of sick people, the associated vaccination, and treatment expenses across a constrained time and space is our main study. The existence and uniqueness of the nonnegative solution for the spatiotemporal SIR model are established. It is also demonstrated that an optimal control exists. In addition, we obtain a description of the optimal control in terms of state and adjoint functions. Then, the optimality system is resolved by a discrete iterative scheme that converges after an appropriate test, similar to the forward-backward sweep method. Finally, numerical approximations are given to show the effectiveness of the proposed control program, which provides meaningful results using different values of the fractional order and $p$, respectively the order of the Caputo derivative and the $p$-Laplacian operators.

Recent advancements in drone technology have shown that commercial off-the-shelf Micro Aerial Drones are more effective than large-sized drones for performing flight missions in narrow environments, such as swarming, indoor navigation, and inspection of hazardous locations. Due to their deployments in many civilian and military applications, safe and reliable communication of these drones throughout the mission is critical. The Crazyflie ecosystem is one of the most popular Micro Aerial Drones and has the potential to be deployed worldwide. In this paper, we empirically investigate two interference attacks against the Crazy Real Time Protocol (CRTP) implemented within the Crazyflie drones. In particular, we explore the feasibility of experimenting two attack vectors that can disrupt an ongoing flight mission: the jamming attack, and the hijacking attack. Our experimental results demonstrate the effectiveness of such attacks in both autonomous and non-autonomous flight modes on a Crazyflie 2.1 drone. Finally, we suggest potential shielding strategies that guarantee a safe and secure flight mission. To the best of our knowledge, this is the first work investigating jamming and hijacking attacks against Micro Aerial Drones, both in autonomous and non-autonomous modes.

In this chapter, we consider a reaction-diffusion SVIR infection model with dis-tributed delay and nonlinear incidence rate. The wellposedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less or equal than one, and that the disease endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than one. Numerical simulations are provided to illustrate the obtained theoretical results.

This article conducts an in-depth investigation of a new spatio-temporal model for the cocaine-heroin epidemiological model with vital dynamics, incorporating the Laplacian operator. The study rigorously establishes the existence, uniqueness, non-negativity, and boundedness of solutions for the proposed model. In addition, the local stability of both a drug-free equilibrium and a drug-addiction equilibrium are analyzed by studying the corresponding characteristic equations. The research provides conclusive evidence that when the basic reproductive number $\mathcal{R}_0$ exceeds 1, the drug-addiction equilibrium is globally asymptotically stable. Conversely, using comparative arguments, it is shown that if $\mathcal{R}_0$ is less than 1, the drug-free equilibrium is globally asymptotically stable. Furthermore, the article includes a series of numerical simulations to visually convey and support the analytical results.

For each left-invariant Riemannian metric on simply connected nonunimodular Lie groups of dimension four, we determine the full group of isometries.

The main aim of this study is to analyze a fractional parabolic SIR epidemic model of a reaction-diffusion, by using the nonlocal Caputo fractional time-fractional derivative and employing the $p$-Laplacian operator. The immunity is imposed through the vaccination program, which is regarded as a control variable. Finding the optimal control pair that reduces the number of sick people, the associated vaccination, and treatment expenses across a constrained time and space is our main study. The existence and uniqueness of the nonnegative solution for the spatiotemporal SIR model are established. It is also demonstrated that an optimal control exists. In addition, we obtain a description of the optimal control in terms of state and adjoint functions. Then, the optimality system is resolved by a discrete iterative scheme that converges after an appropriate test, similar to the forward-backward sweep method. Finally, numerical approximations are given to show the effectiveness of the proposed control program, which provides meaningful results using different values of the fractional order and $p$, respectively the order of the Caputo derivative and the $p$-Laplacian operators.

Given a finite-dimensional complex simple $\omega$-Lie algebras $\mathfrak{}$ over $\mathbb{C}$. We prove that every local ,$2-$local derivation is a derivation and every local (resp. 2-local) automorphisms are automorphisms or an anti-automorphis (resp. automorphism). We characterize also biderivation, $\frac{1}{2}$-derivation and local (2-local) $\frac{1}{2}$-derivation of $\mathfrak{g}$.