The application of mathematical modeling plays a crucial role in understanding and managing marine species and their exploitation. This study explores the integration of bioeconomic modeling and artificial intelligence to optimize fishery management while promoting ecosystem sustainability. Following our previous research, “Bioeconomic Modelling for the Sustainable Exploitation of Three Key Marine Species in Morocco,” the present work builds upon that foundation by extending the existing model and integrating additional biological and economic parameters to enhance its realism and predictive capacity. We first provide a general overview of bioeconomic models, highlighting previous research and the dual objectives of profit maximization and ecological preservation. We then introduce a mathematical model representing the exploitation of a single species within a three-species marine ecosystem. A detailed mathematical analysis is conducted to identify equilibrium points that ensure the persistence of all species, along with their positivity, boundedness, and stability. Building on this foundation, we apply Reinforcement Learning (RL) to the model, demonstrating how AI techniques can guide adaptive harvesting strategies. Finally, we perform a sensitivity analysis on key parameters influencing the RL implementation,
providing insights into the robustness and effectiveness of the approach. Our findings highlight the promising potential of combining bioeconomic theory, mathematical modeling, and AI-driven optimization methods to achieve sustainable marine resource management, and encourage future interdisciplinary research at the intersection of mathematics, ecology, and artificial intelligence.

This paper focuses on the numerical resolution of Maxwell’s equations applied to atmospheric electromagnetic phenomena, particularly lightning discharges. Lightning generates intense transient electromagnetic fields that interact with the ground and nearby structures, posing challenges for accurate modeling and protection design. To analyze these interactions, the two-dimensional Finite-Difference Time-Domain (2D-FDTD) method is employed to solve Maxwell’s equations in the time domain with high spatial and temporal resolution.

This study considers a realistic configuration involving a 168 m tall object interconnected with the lightning channel and a clayey soil characterized by moderate electrical conductivity (σ = 0.0025 S/m) and high permittivity. The simulation framework enables the investigation of the spatiotemporal evolution of the electric and magnetic fields both above and below the ground, capturing the complex coupling between the lightning channel, the tall structure, and the soil.

Results demonstrate that the soil’s electrical properties significantly affect the electromagnetic field amplitudes and waveform shapes, particularly below ground in the near-field region. Variations in conductivity and permittivity alter the current distribution and the attenuation of electromagnetic waves. This work highlights the importance of accurate numerical modeling of soil characteristics in the computational analysis of atmospheric electromagnetic phenomena and contributes to improving the reliability of lightning protection and grounding system design.

Wild boars are among the most widely distributed ungulate species worldwide and play a significant role in maintaining ecological balance within forest ecosystems. Nevertheless, uncontrolled population growth leads to severe agricultural damage and increased traffic accidents, making population regulation necessary. At the same time, wild boars represent an important economic resource and, in some regions, a protected species, requiring management strategies that balance control and conservation.

In this work, we present a mathematical model describing the dynamics of wild boar populations at forest boundaries, with particular emphasis on spillover phenomena into surrounding human-dominated areas. Rather than modeling the entire population, we focus on individuals living near the forest edge, as these are primarily responsible for spillover events. The model incorporates ranger intervention as a control mechanism activated when spillovers occur, representing hunting or containment actions aimed at regulating population size without driving the species toward extinction.

The qualitative analysis of the model reveals the existence of biologically feasible equilibrium points, including a coexistence equilibrium and a ranger-free equilibrium. Using bifurcation theory, we demonstrate the presence of a transcritical bifurcation that governs the stability exchange between these equilibria. Furthermore, under certain parameter conditions, the system undergoes a Hopf bifurcation, leading to the emergence of stable periodic solutions. These oscillations correspond to recurrent spillover events that necessitate periodic deployment of rangers, resulting in increased management costs.

Numerical simulations are provided to support the analytical results and to illustrate the long-term behavior of the system under different management strategies. In particular, the proposed model provides useful insights into sustainable wild boar management and highlights the effectiveness of resource-based control strategies in stabilizing population dynamics.

The mathematical modeling of infectious diseases is essential for understanding transmission mechanisms and the long-term persistence of pathogens. This paper investigates the qualitative dynamics of an SIRS epidemic model, particularly relevant for diseases where immunity is temporary. The study provides a rigorous mathematical framework to describe how the interplay between infection rates and the loss of immunity affects the system's behavior, moving from local stability to a global perspective.

The study employs the qualitative theory of planar differential equations to explore the system’s state space. A central component is the application of the Poincaré compactification technique, which extends the polynomial vector field from the finite plane to the Poincaré disc. This enables the analysis of the system’s behavior at infinity. We characterize all singular points by analyzing Jacobian matrices for finite equilibria and utilizing specialized transformations for infinite singularities at the disc's boundary.

The analysis provides a comprehensive characterization of the system’s equilibria, including disease-free and endemic states, and singularities at the horizon of the Poincaré disc. A significant finding is the identification of a Hopf bifurcation occurring at critical biological thresholds. This bifurcation is responsible for the emergence of limit cycles. Global phase portraits are constructed to visualize trajectories and detail the topological structure of the flow under various parameter regimes.

The investigation reveals that the SIRS model possesses complex dynamical features. The occurrence of limit cycles indicates that the disease can exhibit periodic oscillations, with significant implications for predicting recurring outbreaks. By integrating global analysis at infinity, this research provides a complete topological description of the model, offering valuable insights into nonlinear disease dynamics and public health strategies.

This study presents a comprehensive mathematical model designed to investigate the dynamics of infectious disease spread by integrating two critical
intervention strategies: vaccination and individual awareness. The population is structured into distinct compartments: susceptible, infected, vaccinated, fully aware, and partially aware individuals. In this framework, vaccination serves to reduce the direct risk of infection, while awareness campaigns influence social behavior, thereby slowing down the overall transmission rate. Furthermore, the model accounts for the loss of immunity over time, allowing vaccinated individuals to return to the susceptible class eventually. To capture the spatial dimension of an outbreak, the model is formulated as a system of nonlinear partial differential equations (PDEs) with reaction–diffusion terms. Methodologically, the positivity and global existence of solutions are rigorously established to ensure the model’s mathematical and biological consistency. We derive the equilibrium
points, including the disease-free and endemic states, and calculate the basic reproduction number using the next-generation matrix method. Local stability analysis is conducted to evaluate the system’s long-term behavior near these equilibria.

Numerical simulations are performed to illustrate the theoretical findings and quantify the impact of spatial diffusion on disease persistence.
The results demonstrate that while awareness significantly mitigates the peak of an epidemic, it is not sufficient to eradicate the disease on its own. In contrast, effective and sustained vaccination programs are shown to be the primary driver in reducing infection levels. This work emphasizes the necessity of combining behavioral interventions with clinical strategies to understand and manage real-world epidemic dynamics in spatial environments.

Introduction: This paper establishes a novel averaging principle for stochastic slow-fast systems where the driving noise is subject to Knightian volatility uncertainty, modeled by a d-dimensional G-Brownian motion B(t). Classical averaging theory fails under volatility ambiguity, and we provide a framework to average the fast dynamics in the worst-case sense.

Methode: We introduce a concept of G-invariant measure, which generalizes the classical invariant measure to the sublinear expectation space. This measure encapsulates a set of possible invariant laws for each admissible volatility scenario. Using this, we define the averaged coefficients for the slow component in a worst-case sense. Under appropriate assumptions, we employ Khasminskii's time-discretization technique and tools from G-stochastic calculus to prove the convergence.

Results: Our main result demonstrates that as the timescale separation parameter tends to zero, the slow component of the original multiscale system converges to the solution of a simplified, averaged equation. The convergence is established in two strong senses: in capacity (quasi-surely) and in the L2-norm under the G-expectation.

Conclusions: This work extends the classical stochastic averaging principle to environments with distributional ambiguity. The results offer a robust mathematical tool for simplifying complex multiscale systems—such as those in financial risk, climate economics, or epidemic modeling—where fast variables are subject to uncertain volatility.

In this study, we investigate the cosmological implications of symmetric teleparallel gravity models based on the function f(Q, Lm), where Q is the non-metricity scalar and Lm is the matter Lagrangian. The function f(Q, Lm) allows a natural way of including non-minimal matter-geometry couplings in a second-order formulation. The more minimal and physically motivated polynomial form is analyzed as a possibility to encompass both the early and late-time acceleration of the universe in a single scenario.

In the late universe, we consider the modified Friedmann equations within a spatially flat FLRW background. The model is compared to observational data within the context of a Bayesian analysis. The datasets considered are type Ia supernovae, cosmic chronometers, and BAO observations. The analysis shows that the parameter representing the coupling of matter to geometry is only weakly constrained by the existing observational data, suggesting a near degeneracy to the standard model expansion history.

At high curvature applicable to the early universe, the theory reduces to a quadratic model of non-metricity without extra scalar fields and produces Starobinsky inflation. The predictions for the spectral index (ηs) and tensor-scalar ratio (r) are in accordance with the 2018 Planck constraints.

To extend our study further into the quantum gravity reime, we add corrections due to RGUP in the form of deformation of the metric in a momentum-dependent fashion, which in turn affects matter propagation on top of this same gravitational background, making a non-negligible contribution to the running of some of the inflationary parameters, in particular the spectral index, thus resolving the degeneracy with the classical attractor solution.

In summary, our work demonstrates that the f(Q, Lm) gravity is a well-established set of geometry that is able to account for late-time acceleration, inflation, and quantum geometry in one consistent scheme.

In this work, we present a comprehensive reconstruction of modified Gauss--Bonnet gravity within the framework of Tsallis nonextensive entropy and holographic dark energy. By employing the Tsallis entropy formalism, a particular case of the most generalized Nojiri--Odintsov entropy formalism, the holographic energy density acquires a generalized nonextensive form, which is then embedded into f(G) gravity to generate a purely geometric description of dark energy. The reconstruction procedure is implemented for three different scale factor choices, namely, hybrid, linearly truncated hybrid, and quadratically truncated hybrid, using the Granda--Oliveros infrared cutoff. The resulting f(G) functions are found to exhibit monotonic growth, indicating negligible deviation from General Relativity in the early universe and significant contributions at late times, thereby supporting accelerated expansion. The reconstructed equation-of-state parameter remains negative throughout the evolution, with possible transitions between phantom and quintessence regimes depending on the model parameters. Further, the adiabatic index exhibits a positive and monotonic evolution, thereby confirming the dynamical stability and thermodynamic consistency of the reconstructed f(G) model. Finally, a detailed thermodynamic investigation confirms that the total entropy variation stays positive, ensuring the validity of the Generalized Second Law of Thermodynamics. Overall, the results establish that the Tsallis holographic dark energy model in f(G) gravity yields a thermodynamically consistent and dynamically viable framework for explaining late-time cosmic acceleration.

The investigation of dark energy models outside of general relativity and mainstream cosmology has been driven by observational evidence of the universe's accelerating expansion. In this work, we create a new Barrow–Ricci–Gauss–Bonnet holographic dark energy (BRGB–HDE) model in the context of symmetric teleparallel gravity, in which the non-metricity scalar Q is used to characterize gravity via f(Q). The suggested scenario easily unifies holographic dark energy corrections resulting from curvature invariants with the geometric consequences of non-metricity by integrating Barrow's entropy deformation parameter Δ . This results in a more comprehensive description of cosmic acceleration. We study the model's cosmic dynamics by examining various forms of interaction between dark energy and dark matter, which allows for energy exchange within the dark sector. To assess the model's physical viability and stability, the evolution of important cosmological parameters such as the equation of state and the squared speed of sound is examined. We recreate the f(Q) function that aligns with the hypothesized holographic dark energy density and interaction method. Furthermore, the generalized second law of thermodynamics (GSLT) is investigated using the Barrow entropy formalism, with the apparent horizon of the Universe taken into account. Our findings show that the GSLT is still valid for a wide and physically tolerable range of model parameters. Notably, the model demonstrates smooth transitions between the quintessence and phantom regimes, demonstrating its ability to simulate various stages of cosmic evolution. The suggested BRGB-HDE model in f(Q) gravity offers a consistent and thermodynamically plausible framework for understanding late-time cosmic acceleration.

In this paper, we propose a new method to solve multi proportional delay differential equations. The Haar wavelet collocation method (HWCM) is introduced and applied to proportional delay differential equations involving two or more delay terms. The proportional delay differential equations find applications in population dynamic model where the present system may depend on the gestation period and the maturation period simultaneously. In epidemiological model, the incubation and the immunity period coexist. Individually, the effect of each delay occurs at different pace. However, their combined effect may lead to instability which may be difficult to capture with a single delay. Thus, it has become important to study DDEs with multiple delays.

To show reliability and robustness of the method few numerical examples are presented. Further, numerical solutions obtained by HWCM are compared with the existing exact solutions. The comparison is done by calculating the maximum absolute error and the relative error. Further, to verify the accuracy of the results obtained, rate of convergence is calculated to be approximately 2. It is observed that with the increase in the resolution level, the error decreases and hence the accuracy increases. The findings suggest that HWCM can be extended to neutral time dependent DDE with multiple delays.