The purpose of this paper is to propose a fractal–fractional-order for computer virus propagation dynamics, in accordance with the Atangana–Baleanu operator. We examine the existence of solutions, as well as the Hyers–Ulam stability, uniqueness, non-negativity, positivity, and boundedness based on the fractal–fractional sense. Hyers–Ulam stability is significant because it ensures that small deviations in the initial conditions of the system do not lead to large deviations in the solution. This implies that the proposed model is robust and reliable for predicting the behavior of virus propagation. By establishing this type of stability, we can confidently apply the model to real-world scenarios where exact initial conditions are often difficult to determine. Based on the equivalent integral of the model, a qualitative analysis is conducted by means of an iterative convergence sequence using fixed-point analysis. We then apply a numerical scheme to a case study that will allow the fractal–fractional model to be numerically described. Both analytical and simulation results appear to be in agreement. The numerical scheme not only validates the theoretical findings, but also provides a practical framework for predicting virus spread in digital networks. This approach enables researchers to assess the impact of different parameters on virus dynamics, offering insights into effective control strategies. Consequently, the model can be adapted to real-world scenarios, helping improve cybersecurity measures and mitigate the risks associated with computer virus outbreaks.

This study introduces a novel mathematical model to explore zoonotic disease transmission between humans and baboons. By utilizing fractal-fractional derivatives with a power-law kernel, the model captures time-dependent dynamics that traditional approaches cannot. A Hyers–Ulam stability analysis is used to assess the robustness of the model under small perturbations, demonstrating the existence and uniqueness of the solution. Control strategies such as sterilization, food restrictions, and human interaction are evaluated numerically. Key findings reveal the significant influence of fractal-fractional parameters on disease progression and control measures. Simulations demonstrate the model’s ability to represent real-world dynamics, providing valuable insights into effective interventions, including sterilization, food restrictions, and reduced human–baboon interactions. This framework offers a comprehensive tool for understanding and mitigating zoonotic disease risks.

Zoonotic diseases, which are transmitted between animals and humans, pose significant public health challenges, especially in regions with high human-wildlife interactions. This study presents a novel fractional-order mathematical model to analyze the transmission dynamics of zoonotic diseases between baboons and humans in the Al-Baha region. The model incorporates the Atangana-Baleanu fractional derivative to account for memory effects and spatial heterogeneity, offering a more realistic representation of disease spread. The fractional Euler method is employed for numerical simulations, enabling accurate predictions of infection trends under various fractional orders. Stability analysis, conducted via the Banach fixed-point theorem and Picard iterative method, confirms the model’s robustness, while Hyers-Ulam stability ensures its reliability. Additionally, control strategies, including sterilization, food access restriction, and human interaction reduction, are integrated into the model to assess their effectiveness in disease mitigation. Simulation results highlight the impact of fractional-rder dynamics on disease persistence, showing that lower fractional orders correspond to prolonged infections due to memory effects. These findings underscore the significance of fractional calculus in epidemiological modeling and provide valuable insights for designing effective zoonotic disease control strategies.

This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo (ABC) sense. Unlike traditional epide... | Find, read and cite all the research you need on Tech Science Press

This study presents a comprehensive analysis of zoonotic disease transmission dynamics between baboon and human populations using both deterministic and stochastic modeling approaches. The model is constructed with a symmetric compartmental structure for each species—susceptible, infected, and recovered—which reflects a biological and mathematical symmetry between the two interacting populations. Public health control strategies such as sterilization, restricted food access, and reduced human–baboon interaction are incorporated symmetrically, allowing for a balanced evaluation of their effectiveness across species. The basic reproduction number (${\mathcal{R}}_0$) is derived analytically and examined through sensitivity indices to identify critical epidemiological parameters. Numerical simulations, implemented via the Euler–Maruyama method, explore the influence of stochastic perturbations on disease trajectories. Statistical tools including Maximum Likelihood Estimation (MLE), Mean Squared Error (MSE), and Power Spectral Density (PSD) analysis validate model predictions and assess variability across noise levels. The results provide probabilistic confidence intervals and highlight the robustness of the proposed control strategies. This symmetry-aware, dual-framework modeling approach offers novel insights into zoonotic disease management, particularly in ecologically dynamic regions with frequent human–wildlife interactions.

Human–wildlife conflicts arise from increasing human populations and the growing demand for land for agriculture and urban development. In Saudi Arabia, these dynamics have increased the impact of baboons on human communities, as expanding settlements encroach upon the natural habitats of baboons, while rising baboon populations increasingly invade urban areas in search of food, shelter, and water. We aimed to assess the effects of human–baboon coexistence on residents in the Al-Baha region, Saudi Arabia. From October 2021 to April 2022, we administered a 43-item semi-structured online questionnaire addressing emotional, social, environmental and financial impacts of nearby baboons. A total of 318 residents of the Al-Baha region completed the survey and shared their experiences regarding interactions with hamadryas baboons (Papio hamadryas) near human properties. In addition, three semi-structured life interviews with residents aged over 70 explored historical perceptions. Respondents attributed increased baboon presence to urban expansion, accessible waste, and intentional feeding and strongly supported government-led mitigation plans. Human–baboon interactions in Al Baha produce emotional stress, social disruption, and economic burdens for residents. Findings support integrated management combining public education, improved waste management, non-lethal deterrents, and carefully planned population control measures, developed with community consultation. Limitations of the study include convenience online sampling and reliance on self-reported impacts; future work should quantify baboon abundance and objectively measure economic losses.