A novel SIR-based computer virus propagation model with Beddington-DeAngelis functional response: Stability analysis and practical implications

Understanding the dynamics of the propagation of computer viruses is crucial for the development of effective cybersecurity strategies. This paper proposes a novel compartmental model based on the traditional SIR framework, which incorporats the Beddington-DeAngelis functional response to capture the inhibitory effects of the modern operating systems' built-in security mechanisms. We rigorously establish the well-posedness of the model by proving the non-negativity and boundedness of solutions. The existence and stability of equilibrium points are thoroughly analyzed using the Hurwitz criterion, Lyapunov functions, and Dulac criterion. Numerical simulations validate our theoretical findings and demonstrate the significant role of the system self-protection parameters in controlling virus spread. Unlike previous models, our approach provides explicit connections between the model parameters and real-world cybersecurity metrics, thus offering practical insights for network defense strategies. The model's ability to maintain a persistent infected state aligns with the observed behaviors of modern malware, thus providing a more realistic representation of the dynamics of computer viruses. The study employs advanced visualization techniques, including three-dimensional surface plots to elucidate the complex interactions between protection parameters, thus providing actionable insights for the design and implementation of cybersecurity policies.