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

Honglei Lu; Erxi Zhu; Honglei Lu; Erxi Zhu

doi:10.3934/math.20251205

AIMS Mathematics

2025, Volume 10, Issue 11: 27412-27439. doi: 10.3934/math.20251205

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Theory article

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

Honglei Lu ¹,
Erxi Zhu ^{2
,
,}

1.
College of Internet of Things Engineering, Jiangsu Vocational College of Information Technology, No.1 qianou Road, Huishan District, Wuxi 214153, Jiangsu, China
2.
College of Information Engineering, Changzhou Vocational Institute of Industrial Technology, No. 28, Mingxin Middle Road, Wujin District, Changzhou 213164, Jiangsu, China

Received: 11 September 2025 Revised: 23 October 2025 Accepted: 11 November 2025 Published: 25 November 2025
MSC : 68M12, 93A30

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.
- computer virus propagation,
- SIR model,
- Beddington-DeAngelis functional response,
- global stability,
- Lyapunov function,
- cybersecurity
Citation: Honglei Lu, Erxi Zhu. A novel SIR-based computer virus propagation model with Beddington-DeAngelis functional response: Stability analysis and practical implications[J]. AIMS Mathematics, 2025, 10(11): 27412-27439. doi: 10.3934/math.20251205

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Abstract

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.

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