2 / 2023-12-02 19:39:03

Optimal Control Strategies for Mitigating Network Virus Propagation: A Mathematical Model with Saturated Incidence Rate in Point to Group Information Propagation.

Computer Virus, optimal control, mathematical model, saturated incidence rate, information propagation

This work delves into the dynamic analysis and optimal control strategies for modeling the propagation of computer viruses in point-to-group information networks. Recognizing the critical threat posed by computer viruses since their emergence in the 1980s, particularly in the context of advancing technology and increased reliance on computer networks, we introduce a mathematical model grounded in the susceptible-exposed-infected-recovered (SEIR)  framework. The model incorporates a saturated incidence rate to account for the changing dynamics of virus spread, considering the inevitable response of computer administrators to outbreaks.

The optimal control analysis focuses on three control laws corresponding to antivirus measures applied to susceptible, exposed, and infected populations. We formulate the objective function to minimize the prevalence of the virus and associated control costs. Employing Pontryagin’s Maximum Principle, we derive the necessary conditions for optimal control. The resulting optimal control strategies guide the implementation of antivirus measures to minimize the impact of computer viruses.

The presented model and optimal control strategies are analyzed and validated through numerical simulations. The findings not only contribute to understanding the dynamics of computer virus propagation but also provide practical insights for network managers to enhance cyber security and mitigate economic losses associated with viral outbreaks. Overall, this work establishes a framework for studying the optimal control of computer virus spread in dynamic information networks, bridging mathematical modeling and practical intervention strategies.

This work delves into the dynamic analysis and optimal control strategies for modeling the propagation of computer viruses in point-to-group information networks. Recognizing the critical threat posed by computer viruses since their emergence in the 1980s, particularly in the context of advancing technology and increased reliance on computer networks, we introduce a mathematical model grounded in the susceptible-exposed-infected-recovered (SEIR)  framework. The model incorporates a saturated incidence rate to account for the changing dynamics of virus spread, considering the inevitable response of computer administrators to outbreaks.

The optimal control analysis focuses on three control laws corresponding to antivirus measures applied to susceptible, exposed, and infected populations. We formulate the objective function to minimize the prevalence of the virus and associated control costs. Employing Pontryagin’s Maximum Principle, we derive the necessary conditions for optimal control. The resulting optimal control strategies guide the implementation of antivirus measures to minimize the impact of computer viruses.

The presented model and optimal control strategies are analyzed and validated through numerical simulations. The findings not only contribute to understanding the dynamics of computer virus propagation but also provide practical insights for network managers to enhance cyber security and mitigate economic losses associated with viral outbreaks. Overall, this work establishes a framework for studying the optimal control of computer virus spread in dynamic information networks, bridging mathematical modeling and practical intervention strategies.