“Optimal Control for Virus Spread in Network: A Mathematical Model with Saturated Incidence Rate”

This study explores dynamic analysis and optimal control strategies for modeling the propagation of computer viruses in point-to-group information networks, addressing the significant threat they pose in the modern technological landscape. Grounded in the susceptible-exposed-infected-recovered (SEIR) framework, our mathematical model incorporates a saturated incidence rate to capture the evolving dynamics of virus spread and administrator responses. Our optimal control analysis focuses on three control laws corresponding to antivirus measures targeting susceptible, exposed, and infected populations, with an objective to minimize virus prevalence and associated control costs. Leveraging Pontryagin's Maximum Principle, we derive necessary conditions for optimal control, offering guidance on antivirus measure implementation to mitigate virus impact. Numerical simulations was carried out in other to validate our model and strategies, offering practical insights for network managers to bolster cyber security and minimize economic losses from viral outbreaks. The simulation result shows that by using the optimal control strategies in the model, the population of the infected and exposed computers will reduce to its possible minimal value at a minimum cost. This work establishes a robust framework for studying optimal control of computer virus spread in dynamic networks, merging mathematical modeling with actionable intervention strategies.