SEIQRS model analysis and optimal control with two delays.

Abstract

This paper addresses the limitations of assuming a bilinear infection rate in computer virus propagation models by proposing a more realistic nonlinear dual-delay SEIQRS model. The key focus of the research includes analyzing the local stability of the disease-free equilibrium point and the existence of positive equilibrium points with different delays. To further enhance control effectiveness, time-varying control terms are introduced, and a corresponding Hamiltonian function is constructed. The optimal control strategy is derived using the Pontryagin's maximum principle. Numerical simulation experiments are conducted to validate the dynamic characteristics of the model, and the model's properties are verified on real-time propagation networks. The experimental results demonstrate that appropriate control strategies can effectively suppress the spread of computer viruses.