In this essay, a method is presented for approximating the optimal control problem (OCP) with nonlinear delay differential equations using global collocation at Legendre–Gauss–Radau points. This OCP models the spread of the computer virus. The operational matrices and collocation method together with hybrid Legendre polynomials and block-pulse functions are applied to discretize the model and convert it into a large-scale finite-dimensional nonlinear programming that can be solved by the existing well-developed methods in Matlab software. The numerical simulations show that the proposed collocation method leads to high precision solutions. Finally, the effects of the parameters that appeared in the model are analyzed. The experimental results demonstrate that the strategy for increasing the failure and the retrieval rates and decreasing the epidemic rate and the number of new computers gives a considerable influence on controlling and restraining the propagation of computer viruses.

在本文中，提出了一种方法，该方法使用Legendre–Gauss–Radau点上的全局搭配来逼近带有非线性延迟微分方程的最优控制问题（OCP）。此OCP模拟计算机病毒的传播。应用运算矩阵和搭配方法以及混合的Legendre多项式和块脉冲函数来离散化模型，并将其转换为大规模有限维非线性规划，可以通过Matlab软件中已有的完善方法来求解。数值仿真结果表明，所提出的配置方法可以得到较高的精度。最后，分析了模型中出现的参数的影响。