具有免疫效力的计算机病毒传播模型的动力学分析和优化控制研究

Kinetic analysis and optimal control of computer virus transmission model with immune function

信息时代计算机病毒的传播、爆发对社会生产和人民生活造成严重影响,有效预防和抑制计算机病毒传播尤为重要。结合最优控制方法,建立了一种具有免疫效力的计算机病毒传播模型。由下一代矩阵方法求得基本再生数R_(0),并证明了无病平衡点的全局稳定性,通过敏感性分析找到对R_(0)敏感的参数;构建了Liapunov函数,证明了当R_(0)≤1时无病平衡点的全局稳定性;基于庞特里亚金最值原理得到最优解。用数值模拟方法对不同控制措施下的结果进行对比分析,结果表明,在及时检测并隔离被感染计算机并提高杀毒软件的安装率和保护率的情况下,控制目标的时间最短且控制成本最低。

The spread and outbreak of computer viruses in the information age have had a huge impact on social production and people's lives,and it is particularly important to effectively prevent and suppress the spread of computer viruses.In this paper,a computer virus propagation model with immune function is established making use of the optimal control method.It obtains the basic reproduction number R_(0) based on the method of the next generation matrix;It builds the Liapunov function,and proves the condition of the global stability of the disease-free equilibrium point when R_(0)≤1;The optimal solution is obtained based on Pontryagin's principle of maximum value.Numerical simulation results show that the optimal control model can detect and deal with infected computers while improving the installation and protection rate of antivirus software,and the control target time is the shortest and the control cost is the lowest.