A computer virus model with graded cure rates

作者：Yang, Lu-Xing^*; Yang, Xiaofan; Zhu, Qingyi; Wen, Luosheng

来源：Nonlinear Analysis: Real World Applications , 2013, 14(1): 414-422.

DOI：10.1016/j.nonrwa.2012.07.005

• Computer virus
• Dynamical model
• Equilibrium
• Global stability
• Lyapunov function
• Control strategy

A dynamical model characterizing the spread of computer viruses over the Internet is established, in which two assumptions are imposed: (1) a computer possesses infectivity once it is infected, and (2) latent computers have a lower cure rate than seizing computers. The qualitative properties of this model are fully studied. First, the basic reproduction number, R-0, for this model is determined. Second, by introducing appropriate Lyapunov functions, it is proved that the virus-free equilibrium is globally asymptotically stable if R-0 <= 1, whereas the viral equilibrium is globally asymptotically stable if 1 < R-0 <= 4. Next, the sensitivity analysis of R-0 to three system parameters is conducted, and the dependence of R-0 on the remaining system parameters is investigated. On this basis, a set of policies is recommended for eradicating viruses spreading across the Internet effectively.

• 出版日期2013-2
• 单位重庆大学