非连续免疫策略对计算机病毒SIR模型的影响

研究一类具有非连续免疫策略的计算机病毒模型.运用微分包含的相关知识,给出了该模型的Filippov解的定义,证明了该非连续模型的平衡点存在唯一性.通过计算得到了模型基本再生数R₀,通过构造合适的Lyapunov函数,证明了当R₀>1时,满足初始条件的每一个解都在有限时间内全局收敛于地方平衡点;当R₀<1时,同样的方法可以证明模型的解在有限时间内收敛于无病平衡点.利用MATLAB软件进行数值模拟,验证了理论结果的正确性.

Impact of Discontinuous Immunity on SIR Computer Virus Model

This paper studies the impact of discontinuous immunity on global dynamics of a computer virus model. Using differential inclusion, we define the solution of Filippov, and study existence and uniqueness of equilibrium. We get the basic reproduction number R₀ by calculation. By constructing a Lyapunov function, we show that all solutions converge to disease equilibrium in a finite time when R₀ > 1. Similarly, all solutions converge to free disease equilibrium in a finite time when R₀ < 1. Numerical simulations are carried out to illustrate and expand the theoretical results.