非连续免疫对非线性计算机病毒模型的影响

Impact of Discontinuous Immune on Computer Virus Model with Nonlinear Vaccination Probability

研究了一类具有非连续免疫策略的非线性传染SIR计算机病毒模型.运用右端不连续函数性质及微分包含相关知识,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.通过计算得到模型的基本再生数R0,通过构造合适的Lyapunov函数及运用Lasalle不变集原理,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收敛于有病平衡点;当R0<1时,相同的方法可证明模型的解都在有限时间内收敛于无病平衡点.运用Matlab软件进行了数值模拟,验证了理论结果的正确性.

This paper mainly studies the impact of discontinuous immunity on global dynamics of nonlinear vaccination computer virus model. By using the right hang discontinuity and the knowledge of differential inclusion, we define the solution of Filippov, and prove the existence and uniqueness of equilibrium. We obtain the basicby calculation. By constructing Lyapunov function and using LaSalle invariant set principle, we show that solutions are allconvergence to the disease equilibrium infinite time when R0〉1. Similarly, we can also demonstrate convergence to the free disease equilibrium in finite time when R0〈1 . Numerical simulations are and expand the theoretical results.