IJAM, Volume 28, No. 3 (2015)

Abstract. A spreading model of computer virus on the Internet is presented in terms of the fact that computer virus process includes two stages: free spread stage and response stage. It is proven that the infected nodes are always increasing in the free spread stage. In response stage, it is proven that the viruses will all be cleared when the basic reproductive number is less than unity; otherwise, the relative density of infected nodes will tend to a positive constant. Numerical simulations are carried out to illustrate the main theoretical results.