This paper derives a set of discrete time difference equations that models the spreading process of computer viruses such as Code-Red and Slammer. We show that the derived equations can well evaluate the effect of countermeasures such as patching and disconnecting, which are often used to stop computer viruses, based on simulations and theories. In addition, by showing an exact relationship between the derived equations and a logistic equation, we give a clear answer to the problem: Why does the dynamics of viral spread follow a logistic equation?