This paper mainly studies computer virus propagation models in networks based on the stability and control. The method of this study is through the learning of computer virus emergence, infection and transmission characteristics from the essence to proceed with further discussion and exploration. Then from the perspective of the stability and control, qualitative analysis is carried out and corresponding coping strategies are put forward to deal with the current three common types of the infection and spread of computer viruses in networks. Through the theoretical knowledge and the study of infection and transmission correlation mechanism about network virus control in different types of networks, two kinds of computer virus infection and spread models are built. The first is SIS Model, and the second is SIR Model. Then the two models will be deeply analyzed and explored through building mathematical models, and the two kinds of computer virus infection and spread models are compared and analyzed scientifically based on in-depth analysis. And that is very important for coping with computer virus control popular in network at present.