Interaction of antiworms with a worm population of e.g. hosts of worm infected and hosts of antiworm infected must be considered as a dynamic process. This study is an attempt for the first time to understand how introduction of antiworm affects the dynamic of network worm propagation. In this paper, we create a mathematical model (SIAR model) using ordinary differential equations to describe the interaction of worms and antiworms. Although idealized, the model demonstrates how the combination of a few proposed nonlinear interaction rules between antiworms and worms is able to generate a considerable variety of different kinds of responses. Taking the Blaster and Nachi worms as an example, we give a brief analysis for designing a practical antiworm system. To the best of our knowledge, there is no model for the spread of an antiworm that employs the passive scan and the finite lifetime and we believe that this is the first attempt on understanding the interaction between worms and antiworms.