A major grief of network and data security experts and consultants universally is about the capabilities of infectious malicious proxies (Malware) to overrun the whole systems on networks stations in order to inflict mayhem encompassing identity theft, financial scam and systemic digital assault on infrastructures and national resources. In this work, we studied the interactions of two vulnerable classes with the infected and recovered terminals on the systems network and the active use of anti-malware safety signature as counter- measure. Solving for the local and global stability state, we found them to be both asymptotically stable. The expression derived was simulated using maple mathematical tool. Finally, our results and findings were displayed.