One distress of network and data security professionals and advisers globally is about the abilities of infectious malicious agents (Malware) to invade the entire network terminals to wreak havoc extending from identity theft, financial fraud to systemic digital assault on critical national resources. This work studies the behavioural dynamics of the susceptible, infected, the recovered terminals on the mobile wireless network and the effective use of antivirus security signature as countermeasure. Solving for stability state, we found out that its Eigen value gives a positive value which means that the stability is at an unstable state. Using Homotopy perturbation to calculate the approximate solution of the system. The expression derived was simulated using a mathematical tool (mat lab).