Abstract: This study shows appropriate mathematical concepts for describing persistence by means of simple predator-prey models framed in system of integro-differential equations. Two mathematical models are proposed to study the predator-prey system inside a computer system. In mathematical model 1, the prey consists of infected and the uninfected nodes, whereas, the predator consists of malicious objects. In mathematical model 2, malicious objects constitute the prey and anti-malicious software is the predator. Stability of the result is stated in terms of threshold parameter R0. Explicit formula for the reproductive number R0 is derived and it has been shown that the malicious objects infection-free equilibrium, whose component of infective is zero, is asymptotically stable (globally) if threshold parameter is less than or equal to one and unstable if greater then one. Numerical method is employed to solve the system of equations developed. The simulated results may help us to understand the spread and control of malicious objects in computer network.