Dynamics of attack of malicious codes on the targeted network: Effect of firewall

In this work, a mathematical model has been developed to analyze the spread of a distributed attack on critically targeted resources in a network using firewall security coefficient. The model provides an epidemic framework with two sub-frameworks to consider the difference between the overall behavior of the attacking population and the targeted population. The targeted population and attacking population is divided into five compartments of nodes, viz. Susceptible-Latent-Breaking out-Recovered-Antidotal. With cyber mass action incidence, the boundedness of the system, the feasibility of equilibrium states and their stabilities are analyzed. Basic reproduction number R0 is calculated and it is observed that when R0 <; 1, then the system will have malicious code free stable steady state. Again, when R0 > 1, then endemic steady state exists and will be locally asymptotically stable. The impact of firewall security rule base in controlling transmission of malicious objects is analyzed. We are taking firewall security as a media coverage factor in our computer network model of malicious code propagation. Asymptotic local stability method is used as an alternate to find the stability of the system. Finally, a sensitivity analysis of the system parameters for basic reproduction number and endemic equilibrium points has been carried out using normalized forward sensitivity index. Numerical experimentation has been carried out to simulate the system of equations in support of analytical findings.