Mathematical Model on Distributed Denial of Service Attack in the Computer Network

In this paper, an electronic- epidemic two-folded mathematical model is formulated with help of non-linear ordinary differential equations. Distributed Denial of Service (DDoS) attacks in the computer network are studied. The modeling of both attacking nodes and targeting nodes is performed. Botnet based malicious devices and their threats on computer networks are addressed using appropriate parameters. The basic reproduction numbers for both the attacking and the targeting population are calculated and interpreted. Local and global stability analysis is carried out for the infection-free and endemic equilibrium points. Differential equations are solved with the help of the Runge-Kutta 4th order numerical method and graphs are analyzed using MATLAB software. Simulation shows that the success or failure depends on the number of initially infected computers in the attacking group. The proposed model exhibits the phenomenon of backward bifurcation for different values of transmission parameters. This model gives the theoretical base for controlling and predicting the DDoS attack. This shows the way to minimize the attack in the network. This study will be helpful to identify the botnet devices and run the latest version of antivirus in the network to protect against DDoS attacks from attacking sources. The application of this study is to ascertain online crime and locate the attacking nodes in the field of online transactions of real-life problems that involve the internet and computer networking systems. Moreover, our model can play an important role in policy-making against the distributed attack.