Dynamic Model on the Spread of Bots for an E-Commerce Network

Abstract

The primary goal of e-commerce network is to sell goods and services online. Increasing usages of e-commerce network increases the security loop holes in the network. Nodes of an e-commerce network can be easily compromised by various types of malware. The nature of the spread of malware among the nodes of an e-commerce network can be easily compared with the spread of biological viruses (infectious diseases) within human population of any locality. So we can easily apply the epidemic model for the spread of infectious disease within human population into the spread of malware among the nodes of a computer network. Various types of malware are used to attack the network of an organization, but, here, in this paper we concentrate and formulate a dynamic model for the propagation of bots in an e-commerce network and study its dynamic behavior. After categorizing the nodes of the network, based on their interface to the Internet, we have proposed two submodels to formulate the overall architecture of the model. A schematic compartmental model is designed to represent the propagation of bots within the network and then differential equation model is formulated to represent the dynamics of all the compartments, respectively. The proposed system is solved and the basic reproduction number is also calculated to analyze the stability of the system. At the end, we have shown the result of numerical simulations using MATLAB to support the dynamism of our proposed model.