Modeling and analyzing of botnet interactions

Abstract

The dynamics of interacting botnets and the effects of the strategies selected by interacting botnet owners on the spread of botnets remain unclear. As a result, in this paper, we present a botnet interaction model, obtained by coupling a fast evolutionary game dynamics to a slow population dynamics model, in which two botnet types are considered. We analyze the fast evolutionary game model and obtain two stable equilibria. Additionally, we substitute them into the complete model and get two reduced models. Such models allow us to study the effects of strategies selected by botnet owners. Analysis of the models shows that when all owners adopt the cooperative strategy both types of botnets can survive with much lower contact rates. However, while they choose the competitive strategy one type of botnet will become extinct and the other will persist with a lower infection rate. The equilibrium conditions of the evolutionary game model, which can guide us in designing effective counter-botnet methods, are also obtained.