Spatio-temporal spreading of mobile malware: A model based on difference equations

Abstract

In this work a novel mathematical model to simulate the spatio-temporal spreading of mobile malware is introduced. It is a compartmental model where the mobile devices are grouped into two classes: susceptibles and infected devices, and the malware spreads via bluetooth. There are few models dealing with the spreading of mobile malware using bluetooth connections and all of them only study the temporal evolution. Due to the main characteristics of bluetooth it is of interest to simulate not only the temporal evolution but also the spatial spreading, and consequently, this is the main goal of this work. In our model the global dynamic is governed by means of a system of difference equations and the transmission vector is defined by the bluetooth connections. Explicit conditions for spreading are given in terms of the number of susceptible individuals at a particular time step. These could serve as a basis for design control strategies.