Mathematical analysis of malware propagation in computer networks using an SPIQR epidemic model

Abstract

In modern times, malware poses a significant threat to information security. Consequently, numerous mathematical models have been developed to describe the dissemination of malware. This study presents the SPIQR (susceptible-protected-infectious-quarantined-recovered) model to analyze how malware spreads through computer networks. We initiate our analysis by formulating a nonlinear dynamic equation that delineates the dissemination of malware. Subsequently, we compute the basic reproduction number (BRN), denoted by R₀ for the proposed model. The network's stability is contingent upon the magnitude of R₀. Particularly, if R₀ < 1, the system remains free from malware, while if R₀ >1, the network enters an endemic state. We determine the system's equilibrium points and perform numerical simulations to investigate malware spread within the network, aiming to confirm our theoretical results. In addition, we examine the nodes' communication range to provide more comprehensive data. We also examine the networks' susceptible, protected, infected, quarantined, and recovered node dynamics.