Mathematical modeling and accurate representation of malware spread in a network is a difficult process because of our lack of understanding of several features that form the basis of such spread. Models have been used to analyze and predict the behavior of epidemic spread in networks over the years, to gain a better understanding of the process. The aim of this paper is to understand the process of emergence of vulnerabilities and its relationship with a network epidemic. Eighteen years of vulnerability emergence data has been used in this work. The data includes the total count of vulnerabilities emerging every month. The pattern reveals several important characteristics of the process including frequency peaks at seasonal locations. A steady state distribution of the process is defined. The transition of vulnerability into an exploit is characterized. Finally an interface between this vulnerability model and epidemic models is established through a description of the relationship between the epidemic force of infection and types of vulnerabilities. The paper concludes with several results that can be useful in our attempts to better approximate the spread of malware in networks.
['Kaushik Haldar', 'Bimal Kumar Mishra']
Mathematical model on vulnerability characterization and its impact on network epidemics