Date of Award

Summer 2006

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Vir Phoha


Epidemic models are commonly used to model the propagation of malicious mobile code like a computer virus or a worm. In this dissertation, we introduce stochastic techniques to describe the propagation behavior of malicious mobile code. We propose a stochastic infection-immunization (INIM) model based on the standard Susceptible-Infected-Removed (SIR) epidemic model, and we get an explicit solution of this model using probability generating function (pgf.). Our experiments simulate the propagation of malicious mobile code with immunization. The simulation results match the theoretical results of the model, which indicates that it is reliable to use INIM model to predict the propagation of malicious mobile code at the early infection stage when immunization factor is considered.

In this dissertation, we also propose a control system that could automatically detect and mitigate the propagation of malicious mobile programs at the early infection stage. The detection method is based on the observation that a worm always opens as many connections as possible in order to propagate as fast as possible. To develop the detection algorithm, we extend the traditional statistical process control technique by adding a sliding window. We do the experiment to demonstrate the training process and testing process of a control system using both real and simulation data set. The experiment results show that the control system detects the propagation of malicious mobile code with zero false negative rate and less than 6% false positive rate. Moreover, we introduce risk analysis using Sequential Probability Ratio Test (SPRT) to limit the false positive rate. Examples of risk control using SPTR are presented. Furthermore, we analyze the network behavior using the propagation models we developed to evaluate the effect of the control system in a network environment. The theoretical analysis of the model shows that the propagation of malicious program is reduced when hosts in a network applied the control system. To verify the theoretical result, we also develop the experiment to simulate the propagation process in a network. The experiment results match the mathematical results.