Mathematical Modelling for Analysing and Controlling Malware Propagation in Computer Networks

Abstract

VII newlineAbstract newlineComputer epidemiology is an emerging interdisciplinary field that applies the principles of mathematical epidemiology and dynamical systems to understand the spread of malicious codes within computer networks. This thesis investigates various epidemic-type models adapted for computer networks and presents analytical and numerical approaches to study their behavior, stability, and control measures. The study begins by establishing the foundational concepts of compartmental modeling, equilibrium analysis, and the basic reproduction number and#119877;0, enabling the adaptation of epidemiological frameworks to electronic environments. Several enhanced epidemic models are formulated to capture different dimensions of virus propagation, including exposure stages, quarantine mechanisms, asymptomatic and symptomatic behavior, and network-specific interactions. newlineAn extended e-SEIQRS model is developed to investigate the effects of quarantine and isolation as control strategies. Stability analysis demonstrates that the virus-free equilibrium is achieved when and#119877;0lt1, while numerical simulations illustrate the influence of defense measures on infection suppression. A specialized SEABIR model is introduced for parameter estimation and forecasting, providing improved insight into virus persistence and transmission patterns in dynamic network environments. The thesis further incorporates sensitivity analysis to identify critical parameters governing virus transmission in interconnected networks, highlighting the significance of transmission, recovery, and quarantine rates in determining system vulnerability. To capture complex nonlinear behaviors, an extended SEIR model integrated with artificial neural networks is constructed. Using Levenberg Marquardt and Bayesian regularization training algorithms, the model exhibits strong predictive performance for various data-splitting schemes. Numerical solutions obtained through MATLAB confirm both disease-free and endemic equilibria, supporting the development of efficient cyber-defence strategies. newlineOverall, this research strengthens the theoretical and computational understanding of malware propagation, offering robust modeling tools and analytical techniques for predicting, controlling, and mitigating virus outbreaks in computer networks. The findings provide a foundation for future advancements in optimal control, forecasting algorithms, and intelligent cybersecurity systems. newline