Date of Award

January 2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Bryce Christopherson

Abstract

The Internet of Things (IoT) has made electronic devices more interconnected, which has increased cybersecurity threats while also bringing previously unimaginable convenience. In this study, we explore the dynamics of malware transmission in IoT systems using a mathematical modeling methodology that draws inspiration from epidemiological approaches. To better characterize contemporary cyber-defense tactics like honeypots and proactive device hardening, we specifically suggest the SEIR-DX model, which expands the traditional SEIR framework by adding two extra compartments: Deceptive (D) and Secured (X).

The transitions between the six compartments Susceptible, Exposed, Infected, Recovered, Deceptive, and Secured are described by a system of nonlinear DE. The basic reproduction number R0, which acts as a threshold indicator for possible outbreaks, and the malware-free and endemic equilibrium points are determined qualitatively. The stability of the model is investigated analytically using bifurcation and local stability approaches, and it is verified numerically using simulations. Sensitivity and threshold analysis shed light on how important factors like deception efficacy, transmission rate, and recovery rate affect R0, offering important guidance for intervention tactics. The findings indicate that while larger intake and transmission rates make the problem worse, strengthening device recovery, removal, and deception techniques dramatically lowers malware persistence.

In order to lower the frequency of malware, our results highlight the vital role that proactive deception-based protection and traditional containment play. This study informs practical policy and design concepts for improving the resilience of IoT ecosystems in addition to offering a theoretical basis for cyber-epidemiology.

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