Date of Defense
10-4-2025 3:00 PM
Location
F1-2007
Document Type
Thesis Defense
Degree Name
Master of Science in Mathematics
College
COS
Department
Mathematical Sciences
First Advisor
Prof. Abdessamad Tridane
Keywords
Epidemic models, Stability, Controllability, Stabilizability, Linear systems, Disease transmission, Switching dynamics, Control theory, Mathematical modeling
Abstract
This thesis studies discrete-time linear switched systems and their application to epidemic models. It focuses on three key properties: stability, controllability, and stabilizability. Stability ensures systems return to equilibrium, controllability examines reaching desired states, and stabilizability determines if unstable systems can be controlled. Using mathematical tools and examples, the research shows how switching between disease transmission modes, like quarantine or vaccination, can help control outbreaks. The work highlights the importance of discrete-time models in epidemiology, as real-world data is often collected at discrete intervals, and provides a foundation for future research on more complex epidemic models.
CONTROL SYSTEM PROPERTIES OF DISCRETE-TIME LINEAR SWITCHED SYSTEMS WITH APPLICATION TO EPIDEMIC MODELS
F1-2007
This thesis studies discrete-time linear switched systems and their application to epidemic models. It focuses on three key properties: stability, controllability, and stabilizability. Stability ensures systems return to equilibrium, controllability examines reaching desired states, and stabilizability determines if unstable systems can be controlled. Using mathematical tools and examples, the research shows how switching between disease transmission modes, like quarantine or vaccination, can help control outbreaks. The work highlights the importance of discrete-time models in epidemiology, as real-world data is often collected at discrete intervals, and provides a foundation for future research on more complex epidemic models.
