Department of Applied Mathematics, University of Waterloo
Infectious Disease Modeling with Interpersonal Contact Patterns as a Heterogeneous Network
In this thesis, we study deterministic compartmental epidemic models. The conventional mass-mixing assumption is replaced with infectious disease transmission occurring within a heterogeneous network. Modeling infectious diseases with a heterogeneous contact network divides disease status compartments into further sub-compartments by degree class and thus allows for the number of contacts an individual has to play a role in contracting and transmitting the disease.
Then these epidemiological network models are introduced as switched systems, which are systems that combine continuous dynamics with discrete logic. Many models are investigated, including SIS, SIR, SIRS, SEIR type models, and multi-city models. We analyze the stability and long-term behaviour of these switched network models. Particularly, we consider the transmission rate as a piecewise constant that changes value according to a switching signal. We establish threshold criteria for the eradication of a disease using common Lyapunov function techniques. Simulations are also conducted to support our claims and conclude conjectures about the persistence of the disease.
We test constant control and pulse control schemes including vaccination, treatment, and screening processes for multi-city systems for the application of these infectious disease model. Simulations are given to demonstrate these critical control values for achieving disease eradication. Some conclusions are made and future directions are given.