Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Han, Dan

Committee Co-Chair (if applicable)

Gill, Ryan

Committee Member

Gill, Ryan

Committee Member

Li, Jiaxu

Committee Member

Ewald, Paul

Author's Keywords

SIR; mathematical modeling; stochastic processes


In this paper, a mobility-based SIR model is built to understand the spread of the pandemic. A traditional SIR model used in epidemiology describes the transition of particles among states, such as susceptible, infected, and recovered states. However, the traditional model has no movement of particles. There are many variations of SIR models when it comes to the factor of mobility, the majority of studies use mobility intensity or population density as a measure of mobility. In this paper, a new dynamical SIR model, including the spatial motion of three-type particles, is constructed and the long-time behavior of the first and second moments of this dynamical system are studied. The intermittency and Lyapunov exponents are derived and analyzed as well.