Stochastic Modeling and Applications to Discrete and Continuous Dynamical Systems

Mentors/Advisors: Jason Xu, PhD and Cliburn Chan, PhD Abstract: This dissertation consists of a series of studies that are cohesively presented to address healthcare resource allocation, viral load progression post-therapy, and immune dynamics in the face of infectious diseases, notably COVID-19. It establishes a statistical model for ICU occupancy projection based on public health data, an advanced algorithm for calculating transition probabilities within Markov models, an improved Gompertz model for more accurate viral load analysis, and an intricate model for examining immune response mechanisms. The insights from these studies may contribute to the development of effective health policies and enhance our understanding of infectious disease management.