There are two distinct topics considered in this dissertation. The first is the formulation of a compartmental model using reactive social distancing in which disease transmission changes as a function of the state variables of the model; in this case, the cumulative incidence. The model assumes a single strain epidemic of Covid-19 in the United States and is used to estimate the cumulative number of deaths due to the epidemic where incidence data is used to calibrate and validate the model. The second topic concerns the use of the stochastic threshold to determine disease persistence or extinction. The Covid-19 pandemic has renewed a sense of urgency into the questions of how best to contain and manage a potential pandemic outbreak. As with any novel virus, there will be little to no immunity in the population and no immediate vaccine available. The initial methods to contain and manage such a epidemic will be limited to non-pharmaceutical interventions such as social distancing, mask wearing, and quarantines. The question to examine is given a pandemic outbreak how may we quantify the probability that prophylactically using non-pharmaceutical interventions might be able to stop a local outbreak from either starting or once started stopping it from growing into a major outbreak. For stochastic models, branching process theory can be used to estimate the probability of disease persistence or extinction. Using the Covid-19 pandemic as a case study, a homogeneous and heterogeneous model of the initial outbreak in Washington State will be formulated and the extinction probabilities will be calculated. The effect of heterogeneity on the extinction probabilities will be examined by comparing both models and the use of social distancing and different non-pharmaceutical interventions to decrease the probability of an outbreak will be explored.


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Graduation Date





Shuai, Zhisheng


Doctor of Philosophy (Ph.D.)


College of Sciences

Degree Program

Modeling and Simulation




CFE0008934; DP0026213





Release Date

November 2021

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)

Restricted to the UCF community until November 2021; it will then be open access.