Pant, BinodThe pneumonia-like illness that emerged late in 2019, caused by SARS-CoV-2 (and coined COVID-19), became the greatest public health challenge humans have faced since the 1918/1919 influenza pandemic, causing over 670 million confirmed cases and 7 million fatalities globally. This dissertation contributes in providing deep qualitative insights and understanding on the transmission dynamics and control of the pandemic, using mathematical modeling approaches together with data analytics and computation. Specifically, it addresses some of the pertinent challenges associated with modeling the dynamics of the disease, notably the disproportionate effect of the disease on certain (risk and demographic) populations (inducing various heterogeneities) and behavior changes with respect to adherence or lack thereof to interventions. An $m-$group model, which monitors the temporal dynamics of the disease in m heterogeneous populations, was designed and used to study the impact of age heterogeneity and vaccination on the spread of the disease in the United States. For instance, the disease-free equilibrium for the case of the model with m=1 (i.e., the model with a homogeneous population) was shown to be globally-asymptotically stable for two special cases (when vaccine is perfect or when disease-induced mortality is negligible) whenever the associated reproduction number of the homogeneous model is less than one. The homogeneous model has a unique endemic equilibrium whenever the reproduction threshold exceeds unity (this equilibrium was shown to be globally-asymptotically stable for a special case, using a nonlinear Lyapunov function of Goh-Volterra type). The homogeneous model was fitted to the observed cumulative mortality data for the SARS-CoV-2 pandemic in the United States during the period from January to May of 2022 (when Omicron was the predominant variant). It was shown that vaccine-derived herd immunity (needed to eliminate the disease) cannot be attained using the homogeneous model regardless of the proportion of individuals fully vaccinated. Such vaccine-derived immunity can, however, be achieved using the $m$-group heterogeneous model, with $m=2$ (where the total population is split into two groups: those under 65 years of age, and those 65 years and older), if at least 61\% of the susceptible population is fully vaccinated. Thus, this dissertation shows that heterogeneity reduces the level of vaccine coverage needed to eliminate the pandemic (and models that do not account for heterogeneity may be over-estimating the vaccination coverage needed to achieve herd immunity in the community). To quantify the impact of human behavior changes on the spread and control of the pandemic, we designed a novel behavior-epidemiology model which considers numerous metrics for inducing human behavior changes (such as current level of disease burden and intervention adherence fatigue). Unlike the equivalent model without human behavior explicitly incorporated, the behavior-epidemiology model fits the observed cumulative mortality and predicts the observed daily mortality data very well. It was also shown that the behavior metrics related to the level of SARS-CoV-2 mortality and symptomatic transmission were more influential in inducing positive behavior changes than all other behavior metrics considered. Finally, a model was developed to assess the utility of wastewater surveillance to study the transmission dynamics and control of SARS-CoV-2 in a community. Specifically, we developed and calibrated a wastewater-based epidemiology model using wastewater data from Miami-Dade county, Florida, during the third wave of the SARS-CoV-2 pandemic. The model showed a strong correlation between the observed (detected) weekly case data and the corresponding weekly data predicted by the calibrated model. The model's prediction of the week when maximum number of SARS-CoV-2 cases will be recorded in the county during the simulation period precisely matched the time when the maximum observed/reported cases were recorded (August 14, 2021). Furthermore, the model's projection of the maximum number of cases for the week of August 14, 2021 was about 15 times higher than the maximum observed weekly case count for the county on that day (i.e., the maximum case count estimated by the model was 15 times higher than the actual/observed count for confirmed cases). In addition to being in line with other modeling studies, this result is consistent with the CDC estimate that the reported confirmed case data may be 10 times lower than the actual (since the confirmed data did not account for asymptomatic and presymptomatic transmission). Furthermore, the model accurately predicted a one-week lag between the peak in weekly COVID-19 case and hospitalization data during the time period of the study in Miami-Dade, with the model-predicted hospitalizations peaking on August 21, 2021. Detailed time-varying global sensitivity analysis was carried out to determine the parameters (wastewater-based, epidemiological and biological) that have the most influence on the chosen response function (namely, the cumulative viral load in the wastewater). This analysis identified key parameters that significantly affect the value of the response function (hence, they should be targeted for intervention). This dissertation conclusively showed that wastewater surveillance data can be a very powerful indicator for measuring (i.e., providing early-warning signal and current burden) and predicting the future trajectory and burden (e.g., number of cases and hospitalizations) of emerging and re-emerging infectious diseases, such as SARS-CoV-2, in a community.enDissertationApplied mathematicsCOVID-19ehavior-epidemiology modelheterogeneous modelmathematical modelSARS-CoV-2wastewater model