How do we "bend the curve" or avoid "super-spreader" events? How can the new COVID-19 virus variants affect the path of the pandemic? Who should get vaccinated first? Government and Public Health officials need to pose and answer these questions daily. We, as members of society, ask them all the time. After all, a "once-in-a-century" deadly pandemic is a treasure trove of research topics. Answering many of these questions empowers decision-makers with the tools to save lives.

We initiate our presentation with an in-depth analysis of the SEIR compartment model, which serves as one of the fundamental epidemiological models. This model is a set of differential equations used to relate Susceptible, Exposed, Infected, and Recovered people to understand the disease's behavior better. By developing a good understanding of the base model, we were then able to add different variations to suit better the needs of researching this pandemic. We started by breaking the Recovered category into Deceased and Healed, allowing better observation of the death toll the pandemic has caused. We also looked at incorporating vaccinations into the disease, thereby demonstrating how to model the best possible vaccine distribution to minimize deaths.

An Important aspect of Mathematical Modelling is the communication of the results to decision-makers and a wider audience. Visualization tools such as graphs of daily exposures, infections, hospitalizations, deaths, vaccinations, and cumulative and running averages are illustrative and helpful. Using real-time data to scale and monitor counties' pandemic levels is a powerful and effective tool that we demonstrate via various data visualization methods. Our application also allows for user-selection of databases such as the CDC, John Hopkins, and WHO.

Vaccine distribution poses significant challenges and, in some cases, competing goals that need to be attained. Because of the nature of COVID-19 and its impacts on various segments of the population, we have considered two models, Deceased Reduction and Infection Management. The first is prioritizing the vaccine's distribution among vulnerable population so that fatal outcomes are minimized. The second model minimizes the total number of infections, decreasing the overall impact on the economy and society. We conduct the study utilizing these two models and introduce two distinct objective functions that allow us to meet the desired target goals.

In conclusion, we summarize the challenges that we faced in our COVID-19 mathematical models and outline possible future research topics.