  As of December 2020, the COVID-19 pandemic has infected over 75 million
people, making it the deadliest pandemic in modern history. This study develops
a novel compartmental epidemiological model specific to the SARS-CoV-2 virus
and analyzes the effect of common preventative measures such as testing,
quarantine, social distancing, and vaccination. By accounting for the most
prevalent interventions that have been enacted to minimize the spread of the
virus, the model establishes a paramount foundation for future mathematical
modeling of COVID-19 and other modern pandemics. Specifically, the model
expands on the classic SIR model and introduces separate compartments for
individuals who are in the incubation period, asymptomatic, tested-positive,
quarantined, vaccinated, or deceased. It also accounts for variable infection,
testing, and death rates. I first analyze the outbreak in Santa Clara County,
California, and later generalize the findings. The results show that, although
all preventative measures reduce the spread of COVID-19, quarantine and social
distancing mandates reduce the infection rate and subsequently are the most
effective policies, followed by vaccine distribution and, finally, public
testing. Thus, governments should concentrate resources on enforcing quarantine
and social distancing policies. In addition, I find mathematical proof that the
relatively high asymptomatic rate and long incubation period are driving
factors of COVID-19's rapid spread.
