A Novel Compartmental Approach to Modeling COVID-19 Disease Dynamics and Analyzing the Effect of Common Preventative Measures
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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.
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