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.
翻译:截至2020年12月,COVID-19大流行已经感染了7 500多万人,使其成为现代史上最致命的流行病。这项研究开发了SARS-COV-2病毒的新颖的零散流行病学模型,分析了测试、检疫、社会偏移和接种等共同预防措施的影响。我首先分析了在加利福尼亚圣克拉拉县爆发的疾病,后来又概括了调查结果。结果显示,尽管所有预防性措施都减少了COVID-19和其他现代流行病的传播,但检疫和社会偏移任务减少了COVID-19的传播。该模型在经典SIR模型上扩展了感染率,并为处于孵化期、无症状、检测呈阳性、检疫、接种或死亡的个人引入了单独的区隔板。此外,该模型还说明了不同感染、检测和死亡率。我首先分析了在加利福尼亚圣克拉拉县爆发的疫情,后来又将调查结果概括化。结果显示,尽管所有预防性措施都减少了COVID-19的传播,但检疫和社会偏移任务降低了感染率,随后是最有效的政策,其次是疫苗的分发,最后是公共测试。因此,政府应当将高数学率集中用于执行长期的检疫和数学检验。