Multiple COVID-19 Waves and Vaccination Effectiveness in the United States

Abstract

(1) Background: The coronavirus 2019 (COVID-19) pandemic has caused multiple waves of cases and deaths in the United States (US). The wild strain, the Alpha variant (B.1.1.7) and the Delta variant (B.1.617.2) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) were the principal culprits behind these waves. To mitigate the pandemic, the vaccination campaign was started in January 2021. While the vaccine efficacy is less than 1, breakthrough infections were reported. This work aims to examine the effects of the vaccination across 50 US states and the District of Columbia. (2) Methods: Based on the classic Susceptible-Exposed-Infectious-Recovered (SEIR) model, we add a delay class between infectious and death, a death class and a vaccinated class. We compare two special cases of our new model to simulate the effects of the vaccination. The first case expounds the vaccinated individuals with full protection or not, compared to the second case where all vaccinated individuals have the same level of protection. (3) Results: Through fitting the two approaches to reported COVID-19 deaths in all 50 US states and the District of Columbia, we found that these two approaches are equivalent. We calculate that the death toll could be 1.67-3.33 fold in most states if the vaccine was not available. The median and mean infection fatality ratio are estimated to be approximately 0.6 and 0.7%. (4) Conclusions: The two approaches we compared were equivalent in evaluating the effectiveness of the vaccination campaign in the US. In addition, the effect of the vaccination campaign was significant, with a large number of deaths averted.

Keywords: COVID-19; breakthrough infection; reinfection; vaccination effectiveness.

Figure 1

COVID-19 deaths [7,8], stringency index, vaccine coverage [9], and variant proportions [10,11,12,13] in the US. (a) Red empty circles (and black squares) represent the weekly excess deaths (and reported COVID-19 deaths) in the US. Excess deaths well match reported deaths, showing the high quality of death data. The red bold curve represents the percentage of fully vaccinated individuals, and the blue thin curve represents the stringency index which is a measure of control measure and population compliance. (b) Biweekly reported proportions of samples sequenced in the US. Overall, the Alpha variant replaced the wild strain, and subsequently, the Delta variant replaced the Alpha variant.

Figure 2

Fitting results under case 1. Panels (a–l) The model fit for the 12 most populous states in the US applying the first approach, respectively. Brown curves in the top of the panel show the vaccination (fully vaccinated) in each state. Red circles and green curves are observed and simulated (median, based on 1000 stochastic simulation runs) COVID-19 deaths. The black curve shows the simulated median under the scenario without vaccination. The blue dashed curve indicates the estimated transmission rate.

Figure 3

Fitting results under case 2. Panels (a–l) sowed the model fit for the 12 most populous states in the US applying the second approach, respectively. Others are the same as Figure 2.

Figure 4

The ratio of estimated total deaths in the two scenarios for the 12 states in US with the highest population size fitted under the two approaches. Case 1 ($\psi =1,\eta =0.85$) and Case 2 ($\psi =0.15,\eta =0$) are the two special cases we listed in the Methods section.