Will an imperfect vaccine curtail the COVID-19 pandemic in the U.S.?

Abstract

The novel coronavirus (COVID-19) that emerged from Wuhan city of China in late December 2019 continue to pose devastating public health and economic challenges across the world. Although the community-wide implementation of basic non-pharmaceutical intervention measures, such as social distancing, quarantine of suspected COVID-19 cases, isolation of confirmed cases, use of face masks in public, contact tracing and testing, have been quite effective in curtailing and mitigating the burden of the pandemic, it is universally believed that the use of a vaccine may be necessary to effectively curtail and eliminating COVID-19 in human populations. This study is based on the use of a mathematical model for assessing the impact of a hypothetical imperfect anti-COVID-19 vaccine on the control of COVID-19 in the United States. An analytical expression for the minimum percentage of unvaccinated susceptible individuals needed to be vaccinated in order to achieve vaccine-induced community herd immunity is derived. The epidemiological consequence of the herd immunity threshold is that the disease can be effectively controlled or eliminated if the minimum herd immunity threshold is achieved in the community. Simulations of the model, using baseline parameter values obtained from fitting the model with COVID-19 mortality data for the U.S., show that, for an anti-COVID-19 vaccine with an assumed protective efficacy of 80%, at least 82% of the susceptible US population need to be vaccinated to achieve the herd immunity threshold. The prospect of COVID-19 elimination in the US, using the hypothetical vaccine, is greatly enhanced if the vaccination program is combined with other interventions, such as face mask usage and/or social distancing. Such combination of strategies significantly reduces the level of the vaccine-induced herd immunity threshold needed to eliminate the pandemic in the US. For instance, the herd immunity threshold decreases to 72% if half of the US population regularly wears face masks in public (the threshold decreases to 46% if everyone wears a face mask).

Keywords: COVID-19; Non-pharmaceutical intervention; SARS-CoV-2; Social distancing; Vaccination.

Fig. 1

Flow diagram of the model (2.1).

Fig. 2

(a) Data fitting of the model (2.1) in the absence of vaccination using COVID-19 mortality data for the US (Centers for Disease Control and Prevention, 2019; World Health Organization, 2019). (b) Simulations of the model (2.1) (using the estimated parameters) illustrating the daily mortality curve. The red dots represent data points, while the solid blue line represent predictions of death from model (2.1) for the period between March 1, 2020 through June 23, 2020.

Fig. 3

Simulations of the model (2.1), showing the cumulative COVID-19 mortality as a function of time for various levels of herd immunity threshold ($f_v$). (a) $f_v<f_v^c(r=0.2)$ (b) $f_v=f_v^c(r=0.35)$ (c) $f_v>f_v^c(r=0.7)$. Other parameter values used are as given in Table 3. For these simulations, the vaccination program is assumed to be implemented at the onset of the pandemic (starting March 1, 2020).

Fig. 4

Effect of vaccination coverage. Simulations of the model (2.1) showing the effect of the vaccination rate (${\xi }_v$) on COVID-19 burden measure in terms of (a) cumulative deaths and (b) daily deaths. Parameter values used are as given in Table 3, with $c_M={\epsilon }_M=0$ and various values of ${\xi }_v$.

Fig. 5

Simulations of the model (2.1) for the impact various effectiveness of social distancing control measures in the presence of vaccination on (a) cumulative deaths, (b) daily deaths. Mild, moderate, and strict (high) social distancing corresponds to 10%, 30%, and 50%, decrease in the values of the community contact rates ${\beta }_e$, ${\beta }_a$, and ${\beta }_s$ from their baseline values, respectively. Parameter values used are as given in Table 3.

Fig. 6

Effects of vaccination as the only intervention strategy. Contour plots of the control reproduction number (${\mathcal{R}}_c$) of the model (2.1), as a function of vaccine coverage ($f_v$) and vaccine efficacy (${\epsilon }_v$), for the baseline scenarios in Table 3 and in the absence of mask usage in public for the US. Parameter values used are as given in Table 3 with ${\epsilon }_M=c_M=0$.

Fig. 7

Effect of combined vaccination and social distancing strategies. Contour plots of the control reproduction number (${\mathcal{R}}_c$), as a function of vaccine coverage ($f_v$) and vaccine efficacy (${\epsilon }_v$) for the special case of the model (2.1) with no mask use in public. (a) mild social distancing (i.e., 10$\text{\%}$ decrease in ${\beta }_e$, ${\beta }_s$ and ${\beta }_a$). (b) Moderate social distancing (i.e., 30$\text{\%}$ decrease in ${\beta }_e$, ${\beta }_s$ and ${\beta }_a$). (c) Strict social distancing (i.e., 50$\text{\%}$ decrease in ${\beta }_e$, ${\beta }_s$ and ${\beta }_a$). Parameter values used are as given in Table 3.

Fig. 8

Contour plots of the control reproduction number (${\mathcal{R}}_c$), as a function of vaccine coverage ($f_v$) and vaccine efficacy (${\epsilon }_v$) for (a) 10% mask compliance, (b) 30$\text{\%}$ mask compliance, and (c) 50$\text{\%}$ mask compliance. Parameter values used are as given in Table 3 with various values of $c_M$.