Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus

Abstract

A pandemic of a novel Coronavirus emerged in December of 2019 (COVID-19), causing devastating public health impact across the world. In the absence of a safe and effective vaccine or antivirals, strategies for controlling and mitigating the burden of the pandemic are focused on non-pharmaceutical interventions, such as social-distancing, contact-tracing, quarantine, isolation, and the use of face-masks in public. We develop a new mathematical model for assessing the population-level impact of the aforementioned control and mitigation strategies. Rigorous analysis of the model shows that the disease-free equilibrium is locally-asymptotically stable if a certain epidemiological threshold, known as the reproduction number (denoted by ℛ_c), is less than unity. Simulations of the model, using data relevant to COVID-19 transmission dynamics in the US state of New York and the entire US, show that the pandemic burden will peak in mid and late April, respectively. The worst-case scenario projections for cumulative mortality (based on the baseline levels of anti-COVID non-pharmaceutical interventions considered in the study) decrease dramatically by 80% and 64%, respectively, if the strict social-distancing measures implemented are maintained until the end of May or June, 2020. The duration and timing of the relaxation or termination of the strict social-distancing measures are crucially-important in determining the future trajectory of the COVID-19 pandemic. This study shows that early termination of the strict social-distancing measures could trigger a devastating second wave with burden similar to those projected before the onset of the strict social-distancing measures were implemented. The use of efficacious face-masks (such as surgical masks, with estimated efficacy ≥ 70%) in public could lead to the elimination of the pandemic if at least 70% of the residents of New York state use such masks in public consistently (nationwide, a compliance of at least 80% will be required using such masks). The use of low efficacy masks, such as cloth masks (of estimated efficacy less than 30%), could also lead to significant reduction of COVID-19 burden (albeit, they are not able to lead to elimination). Combining low efficacy masks with improved levels of the other anti-COVID-19 intervention strategies can lead to the elimination of the pandemic. This study emphasizes the important role social-distancing plays in curtailing the burden of COVID-19. Increases in the adherence level of social-distancing protocols result in dramatic reduction of the burden of the pandemic, and the timely implementation of social-distancing measures in numerous states of the US may have averted a catastrophic outcome with respect to the burden of COVID-19. Using face-masks in public (including the low efficacy cloth masks) is very useful in minimizing community transmission and burden of COVID-19, provided their coverage level is high. The masks coverage needed to eliminate COVID-19 decreases if the masks-based intervention is combined with the strict social-distancing strategy.

Keywords: COVID-19; Contact-tracing; Face-mask; Isolation; Mathematical model; Non-pharmaceutical intervention; Quarantine; SARS-CoV-2; Social-distancing.

Fig. 1

Flow diagram of the model (2.1) showing the transition of individuals between mutually-exclusive compartments based on disease status.

Fig. 2

Time series plot showing a least squares fit of system (2.1) to New York state (a), and entire US (b), COVID-19 related death data , , , . The red dots represent data points, while the solid blue lines represent predictions of death from system (2.1).

Fig. 3

Effect of social-distancing ($\beta$). Simulations of the model (2.1), showing daily hospitalizations (and self-isolation) and cumulative mortality, as a function of time, for various values of social-distancing effectiveness (measured in terms of efficacy and adherence/coverage levels). (a) Daily hospitalizations for the state of New York. (b) Daily hospitalizations in the entire US. (c) Cumulative mortality for the state of New York. (d) Cumulative mortality for the entire US. Parameter values used are as given in Table 3, Table 4, with various values of $\beta$.

Fig. 4

Effect of duration and timing of the termination of the strict social-distancing ($\beta$) measures currently in place in New York state and the entire US. Simulations of the model (2.1), showing the effect of the duration and timing of the termination of the strict social-distancing measures against COVID-19. (a) Cumulative mortality for the state of New York if the current strict social-distancing regimen is terminated by the end of April 2020. (b) Cumulative mortality for the state of New York if the current strict social-distancing regimen is terminated by the end of May 2020. (c) Cumulative mortality for the state of New York if the current strict social-distancing regimen is terminated by the end of June 2020. (d) Cumulative mortality for the entire US if the current strict social-distancing regimen is terminated by the end of April 2020. (e) Cumulative mortality for the entire US if current strict social-distancing regimen is terminated by the end of May 2020. (f) Cumulative mortality for the entire US if current strict social-distancing regimen is terminated by the end of June 2020. Blue curves represent the effect of implementing the current strict social-distancing measures from the very beginning of the COVID-19 pandemic, in New York state (March 1, 2020) and the entire US (January 20, 2020), and maintained until early December, 2020. Magenta curves represent the effect of implementing the current strict social-distancing measures on the actual days they were implemented in New York state (March 22, 2020) and the entire US (March 16, 2020) and maintained until early December, 2020. Red curves represent the effect of terminating the current strict social-distancing regimen by the end of April, 2020 (Plots (a) and (d)), end of May, 2020 (Plots (b) and (e)) and end of June, 2020 (Plots (c) and (f)). With the exception of blue curves, solid dotted vertical lines indicate the start of the current strict social-distancing regimen (March 16, nationwide, and March 22, 2020 for the state of New York), dashed vertical lines indicate when the current strict social-distancing is terminated, and the green horizontal line segments indicate the duration of the strict social-distancing regimen. Parameter values used are as given in Table 3, Table 4, with various values of $\beta$.

Fig. 5

Effect of quarantine of individuals suspected of being exposed to COVID-19. Simulations of the model (2.1), showing daily hospitalizations, as a function of time, for various values of the efficacy of quarantine (${\theta }_j$) to prevent infection during quarantine and efficacy of isolation or hospitalization to prevent isolated/hospitalized patients from mixing with the rest of the population (${\theta }_q$). (a) Effect of quarantine efficacy (${\theta }_j$) on daily hospitalizations for the state of New York. (b) Effect of quarantine efficacy (${\theta }_j$) on daily hospitalizations for the entire US. (c) Effect of quarantine (${\theta }_j$) and isolation (${\theta }_q$) on daily hospitalizations for the state of New York. (d) Effect of quarantine (${\theta }_j$) and isolation (${\theta }_q$) on daily hospitalizations for the entire US. Parameter values used are as given in Table 3, Table 4, with various values of ${\theta }_j$ and ${\theta }_q$.

Fig. 6

Effect of contact-tracing (${\alpha }_u$ and ${\sigma }_a$). Simulations of the model (2.1), showing the number of new COVID-19 cases for various levels of contact-tracing effectiveness (measured based on increases in the values of the contact-tracing parameters, ${\alpha }_u$ and ${\sigma }_a$ from their baseline values, as a function of time. (a) Number of new cases for the state of New York. (b) Number of new cases for the entire US. Parameter values used are as given in Table 3, Table 4, with various values of ${\alpha }_u$ and ${\sigma }_a$.

Fig. 7

Effect of face-mask use in public. Simulations of the model (2.1), showing daily hospitalizations, as a function of time, for various efficacies of face-masks (${ϵ}_M$) and coverage ($c_M$). (a) $25\text{\%}$ mask efficacy for the state of New York. (b) $50\text{\%}$ mask efficacy for the state of New York. (c) $75\text{\%}$ mask efficacy for the state of New York. (d) $25\text{\%}$ mask efficacy for the entire US. (d) $50\text{\%}$ mask efficacy for the entire US. (c) $75\text{\%}$ mask efficacy for the entire US. Parameter values used are as given in Table 3, Table 4, with various values of ${ϵ}_M$ and $c_M$.

Fig. 8

Effect of face-masks use in public. (a) Contour plot of the control reproduction number (${ℛ}_c$), as a function of face-mask efficacy (${ϵ}_M$) and mask coverage ($c_M$), for the state of New York. (b) Profile of the control reproduction number (${ℛ}_c$), as a function of face-mask coverage ($c_M$) for the state of New York. (c) Contour plot of the control reproduction number (${\mathcal{R}}_c$), as a function of face-mask efficacy (${ϵ}_M$) and mask coverage ($c_M$), for the entire US. (d) Profile of the control reproduction number (${ℛ}_c$), as a function of mask coverage ($c_M$) for the entire US. Parameter values used are as given in Table 3, Table 4, with various values of ${ϵ}_M$ and $c_M$.

Fig. 9

Effect of combined use of face-masks in public and strict social-distancing. Profile of the control reproduction number (${ℛ}_c$), as a function of mask coverage ($c_M$) for different percentage reductions in the baseline value of the effective contact rate ($\beta$) for (a) the state of New York, (b) the entire US. Parameter values used are as given in Table 3, Table 4, with various values of ${ϵ}_M$ and $c_M$.