Predictions, role of interventions and effects of a historic national lockdown in India's response to the COVID-19 pandemic: data science call to arms

Abstract

With only 536 cases and 11 fatalities, India took the historic decision of a 21-day national lockdown on March 25. The lockdown was first extended to May 3 soon after the analysis of this paper was completed, and then to May 18 while this paper was being revised. In this paper, we use a Bayesian extension of the Susceptible-Infected-Removed (eSIR) model designed for intervention forecasting to study the short- and long-term impact of an initial 21-day lockdown on the total number of COVID-19 infections in India compared to other less severe non-pharmaceutical interventions. We compare effects of hypothetical durations of lockdown on reducing the number of active and new infections. We find that the lockdown, if implemented correctly, can reduce the total number of cases in the short term, and buy India invaluable time to prepare its healthcare and disease-monitoring system. Our analysis shows we need to have some measures of suppression in place after the lockdown for increased benefit (as measured by reduction in the number of cases). A longer lockdown between 42-56 days is preferable to substantially "flatten the curve" when compared to 21-28 days of lockdown. Our models focus solely on projecting the number of COVID-19 infections and, thus, inform policymakers about one aspect of this multi-faceted decision-making problem. We conclude with a discussion on the pivotal role of increased testing, reliable and transparent data, proper uncertainty quantification, accurate interpretation of forecasting models, reproducible data science methods and tools that can enable data-driven policymaking during a pandemic. Our software products are available at covind19.org.

Keywords: Basic reproduction number; Coronavirus; Credible interval; India; Intervention forecasting; SIR model.

Appendix Figure 1:

The SIR model with (A) or without (B) considering human intervention by introducing a transmission rate modifier π(t).

Appendix Figure 2.

Implied R₀ schedules corresponding to the hypothetical scenarios under slow adherence.

Appendix Figure 3.

Short-term daily growth in cumulative case counts in India assuming a 2- week delay in people’s adherence to restrictions. Observed data are shown for days up to April 14. Predicted future case counts for April 15 until April 30 are based on observed data until April 14 using the eSIR model.

Appendix Figure 4.

Long-term daily growth in case counts in India per 100,000 people assuming a 2-week delay and how that is affected by different non-pharmaceutical intervention strategies. Predicted cumulative (a) and incident (b) case counts from April 30 to July 31 from the eSIR model are shown, based on observed data until April 14. a. Predicted number of COVID-19 cases in India under hypothetical scenarios b. Predicted number of new COVID-19 cases in India under hypothetical scenarios

Appendix Figure 5.

Trace plots and posterior density plots for the underlying model parameters β (a), γ (b), and R₀ (c), posterior distributions for the predictions Y and the latent proportions θ for the I (d) and R (e) compartments over time, and estimates and posterior distribution of the daily prevalence of active cases over time or $\frac{d{\theta }_t^I}{dt}$ (f). These plots correspond to the 21-day lockdown with moderate return scenario under quick adherence. a. Trace plots and posterior density plots for β b. Trace plots and posterior density plots for γ c. Trace plots and posterior density plots for R₀ d. Posterior distribution for the predictions Y and the latent proportions θ for the I (infected) compartment e. Posterior distribution for the predictions Y and the latent proportions θ for the R (removed) compartment f. Estimates and posterior distribution of the daily prevalence of active cases over time or $\frac{d{\theta }_t^I}{dt}$

Appendix Figure 5.

Trace plots and posterior density plots for the underlying model parameters β (a), γ (b), and R₀ (c), posterior distributions for the predictions Y and the latent proportions θ for the I (d) and R (e) compartments over time, and estimates and posterior distribution of the daily prevalence of active cases over time or $\frac{d{\theta }_t^I}{dt}$ (f). These plots correspond to the 21-day lockdown with moderate return scenario under quick adherence. a. Trace plots and posterior density plots for β b. Trace plots and posterior density plots for γ c. Trace plots and posterior density plots for R₀ d. Posterior distribution for the predictions Y and the latent proportions θ for the I (infected) compartment e. Posterior distribution for the predictions Y and the latent proportions θ for the R (removed) compartment f. Estimates and posterior distribution of the daily prevalence of active cases over time or $\frac{d{\theta }_t^I}{dt}$

Appendix Figure 5.

Trace plots and posterior density plots for the underlying model parameters β (a), γ (b), and R₀ (c), posterior distributions for the predictions Y and the latent proportions θ for the I (d) and R (e) compartments over time, and estimates and posterior distribution of the daily prevalence of active cases over time or $\frac{d{\theta }_t^I}{dt}$ (f). These plots correspond to the 21-day lockdown with moderate return scenario under quick adherence. a. Trace plots and posterior density plots for β b. Trace plots and posterior density plots for γ c. Trace plots and posterior density plots for R₀ d. Posterior distribution for the predictions Y and the latent proportions θ for the I (infected) compartment e. Posterior distribution for the predictions Y and the latent proportions θ for the R (removed) compartment f. Estimates and posterior distribution of the daily prevalence of active cases over time or $\frac{d{\theta }_t^I}{dt}$

Appendix Figure 6.

Cumulative (a) and incidence (b) graphs for forecasting models assuming a 2-week delay under 21-, 28-, 42-, and 56-day lockdown scenarios using observed data through April 14. a. Predicted number of COVID-19 infections under varying lockdown lengths b. Predicted number of daily COVID-19 infections under varying lockdown lengths

Appendix Figure 7.

Implied R₀ schedules corresponding to quick and slow adherence for the hypothetical lockdown duration scenarios. a. R₀ over time by scenario b. R₀ over time by scenario

Appendix Figure 8.

Posterior distributions of the projected case-counts and latent proportions under sensitivity scenarios. a. Scenario with 10 times the number of reported cases (e.g., under-reporting) b. Scenario using metro population (e.g., to mimic case-clustering) c. Scenario with prior mean of R₀ = 2 d. Scenario with prior mean of R₀ = 3 e. Scenario with prior mean of R₀ = 4

Appendix Figure 8.

Posterior distributions of the projected case-counts and latent proportions under sensitivity scenarios. a. Scenario with 10 times the number of reported cases (e.g., under-reporting) b. Scenario using metro population (e.g., to mimic case-clustering) c. Scenario with prior mean of R₀ = 2 d. Scenario with prior mean of R₀ = 3 e. Scenario with prior mean of R₀ = 4

Appendix Figure 9.

Model Calibration: Relative comparison of predictions using observed data up to a certain date (April 1, 7 and 14). Observed data (gray) is provided through April 30.

Appendix Figure 10a.

Daily testing patterns in selected countries

Appendix Figure 10b.

Testing numbers and proportions for 61 countries around the world affected by COVID-19

Figure 1.

Description of the cases, recovered and fatalities in India with landmark policy/recommendations. Data used up to April 14.

Figure 2.

Early phase of the epidemic and daily growth in cumulative COVID-19 case counts in India compared to other countries affected by the pandemic using data through April 14.

Figure 3.

Implied R₀ schedules corresponding the hypothetical scenarios under quick adherence. Corresponding plot for slow adherence is in Appendix Figure 2.

Figure 4.

Short-term daily growth in cumulative case counts in India assuming a 1-week delay in people’s adherence to restrictions. Observed data are shown for days up to April 14. Predicted future case counts for April 15 until April 30 are based on observed data until April 14 using the eSIR model. The dashed horizontal line represents the upper 95% credible limit for estimates under “lockdown with moderate release” scenario. Corresponding graph following a 2-week delay schedule can be found in Appendix Figure 3.

Figure 5.

Long-term daily growth in case counts in India per 100,000 people assuming a 1-week delay and how that is affected by different non-pharmaceutical intervention strategies. Predicted cumulative (a) and incident (b) case counts from May 1 to July 31 from the eSIR model are shown, based on observed data until April 14. Corresponding plots for slow adherence are in Appendix Figure 4. a. Predicted number of COVID-19 cases in India under hypothetical scenarios b. Predicted number of new COVID-19 cases in India under hypothetical scenarios

Figure 6.

Cumulative (a) and incidence (b) graphs for forecasting models assuming a 1-week delay under 21-, 28-, 42-, and 56-day lockdown scenarios using observed data through April 14. Corresponding plots for slow adherence are in Appendix Figure 4. a. Predicted number of COVID-19 infections under varying lockdown lengths b. Predicted number of daily COVID-19 infections under varying lockdown lengths