The impact of multiple non-pharmaceutical interventions on controlling COVID-19 outbreak without lockdown in Hong Kong: A modelling study

Our model derived the true daily infection rate and Re along with the dynamics of reported cases, and quantified the contribution of each individual NPI (Figure 3A, B, C). The model assumed that the outbreak was triggered by undetected imported cases (infected individuals exempted from quarantine and not tested on arrival), and amplified by relaxations of social distancing, on 19 June and 3 July (R1 and R2; see Table 1). After the outbreak began, social distancing measures were strengthened four times (Table 1), sequentially reducing the maximum number of people who could gather in public places or restaurants from 50 to 8, then 4, then 2, as well as mandating mask-wearing in all indoor public places.

The model estimated that, immediately after the second relaxation of social distancing (R2) on 3 July, before the first case in the outbreak was reported, the effective reproduction number, Re, rapidly increased from 0.7 to greater than 2, following an assumed logistic curve (Figure 3C). Starting on 9 July, there was a second sharp increase of Re to 3.2, before the first intervention, T1, on 11 July (Figure 3C). This second increase was caused by the effect, in the model, of decreasing efficiency in contact tracing and testing because the number of reported cases was larger than the capacity thresholds of contact tracing and testing (both about 20 cases; see Methods and Table S3). E.g. the average cumulative number of reported cases within 10 days had reached 110 on 10 July, when the peak of Re occurred. This reduction is reflected in the model’s prediction of rising trends in the proportion of both un-traced cases and those with confirmation delay (Figure 4).

The model captured the rapid increase of local cases during the first three weeks of the outbreak (Figure 3A) and revealed the impact of Tightening 1 (T1: maximum gathering number reduced from 50 to 8 persons). Although this single intervention imposed virtually the same restrictions as were in place before R1, it reduced Re only to 1.3 (relative reduction: 60.7% (95% CI 52.1–69%)) (Figure 3C and Table 1). The model suggested that this failure to reverse completely the trend of local spreading resulted from the increasing proportion with confirmation delay (Figure 4). Tightening 2 (T2: reducing the maximum gathering from 8 to 4) had little additional impact (13.9% (95%CI 3.4–20.8%)). Neither T1 nor the combination of T1 and T2 prevented the outbreak from growing exponentially. For a week, Re remained at about 1.3 (Figure 3C).

The extreme measures introduced on 29 July (T4) had a substantial effect on Re (22.5% (95%CI 6.1–35.1%)), and the daily number of confirmed cases began to decline around that time. However, the modelling results show that the daily rate of infections had already started to decline (Figure 3B) mainly because of targeting group testing (TT; 20.3% (95%CI 14.1–25.9%)) and the face-mask rule (T3; 17.5% (95%CI 1.9–36.4%)), which were introduced several days earlier. T3 and TT, combined with the effect of the early gathering restrictions (especially T1), reduced Re to 0.9 around 23 July (Figure 3C). The outbreak had effectively been suppressed by the NPIs introduced before T4.

The value of incorporating dynamics of contact-tracing efficiency is amply demonstrated by the result of re-running the model without incorporating variation in efficiency (see Supplementary Material). While this simplified ‘reduced’ model predicted the overall time-course of observed cases fairly well (Figure 3D), the striking correlation between NPIs and infection rate seen in Figure 3B was eroded (Figure 3E). The projected dynamics of Re showed a single rise before the outbreak (Figure 3F) and failed to demonstrate the lack of reversibility resulting from load on the contact-tracing system: Re returned to virtually its initial value, slightly above 1.0, after T1 and T2. In the ‘reduced’ model, T3, during the plateau, had almost no impact on Re or infections, while T4 had a dramatic effect (Figure 3E, F). The decline in infections before T4, revealed by the full model (Figure 3B), was unseen.

The prediction of daily infections from the ‘reduced’ model (Figure 3E) was more similar in shape to that of daily case numbers (Figure 3D) than for the outputs of the full model (compare Figure 3A,B). The dynamics of infection (Figure 3E) and of Re (Figure 3F), in relation to NPIs, were substantially different from those of the full model (Figure 3B,C).

The dotted curve in Figure 3C shows the estimated Re profile for all social distancing interventions but without the improvements in tracing and testing efficiency (TT and IB). Confirmation time would have grown more rapidly, hence extending and flattening the plateau, causing the projected daily case number to be temporarily lower than the reported numbers (dotted line, T1–4, in Figure 3A).

The model captured the decrease in efficiency of contact tracing during epidemic growth and the restoration of efficiency about 5 days after targeted group testing (TT) was introduced (Figure 4A). Percentage without epi‑link reduced from 47% to 37% within a week. Boosting of isolation capacity (IB) appeared to have only a minor effect on efficiency, and therefore on Re (Table 1). The validity of the model is shown by the fact that it also captured the proportion with confirmation delay amongst cases with an epi‑link (Figure 4B). This increased rapidly when the daily case number was growing and remained at a high level until a few days after the introduction of TT. In contrast, the ‘reduced’ model comprehensively failed to predict the time-courses of either epi‑linkage or confirmation delay (Figure 4). The ‘reduced’ model only successfully captured the observed smoothed curve in 2 out of 40 days (within 95% credible interval) whereas the full model captured 25 days in epi‑linkage. Similarly, for confirmation delay, 7 out of 40 days were captured from the ‘reduced’ model while 30 out of 40 days were captured from the full model. Note that the two indicators from the ‘reduced’ model changed slightly over time because of the transient dynamics of the relevant statuses of the four types of cases, even though confirmation time was fixed.

Improvement in the efficiency of tracing and testing together with the strengthened social distancing measures (T1–3), successfully curtailed the growth of the outbreak. The stringent social distancing measures in T4 lowered the number of cases, hence reducing the load in trace-and-test and further improving the efficiency of tracing and testing (Figure 4B). Together, these NPIs successfully suppressed the third wave.