Results
Since Wuhan was locked down on January 23rd, 2020, almost all regions across the country have imposed travel restriction and, at the same time, the case confirmation speed has been improved due to development of new coronavirus nucleic acid-based detection technologies. Under the scenario of adopting the strongest prevention and control strategy and improving the level of detection and treatment in China, the previously estimated basic reproduction number is no longer suitable for evaluating the epidemic trend in the near future. Therefore, we use the updated data to parameterize the proposed model (Tang et al., 2020) and re-estimate the 2019-nCov transmission risk.
To estimate the effective daily reproduction ratio, we initially get the time-dependent contact rate c(t) and δI(t) as Fig. 1 (a). Using the discrete values of contact rate c(t) and diagnose rate δI(t), we can calculate the effective daily reproduction ratio, shown in Fig. 1(b). It follows that under the strict prevention and control measures, the effective daily reproduction ratio Rd(t) has been less than 1 since January 26th, 2020, that is, the number of new infections has begun to decline. Note that the effective daily reproduction ratio declined from January 23rd, 2020 to January 25th, 2020, as a combination of the restrictive measures, including the lock-down of Wuhan, contact tracing followed by quarantine and isolation, that have been implemented. In practice, this time variation of the contact and diagnose rates leads to sub-exponential rather than exponential growth dynamics, and hence provides better estimates of epidemic size compared to fully exponential growth models. We refer to (Pell, Kuang, Viboud, & Chowell, 2018; Smirnova & Chowell, 2017) for earlier studies on sub-exponential growth of modern epidemics.
Fig. 1 (A) Time-dependent contact rate c(t) and diagnose rate δI(t); (B) Effective daily reproduction ratio Rd(t), declining due to reduction of c(t) and increase of δI(t).
Near-casting in a rapidly evolving situation requires timely information of the implementation of public health interventions. We emphasize that this information is not only about the policy and decision, but also the implementation which is highly dependent on the resources available. We illustrate this with two simulated predictions: one based on the assumption that the interventions implemented during January 23rd, 2020 to January 29th, 2020 will be sustained, and another one based on additional data beyond January 29th, 2020.
We first plot the time series on the predicted number of reported cases, i.e., the number of hospitalized individuals H(t) and the predicted cumulative cases based on the updated parameters listed in Table 1, and shown in Fig. 2 . It shows that the number of hospitalized individuals will peak on around February 4th, 2020 (Fig. 2(A, C)), while the predicted number of cumulative cases will continue to grow for some duration but with a slower growth rate (Fig. 2(D)). Moreover, sensitivity analysis revealed that further enhanced measures can reduce the peak value and hence decrease the predicted cumulative case numbers ((Fig. 2(A and B)). We caution that increasing the number of susceptible individuals may lead to an increase in the peak value and enlarge the predicted cumulative case numbers ((Fig. 2(C and D)), emphasizing the importance of sustaining the implemented control strategies such as self-isolation in order to reduce the susceptibility. We emphasize that the peak time is defined here as the time when the number of confirmed cases reaches the maximum, so sustaining the intervention measures is critical.
Fig. 2 Predictions and effect of control measures on infection based on assumption that parameters obtained from fitting the data from January 23rd to January 29th, 2020 (and hence the interventions) remain unchanged. (A–B) Decreasing the minimum contact rate after January 29th, 2020; (C–D) Decreasing/increasing the susceptible population size as of January 29th, 2020.
We repeated the procedure as above but fitted our model to the data of confirmed cases between January 23rd and February 1st, 2020 (Fig. 3 ) and observed the improved δI(t). As a result, in comparison with the results in Fig. 2, we obtained higher projected cumulative confirmed cases and delayed peak time.
Fig. 3 Best fitting of the model to the data of cumulative confirmed cases between January 23rd and February 1st, 2020: the projected number of infected (A), quarantined infected (B), and cumulative confirmed cases (C).