In this study, the model estimation is consistent with the number of cases detected in Wuhan in mid-May. In comparison with reproduction numbers in other published studies, the estimate in the first period is in the range but on the higher side (11-13). It is possibly due to most of the other published reproduction numbers being estimated for the period after first period in this study (January 9) and that earlier data were not as complete, which might lead to an overestimation in reproduction number. Furthermore, the results suggested that COVID-19 was highly covert, the spread of the disease in Wuhan was mostly caused by hidden carriers, and the probability of resurgence was high even if the measures were retained for 14 consecutive days after reaching 0 new reported cases, which may explain the resurgence in new infections over the past few months in other countries. As a result, continuous and sometimes even painstaking endeavors have to be made in order to contain the spread of the pandemic. Large-scale testing is encouraged towards the end of a significant outbreak to identify and quarantine hidden carriers before a city or nation can be safely reopened. In particular, the model implies that it takes more than 4 months in Wuhan from a strict lockdown to the final clearance of all active infections.
The model in this study can be extended to fit pandemic data outside Wuhan, though modifications are needed with respect to specific countries or regions. For example, in the United States, statistics on daily reported cases are publicly available, but 1) no distinction is made between symptomatic and asymptomatic cases, 2) the dates of symptoms onset are mostly unavailable, 3) most reported cases are only required to self-isolate, which means that even if a case is reported, there is still a chance of infecting others. Moreover, we also need to track the changes of non-pharmaceutical interventions within the region of interest, to which (14) can be a helpful reference. To accommodate such differences, an additional compartment is needed for reported cases.
To conclude, the proposed model reflects the unique features of COVID-19, the changes in the diagnostic criteria, and the escalating containment measures, and hence the corresponding model estimates offer a better understanding of the diagnostic rate and the probability of resurgence under different policies. COVID-19 is highly covert, 74% (71%–77%) of the virus carriers had no/mild symptoms, 80% (77%–83%) of the spread of the disease was caused by those hidden carriers, and as a result, the probability of resurgence is high.
This study shares some limitations in Hao et al. (2020), for example, the assumption of homogeneous transmission rate within the population while ignoring heterogeneity between groups by sex, age, geographical region, socioeconomic status. Moreover, the population movement in this study is modelled under the same relatively simple setting as in Hao et al. (2020). This is acceptable for the case of Wuhan due to the travel restriction since January 23. More sophisticated modelling on travel flows is needed in order to generalize this model to other regions. Finally, the recently reported SARS-CoV-2 mutants may pose potential challenge to the generalization of the proposed model. Even when control measures remain unchanged, the emergence and spread of new COVID-19 variants may change the transmission rate and thus make the epidemic trend deviate from our prediction. These will be explored in future research when more relevant epidemiological data are available.
Conflicts of interest: The Authors declare that there is no conflict of interest.
Funding: National Natural Science Foundation of China grant 8204100362 and The Bill & Melinda Gates Foundation (INV-016826).
Acknowledgements: Authors of Hao et al. (2020).