Methods and Applications: Determining the Covertness of COVID-19 — Wuhan, China, 2020

Introduction: The coronavirus disease 2019 (COVID-19) pandemic has been going on for over a year and has reemerged in several regions. Therefore, understanding the covertness of COVID-19 is critical to more precisely estimating the pandemic size, especially the population of hidden carriers (those with very mild or no symptoms).

Methods: A stochastic dynamic model was proposed to capture the transmission mechanism of COVID-19 and to depict the covertness of COVID-19. The proposed model captured unique features of COVID-19, changes in the diagnosis criteria, and escalating containment measures.

Results: The model estimated that, for the epidemic in Wuhan, 79.8% (76.7%–82.7%) of the spread was caused by hidden carriers. The overall lab-confirmation rate in Wuhan up until March 8, 2020 was 0.17 (0.15–0.19). The diagnostic rate among patients with significant symptoms went up to 0.82 on March 8, 2020 from 0.43 on January 1, 2020 with escalating containment measures and nationwide medical supports. The probability of resurgence could be as high as 0.72 if containment measures were lifted after zero new reported (lab-confirmed or clinically confirmed) cases in a consecutive period of 14 days. This probability went down to 0.18 and 0.01 for measures lifted after 30 and 60 days, respectively.

Discussion: Consistent with the cases detected in Wuhan in mid-May, 2020, this study suggests that much of the COVID-19 pandemic is underreported and highly covert, which suggests that strict measures must be enforced continuously to contain the spread of the pandemic.

The outbreak of coronavirus disease 2019 (COVID-19) has been going on for over a year and has been deemed as a once-in-a-century health crisis (1). Many countries that believed they had gone through the worst are now again grappling with new outbreaks (1). A major driving force in the persistence of COVID-19 is transmission caused by hidden carriers with very mild or no symptoms who are unaware of their infection (2). Due to the covertness of COVID-19 and overburdened medical resources, low diagnostic rates have been observed globally. The number of infected cases estimated by seroprevalence in various regions of the US were 6 to 24 times higher than the reported number (3). Therefore, understanding the covertness of COVID-19 is critical to getting a more precise picture of the pandemic size, especially the population of hidden carriers, and accordingly, making public health decisions such as the timing to lift containment measures.

Previous studies have unraveled the covert features of COVID-19, including incubation period, proportion and transmissibility of asymptomatic infections (4-7), and overall reporting rates (7-8). Hao et al. (2020) provided an important perspective on the transmission dynamics of COVID-19 in Wuhan. The key finding inferred that 87% of the infections before March 8, 2020 were not lab-confirmed (note that a lab-confirmed case is defined as a case who is symptomatic and tested positive for COVID-19; clinically-confirmed cases and detected asymptomatic cases were excluded) (8). However, due to limitations such as violation of the homogeneity assumption in compartment dynamic models, flawed inference of transmissibility parameters, and the inability to distinguish the covert nature of COVID-19 from external factors (i.e., overburdened medical recourses), the study failed to capture some important information of covertness which led to an overoptimistic estimate on the all-clearance date in Wuhan (see Supplymentary Material Appendix A for details).

In this paper, inspired by the SAPHIRE model in Hao et al. (2020), an improved dynamic model was proposed to depict the covertness of COVID-19 to gain a better understanding of the diagnostic rate and the probability of resurgence under different policies.

The proposed model included 6 compartments: susceptible ($ S $), exposed ($ E $), presymptomatic infectious ($ P $), infectious with significant symptoms ($ I $), infectious without significant symptoms ($ A $), and removed ($ R $). The individuals in $ I $ had significant symptoms that would be diagnosable but might not be lab-confirmed. For example, when the medical system was seriously overburdened, even a severe symptomatic case might not be diagnosed or hospitalized promptly before the viral load had dropped to the level that the infection could no longer be detected by tests. Meanwhile, compartment $ A $ included hidden carriers who were unlikely to be detected. Therefore, compared to the original SAPHIRE model, individuals in $ A $ or $ I $ would now show better homogeneity, which was a required underlying assumption in compartmental dynamic models. Individuals in $ A $ could only transit to $ R $ by losing transmissibility pathologically, while patients in $ I $ might reach $ R $ either by losing their transmissibility pathologically or by isolation upon lab-confirmation or clinical diagnosis. The transmission rate was set to vary over different time periods based on the local social events, medical resources, and implementation of containment measures. The covertness of COVID-19 can be better understood by dividing the diagnostic rate (hereafter referred to as lab-confirmation rate) into the following two components:

1) the natural characteristics of COVID-19 on covertness, i.e. the fraction of those infectious virus carriers without significant symptoms throughout their course of disease;

2) factors related to medical resources and containment measures, which could be replenished and help improve the diagnostic rate in the later stages of the outbreak.

In the proposed model, these components were estimated separately. In addition, in reality, transmissibility decreased towards the end of the infectious period (9), hence, the assumption of a constant transmission rate throughout compartment $ I $ and $ A $ might potentially lead to an overestimation of effective reproduction number $ {R}_{e} $ in the early stages. The proposed model had also taken these issues into consideration (see Appendix B for the solution details and ODE system description).

The same data from January 1 to February 29 from Wuhan in Hao et al. (2020) were used here for comparison. A total of 5 time periods were identified as in Hao et al. (2020) in Wuhan for the transmission rate to vary. Based on the stochastic dynamic model, the effective reproduction $ {R}_{e} $ in Wuhan was 4.49 (4.01–5.00) and 4.10 (3.71–4.52), respectively, in the first 2 periods of January 1–9 (before Chunyun, the period of intense travel preceding the Spring Festival) and January 10–22 (Chunyun), then dropped dramatically to 1.00 (0.92–1.07), 0.43 (0.40–0.46), and 0.27 (0.22–0.33) in the later 3 periods (Figure 1B). These implied that the pandemic had been preliminarily controlled since the third period. It was estimated that 79.8% (76.7%–82.7%) of the spread of the disease was caused by hidden carriers (namely population in $ A $ and $ P $). The estimated cumulative number of infections up until March 8 was 194,302 (170,190–220,691) and the overall lab-confirmation rate was 0.17 (0.15–0.19), which was of a similar order as in Hao et al (2020).

Figure 1. 

Results of primary analysis: epidemic trends, effective reproduction numbers, ascertainment probabilities, and probabilities of resurgences. (A) Fitting and prediction using parameters from the fifth period (February 17–29), the shaded area is the 95% credible intervals, and the colored points are the mean values based on 20,000 MCMC samples. (B) Distribution of $ {R}_{e} $ estimates from 20,000 MCMC samples. (C) Diagnostic rate among patients with significant symptoms. (D) Probability of resurgence if control measures were lifted after zero new lab-confirmed cases for $ t $ days consecutively.

Note: (C) the y-axis is the probability that a patient with significant symptom can be ascertained. Abbreviation: MCMC=Markov chain Monte Carlo.

However, such a low lab-confirmation rate was mostly caused by the high proportion of asymptomatic or very mild cases which was estimated to be 0.74 (0.71–0.77), while the diagnostic rate among patients with significant symptoms (namely patients in $ I $) went up to 0.82 on March 8 from 0.43 on January 1 because of the escalating containment measures and nationwide medical support (Figure 1C). This estimation indicated that most of those with significant symptoms in Wuhan would be promptly diagnosed in the later stage of the outbreak. The clearance of all active infections would occur on June 3 (May 15 to July 5) assuming the trend remained unchanged as in the fifth period. These estimates were significantly more consistent with the confirmed cases reported in Wuhan in May, and the hidden carriers detected in subsequent city-wide testing (10). In regard to the decision making of continuous surveillance and interventions, the model found that if all measures were lifted after zero new reported (lab-confirmed or clinically-confirmed) cases in a consecutive period of 14 days, the probability of resurgence was still as high as 0.72 (Figure 1D). This probability went down to 0.18 and 0.01 if measures were lifted after zero new confirmed case in a consecutive period of 30 and 60 days, respectively. See Appendix C for more details.

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).