Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study.

BACKGROUND: The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. METHODS: By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. RESULTS: We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. CONCLUSIONS: We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

Evaluation of undetected cases during the COVID-19 epidemic in Austria.

BACKGROUND: Knowing the number of undetected cases of COVID-19 is important for a better understanding of the spread of the disease. This study analyses the temporal dynamic of detected vs. undetected cases to provide guidance for the interpretation of prevalence studies performed with PCR or antibody tests to estimate the detection rate. METHODS: We used an agent-based model to evaluate assumptions on the detection probability ranging from 0.1 to 0.9. For each general detection probability, we derived age-dependent detection probabilities and calibrated the model to reproduce the epidemic wave of COVID-19 in Austria from March 2020 to June 2020. We categorized infected individuals into presymptomatic, symptomatic unconfirmed, confirmed and never detected to observe the simulated dynamic of the detected and undetected cases. RESULTS: The calculation of the age-dependent detection probability ruled values lower than 0.4 as most likely. Furthermore, the proportion of undetected cases depends strongly on the dynamic of the epidemic wave: during the initial upswing, the undetected cases account for a major part of all infected individuals, whereas their share decreases around the peak of the confirmed cases. CONCLUSIONS: The results of prevalence studies performed to determine the detection rate of COVID-19 patients should always be interpreted with regard to the current dynamic of the epidemic wave. Applying the method proposed in our analysis, the prevalence study performed in Austria in April 2020 could indicate a detection rate of 0.13, instead of the prevalent ratio of 0.29 between detected and estimated undetected cases at that time.

Undetected infectives in the Covid-19 pandemic.

OBJECTIVES: Epidemiological investigations and mathematical models have revealed that the rapid diffusion of Covid-19 can mostly be attributed to undetected infective individuals who continue to circulate and spread the disease: finding their number would be of great importance in the control of the epidemic. METHODS: The dynamics of an infection can be described by the SIR model, which divides the population into susceptible (S), infective I, and removed R subjects. In particular, we exploited the Kermack-McKendrick epidemic model, which can be applied when the population is much larger than the fraction of infected subjects. RESULTS: We proved that the fraction of undetected infectives, compared to the total number of infected subjects, is given by 1-1R0, where R0 is the basic reproduction number. The mean value R0=2.102.09-2.11 for the Covid-19 epidemic in three Italian regions yielded a percentage of undetected infectives of 52.4% (52.2%-52.6%) compared to the total number of infectives. CONCLUSIONS: Our results, straightforwardly obtained from the SIR model, highlight the role of undetected carriers in the transmission and spread of the SARS-CoV-2 infection. Such evidence strongly recommends careful monitoring of the infective population and ongoing adjustment of preventive measures for disease control until a vaccine becomes available for most of the population.

Estimating the undetected infections in the Covid-19 outbreak by harnessing capture-recapture methods.

OBJECTIVES: A major open question, affecting the decisions of policy makers, is the estimation of the true number of Covid-19 infections. Most of them are undetected, because of a large number of asymptomatic cases. We provide an efficient, easy to compute and robust lower bound estimator for the number of undetected cases. METHODS: A modified version of the Chao estimator is proposed, based on the cumulative time-series distributions of cases and deaths. Heterogeneity has been addressed by assuming a geometrical distribution underlying the data generation process. An (approximated) analytical variance of the estimator has been derived to compute reliable confidence intervals at 95% level. RESULTS: A motivating application to the Austrian situation is provided and compared with an independent and representative study on prevalence of Covid-19 infection. Our estimates match well with the results from the independent prevalence study, but the capture-recapture estimate has less uncertainty involved as it is based on a larger sample size. Results from other European countries are mentioned in the discussion. The estimated ratio of the total estimated cases to the observed cases is around the value of 2.3 for all the analyzed countries. CONCLUSIONS: The proposed method answers to a fundamental open question: "How many undetected cases are going around?". CR methods provide a straightforward solution to shed light on undetected cases, incorporating heterogeneity that may arise in the probability of being detected.