Data resources
We obtained the daily number of newly confirmed cases, cumulative number of confirmed cases, daily number of new deaths, cumulative number of deaths, daily number of new recoveries and cumulative number of recoveries in both Wuhan city and Hubei province from January 10, 2020 to March 30, 2020 from the Outbreak Notification of National Health Commission (NHC) of People’s Republic of China14,15. Challenges we faced were the accessibility of existing cases in ICU, therefore, we included existing number of cases in ICU only in Hubei province15 from January 10, 2020 to March 30, 2020 in our further study. We estimated the actual daily number of beds needed in isolation ward and ICU by subtracting the cumulative number of deaths and recoveries from the cumulative number of confirmed cases.
Model construction
In our modified SIR model, we divided the whole population of Wuhan (11 million) into three compartments16-19, i.e., susceptible (S), infectious (I) and removal (R). Individuals who die of or recover from the infection would be moved into the removal compartment and we assume recovered individuals would have acquired immunity20, 21. Specially, weconstructed a SIR model using discrete-time Markov chain22-24 to simulate daily epidemic dynamics and transition between different compartments to predict the burden on the public health system in the early stage of the COVID-19 epidemic in Wuhan. In the discrete-time Markov chain, one cycle in our model represents one day in actual time. Given that early investigation has suggested human-to-human transmission occurred among close contacts since the mid-December 201925, we set the first day of our model on 15th December 2019. Since we aimed to investigate the application of SIR model in the early stage of an epidemic, we ended our projection on 31st March 2020, when the peak of epidemic has passed, and the daily number of newly confirmed cases dropped to a relatively low level.
Parameters and Scenarios
The parameters fed into the SIR model represent the transition probabilities from one status to another within each cycle (Table 1). In our analysis, we considered eight scenarios based on the progression of the epidemic. Different scenarios used parameters estimated based on the data available at different stages of the epidemic (from 100 to 12,800 cumulative confirmed cases). The parameters affected by the scenarios are “DailyNewCase.Rate”, “DailyRemoval.Rate” and “ICU.Rate”. “DailyNewCase.Rate” was estimated based on daily number of newly confirmed cases in Wuhan city, while “DailyRemoval.Rate” and “ICU.Rate” were estimated based on daily number of removal cases, daily number of existing confirmed cases and daily number of existing ICU cases in Hubei province since such data were not released at the city level.
Table 1. Parameters, interpretation, and sources included in SIR Model
Specifically, Scenario 1 estimated these parameters based on data on the day when the reported cumulative confirmed cases reached 100; Scenario 2 estimated these parameters based on data between the day of 100 and the day of 200 cumulative confirmed cases; Scenario 3 estimated these parameters based on data between the day of 200 and the day of 400 cumulative confirmed cases; and the remaining five scenarios were constituted by the intervals in which the number of cumulative confirmed cases doubled (Supplementary Table 1). Additionally, we performed a sensitivity analysis based on parameters estimated using data from the day of 800 to the day of 3,200 cumulative confirmed cases.
Considering that undiagnosed infectious individuals would most likely experienced mild symptoms, we hypothesized the average time needed for recovery (Days undiagnosed) for undiagnosed infectious individuals to be 12.5 days26 and the probabilities of self-recovering (Self.Recovery.Rate) without hospitalization within any given day to be 1/12.5. Additionally, we assumed three scenarios of diagnosis rate (Dx.Rate), i.e., 50%, 70%, and 90%. Therefore, the undiagnosed rate was calculated using diagnosis rate divided by days undiagnosed. An overall death rate of 14% among the hospitalized cases was used according to the investigation by researchers from the University of Hong Kong27. Additionally, to model the effect of public health intervention implemented in Wuhan, we assumed 30%, 50%, 70%, and 90% efficacy in each scenario when comparing to the RWD. All the model inputs of different scenarios are shown in Supplementary Table 1.
The number of beds needed in isolation ward was the sum of daily total isolation ward patients and daily total undiagnosed cases. While the number of beds needed in ICU was equal to the number of daily total ICU cases.
Transition and Markov chain
Specifically, in our model, as shown in Figure 1, “susceptible” population in Wuhan is categorized into the susceptible compartment (S). When the susceptible become infected (I) with the rate of , they will be categorized into either the “undiagnosed” state with the rate of “1- Dx.Rate” or “confirmed cases” state with the rate of “Dx.Rate”. Meanwhile, some confirmed cases will be categorized into “isolation ward” state with the rate of “1-ICU.Rate (Hubei)”, and others will be categorized into “ICU” state with the rate of “ICU.Rate (Hubei)”
Undiagnosed cased will remain undiagnosed and self-recover with rate of “Self.Recovery.Rate”, or become confirmed cases with rate of “UnDxCase.Rate”, and be admitted to isolation ward or ICU. Confirmed cases in the isolation ward will recover (R) or be admitted to ICU if their symptoms deteriorate. Confirmed cases in the ICU will recover (R) or die of the infection (R). We considered “Removal” as those recovered or dead from the health system. The total number of removals (recovered plus dead from the health system) should be calculated as total number of daily confirmed cases times the rate “DailyRemoval.Rate (Hubei)”.
Comparison of SIR projection and RWD
We compared our projection of scenarios of different public health interventions to the RWD to validate the application of our model. Specifically, we calculated the Root Mean Square Errors (RMSEs) to check how our projection result fit the RWD. For each scenario, we calculated RMSE for the projection from the first day of which data for parameter estimation were available to the day of RWD peak (18th Feb 2020), e.g., RMSE for Scenario 1 was calculated based on projection from the day reached 100 cumulative cases to the day of RWD peak and RMSE for Scenario 5 was calculated based on projection from the day reaching 1600 cumulative cases to the day of RWD peak.
Patient and Public involvement
Patients or the public were not involved, and it was not appropriate or possible to involve patients or the public in the design, or conduct, or reporting, or dissemination plans of our research.