The reported data for COVID-19 used in this study were collected from the official website of the City of New York (4, 14), including the cumulative number of confirmed cases (Supplementary Data.xlsx, columns 2–6), the cumulative number of deaths (Supplementary Data.xlsx, columns 7–11) and the cumulative number of hospitalizations (Supplementary Data.xlsx, columns 12–16) for 5 age groups (0–17, 18–44, 45–64, 65–74, and 75–100) from March 24, 2020 to June 7, 2020. From the reported data we could see that the age group over 65 had a higher mortality rate, the total number of confirmed cases was higher between the ages of 18 and 64 (see Supplementary Figure 1) (10, 15–17). All of these data were used to estimate the unknown parameters and initial values of the mathematical model.

Based on the transmission characteristics of COVID-19 and age-specific reported data in NYC, we developed an age-structured susceptible-infected-confirmed-hospitalized-recovered (SICHR) model at the population level (a detailed model description was provided in the first and second section of Supplementary Material) (18–26). The model structure for each age group was depicted in Figure 1. Based on the COVID-19 reported data from March 24 to June 7, 2020 in NYC (Supplementary Data), we used the Markov Chain Monte Carlo (MCMC) approach to estimate the unknown parameter values and initial values of the SICHR model as well as their 95% confidence intervals (Supplementary Table 1). The detailed description of other variables and their sources were summarized in the third section of Supplementary Material.

We considered the COVID-19 outbreak in NYC from March 24 to June 7 (before the first releasing) as the baseline for this study. We compared the estimated values with the three types of reported data for COVID-19 in NYC, including the cumulative number of confirmed cases (Supplementary Figure 2), the cumulative number of deaths and the cumulative number of hospitalizations for five age groups from March 24, 2020 to June 7, 2020 (Supplementary Figures 3, 4). The results showed that the estimated values fitted the reported data very well. Therefore, the mathematical model and estimated parameters were credible and can be used to explore how to reduce the transmission risk of COVID-19 more effectively.

We considered two scenarios: one was that all confirmed cases could be hospitalized from three different times, that was, from March 26, April 5 and April 15, 2020, respectively; the other was that all infected people were confirmed from March 26, April 5 and April 15, 2020, respectively. We chose March 26, April 5, and April 15 because these dates were within a few days before and after the peak of the number of new confirmed cases in NYC. Besides, confirmed cases with mild symptoms were considered to be staying at home due to limited medical resources during the pandemic. However, this may lead to potential secondary household infections. Moreover, several studies have shown that mobile cabin hospitals could effectively alleviated the shortage of medical resources and conducted centralized isolation and scientific treatment for confirmed mild cases, which could effectively treat patients with COVID-19 who had mild symptoms (7–9). Therefore, we assumed that if NYC imitated the experience from the Wuhan mobile cabin hospitals, and there were enough mobile cabin hospitals conducting centralized isolation and scientific treatment for confirmed mild cases in NYC, just like in Wuhan, China, then the spread of the COVID-19 would have been prevented effectively.

To evaluate the impact of all hospitalized, we estimated the cumulative number of deaths for five age groups by assuming that the death rate of hospitalized cases was a decreasing function over time when more healthcare resources became available (27–29). Here, we assumed that the healthcare resources in NYC were adequate from March 26, April 5, and April 15, 2020, respectively. Particularly, we used an exponentially decreasing function μ_i(t) = μ_iexp(−at)+b to describe the mortality in hospitalized cases, where a was the exponential decline rate and b was the minimal death rate due to infection. By fitting the case fatality ratio (reported deaths among total cases) for COVID-19 in Wuhan, China (29), we obtained a = 0.0665 (95%CI, 0.0633–0.0697) and b = 0.00020 (95% CI, 0.00017–0.00023). Besides, when the confirmed cases who stayed at home were quarantined and treated at hospital, we no longer considered their deaths. To evaluate the impact of all diagnosed, we also estimated the daily number of new infections for five age groups by assuming that all infected people were confirmed from March 26, April 5, and April 15, 2020, respectively.

In order to evaluate the risk of a second wave of COVID-19 in NYC when different age groups were released from June 8, 2020, we estimated the daily number of new confirmed cases for different age groups. Due to the higher mortality rate in the age group over 65 years old, here we no longer considered the case of releasing the age group over 65 years old separately. Specifically, we considered three scenarios: releasing 0–64 age groups, releasing only one age group, releasing two age groups. In addition, we assumed that the contact rates had been reduced by 80% during the time of COVID-19 epidemic (30–32). In particular, compared with the current practice, we estimated that under what level of contact rate, a smaller second wave or a larger second wave of COVID-19 would have been prevented in NYC.

Considering the healthcare capacity of NYC hospitals, we further performed sensitivity analysis to evaluate the cumulative number of deaths in NYC by assuming that 100, 90, 80, and 70% of all confirmed cases were hospitalized from March 26, April 5, and April 15, 2020, respectively. Here, based on the exponentially decreasing death rate μ_i(t) = μ_iexp(−at)+b, we assumed that the exponential decline rate of death rate was 100 % a, 90 % a, 80 % a and 70 % a, respectively.

The results showed that in comparison with the current practice, if all confirmed cases were hospitalized from March 26, April 5, and April 15, 2020; then as of June 7, the total number of deaths in NYC decreased by 11,802, 11,134, and 9,091, respectively, and the corresponding percentages reduction were 67.24, 63.43, and 51.79%, respectively (Figure 2A). Particularly, for the 75–100 age group, compared with the current practice, the total number of deaths in NYC reduced by 5,367, 5,083, and 4,158, respectively (Figure 2F). Correspondingly, the percentages reduction were 63.48, 60.13, and 49.18%. It could be seen that the earlier the hospitalization of all confirmed cases, the greater the reduction in the total number of deaths (Figures 2A–F).

The results showed that under the current practice, on April 22, 2020, the number of new infections in NYC reached 43,795. If all infected people were diagnosed from March 26, April 5, and April 15, 2020, then the number of new infections on April 22 in NYC were only 868, 2,679 and 11,353, respectively, a decrease of 98.02, 93.88, and 74.08%, respectively. In addition, as of June 7, 2020, the cumulative number of infected individuals in NYC reduced by 2,110,764, 1,761,081, and 1,508,130, respectively, a decrease of 79.37, 66.22, and 56.71% (Figure 3A). Particularly, for the 18–44 age group, compared with the current practice, if all infected people were diagnosed from March 26, April 5, and April 15, 2020, then on April 22, 2020, the number of new infections in 18–44 age group reduced by 20,451, 19,593, and 15,465, a decrease of 98.05, 93.94, and 74.15%, respectively. Moreover, as of June 7, 2020, the cumulative number of infected individuals in 18–44 age group reduced by 1,002,674, 837,534, and 717,315, respectively, a decrease of 79.40, 66.32, and 56.80% (Figure 3C). We can see that the earlier the diagnosis of all infected people, the greater the reduction in the total number of infected individuals (Figures 3A–F). However, it should be reemphasized the fact that for the purpose of this analysis, confirmed cases were considered to be staying at home, and only leading to potential secondary household infections.

The results showed that under the current practice, the daily number of confirmed cases in NYC reached its peak around April 6, 2020 (with a peak value of 4,787 cases). When all 0–64 age groups in NYC were released from June 8, if the contact rates made by all age groups remained below 29% of the pre-pandemic level, then a second wave of COVID-19 could be prevented in NYC. However, if the contact rates made by all age groups increased to above 45% of the pre-pandemic level, then a second wave could occur, which was greater than the current outbreak (Figure 4A, Supplementary Figure 5). Particularly, if the contact rates made by all age groups increased to 100% of the pre-pandemic level, then the daily number of confirmed cases in NYC reached its peak on June 19, 2020, and the peak value was about 24,490 cases (about 4.12-fold greater than the current outbreak) (Figure 4A, Supplementary Figure 5). As of October 9, compared with the current practice, the cumulative number of confirmed cases in NYC increased by 322,615.

The results showed that when only the 0–17 age group in NYC was released from June 8, if the contact rate made by the 0–17 age group remained below 61% of the pre-pandemic level, then a second wave of COVID-19 could be prevented in NYC. Even if the contact rate made by the 0–17 age group increased to 100% of the pre-pandemic level, a greater second wave was unlikely in NYC (Figure 4B, Supplementary Figure 6).

When only the 18–44 age group in NYC was released from June 8, if the contact rate made by the 18–44 age group increased to above 37% of the pre-pandemic level, then a smaller second wave of COVID-19 could occur in NYC (Figure 4C, Supplementary Figure 7). Besides, if the contact rate made by the 18–44 age group increased to above 65% of the pre-pandemic level, then a greater second wave could occur (Figure 4C, Supplementary Figure 7). Particularly, if the contact rate made by the 18–44 age group increased to 100% of the pre-pandemic level, then the daily number of confirmed cases in NYC reached its peak on June 26, 2020, and the peak number was about 12,288 cases (Figure 4C, Supplementary Figure 7). In this case, as of October 9, compared with the current practice, the cumulative number of confirmed cases in NYC increased by 226,966.

When only the 45–64 age group in NYC was released from June 8, if the contact rate made by the 45–64 age group remained below 34% of the pre-pandemic level, then a second wave of COVID-19 could be prevented in NYC (Figure 4D, Supplementary Figure 8). However, if the contact rate made by the 45–64 age group increased to above 59% of the pre-pandemic level, then a second wave could occur, which was greater than the current outbreak (Figure 4D, Supplementary Figure 8).

When only the 0–17 and 18–44 age groups in NYC were released from June 8 (Figures 5A–F), if the contact rates made by the 0–17 and 18–44 age groups remained below 36% of the pre-pandemic level, then a second wave of COVID-19 could be prevented in NYC (Figure 5A). However, if the contact rates made by the 0–17 and 18–44 age groups increased to above 61% of the pre-pandemic level, then a greater second wave could occur in NYC (Figure 5A). Particularly, if the contact rates made by the 0–17 and 18–44 age groups increased to 100% of the pre-pandemic level, then the daily number of confirmed cases in NYC reached its peak on June 26, 2020, and the peak value was about 14,203 cases (about 1.97-fold greater than the current outbreak) (Figure 5A). As of October 9, 2020, compared with the current practice, the cumulative number of confirmed cases in NYC increased by 253,443.

When only the 18–44 and 45–64 age groups in NYC were released from June 8 (Figures 6A–F), if the contact rates made by the 18–44 and 45–64 age groups increased to above 29% of the pre-pandemic level, then a smaller second wave of COVID-19 could occur in NYC (Figure 6A). Furthermore, if the contact rates made by the 18–44 and 45–64 age groups increased to above 48% of the pre-pandemic level, then a greater second wave could occur in NYC (Figure 6A). Particularly, if the contact rates made by the 18–44 and 45–64 age groups increased to 100% of the pre-pandemic level, then the daily number of confirmed cases in NYC reached its peak on June 20, 2020, and the peak value was about 21,933 cases (about 3.58-fold greater than the current outbreak) (Figure 6A). As of October 9, 2020, compared with the current practice, the cumulative number of confirmed cases in NYC increased by 293,094.

The results showed that the cumulative number of deaths in NYC fluctuated within a small range with the different hospitalization rates. Compared with the current practice, if 100, 90, 80, and 70% of all confirmed cases were hospitalized from March 26, 2020, then the cumulative number of deaths in NYC reduced by 11,802, 11,219, 10,543, and 9,758, respectively, and the corresponding percentages reduction were 67.24, 63.9, 60.07, and 55.59%, respectively (Supplementary Figure 9). Besides, if 100, 90, 80, and 70% of all confirmed cases were hospitalized from April 5, 2020, then the percentages reduction in deaths were 63.43, 60.48, 57.01, and 52.93%, respectively (Supplementary Figure 9).