Impact of Hospital Bed Shortages on the Containment of COVID-19 in Wuhan

Abstract

The global outbreak of COVID-19 has caused worrying concern amongst the public and health authorities. The first and foremost problem that many countries face during the outbreak is a shortage of medical resources. In order to investigate the impact of a shortage of hospital beds on the COVID-19 outbreak, we formulated a piecewise smooth model for describing the limitation of hospital beds. We parameterized the model while using data on the cumulative numbers of confirmed cases, recovered cases, and deaths in Wuhan city from 10 January to 12 April 2020. The results showed that, even with strong prevention and control measures in Wuhan, slowing down the supply rate, reducing the maximum capacity, and delaying the supply time of hospital beds all aggravated the outbreak severity by magnifying the cumulative numbers of confirmed cases and deaths, lengthening the end time of the pandemic, enlarging the value of the effective reproduction number during the outbreak, and postponing the time when the threshold value was reduced to 1. Our results demonstrated that establishment of the Huoshenshan, Leishenshan, and Fangcang shelter hospitals avoided 22,786 people from being infected and saved 6524 lives. Furthermore, the intervention of supplying hospital beds avoided infections in 362,360 people and saved the lives of 274,591 persons. This confirmed that the quick establishment of the Huoshenshan, Leishenshan Hospitals, and Fangcang shelter hospitals, and the designation of other hospitals for COVID-19 patients played important roles in containing the outbreak in Wuhan.

Keywords: COVID-19 outbreak; effective reproduction number; hospital beds; sensitivity analysis; transmission model.

Figure 1

The data on COVID-19 in Wuhan from 10 January to 12 April. (a) Cumulative number of confirmed cases; (b) cumulative number of recovered cases; (c) cumulative number of deaths; and, (d) number of hospital beds.

Figure 2

Flow diagram to illustrate the infection dynamics of COVID-19 in Wuhan city. Integrated control measures including intensive contact tracing, quarantine and isolation are illustrated.

Figure 3

Fitting result for the data from 10 January to 12 April 2020 in Wuhan. (a) Fitting of cumulative number of confirmed cases; (b) fitting of cumulative number of recovered cases; and (c) fitting of cumulative number of deaths. The red circles represent the reported data, the black curves are the best fitting curves of model (2) to these data, and the gray regions are the 95% confidence intervals.

Figure 4

(a) Comparison of numbers of empty hospital beds and patients. The black, blue and red curves represent the numbers of empty hospital beds, confirmed but not hospitalized patients and patients seeking hospital beds, respectively. (b) Estimated effective reproduction number. The shadowed regions are the 95% confidence intervals.

Figure 5

Partial rank correlation coefficients (PRCCs) of $R_e\left(t\right)$ for $M,t_s,r,\beta ,c_1,q_1,\theta ,{\delta }_{I_1},{\delta }_{q_1},{\gamma }_{H_1},{\alpha }_{H_1}$. The Latin Hypercube Sampling was done with 10,000 bins.

Figure 6

Contour plots of (a) the end time, (b) the final number of confirmed cases, (c) the final number of deaths, and (d) the final number of recovered cases with respect to M and r. The circles represent the positions of $(M,r)$ that we have estimated.

Figure 6

Contour plots of (a) the end time, (b) the final number of confirmed cases, (c) the final number of deaths, and (d) the final number of recovered cases with respect to M and r. The circles represent the positions of $(M,r)$ that we have estimated.

Figure 7

Contour plots of (a) the end time, (b) the final number of confirmed cases, (c) the final number of deaths, and (d) the final number of recovered cases with respect to M and $t_s$. The circles represent the positions of $(M,t_s)$ that we have estimated.

Figure 8

Contour plots of (a) the end time, (b) the final number of confirmed cases, (c) the final number of deaths, and (d) the final number of recovered cases with respect to r and $t_s$. The circles represent the positions of $(r,t_s)$ we have estimated.

Figure 8

Contour plots of (a) the end time, (b) the final number of confirmed cases, (c) the final number of deaths, and (d) the final number of recovered cases with respect to r and $t_s$. The circles represent the positions of $(r,t_s)$ we have estimated.

Figure 9

Impact of hospital beds. Impact of the maximum capacity of hospital beds M on: (a) the number of hospital beds, (b) the cumulative number of confirmed cases, (c) the cumulative number of deaths, and (d) the effective reproduction number; impact of the increasing rate of hospital beds r on: (e) the number of hospital beds, (f) the cumulative number of confirmed cases, (g) the cumulative number of deaths, and (h) the effective reproduction number; impact of the intervention time $t_s$ of supplying hospital beds on: (i) the number of hospital beds, (j) the cumulative number of confirmed cases, (k) the cumulative number of deaths, and (l) the effective reproduction number.