key: cord-0770836-6qmpc41g
authors: Xu, Y.; Zhang, C.; Qian, L.
title: Medical Capacity Shortages Facilitated the Rapid Dissemination of COVID-19 in Wuhan, New York State, and Italy
date: 2020-11-07
journal: nan
DOI: 10.1101/2020.11.05.20226530
sha: 8c1a01aa30753eb2ca37c589dbe59aea2601a91f
doc_id: 770836
cord_uid: 6qmpc41g

During the coronavirus disease 2019 (COVID-19) outbreak, every public health system faced the potential challenge of medical capacity shortages. Infections without timely diagnosis or treatment may facilitate the stealth transmission and spread of the virus. Using infection and medical capacity information reported in Wuhan in China, New York State in the United States, and Italy, we developed a dynamic susceptible-exposed-infected-recovered (SEIR) model to estimate the impact of medical capacity shortages during the COVID-19 outbreak at the city, state, and country levels. After accounting for the effects of travel restrictions and control measures, we find that the number of infections in Wuhan could have been 39% lower than the actual number if the medical capacity were doubled in this city. Similarly, we find the less shortages in medical capacity in both New York state and Italy, the faster decline in the daily infection numbers and the fewer deaths. This study provides a method for estimating potential shortages and explains how they may dynamically facilitate disease spreading during future pandemics such as COVID-19.

The global spread of coronavirus disease 2019 (COVID-19) has overwhelmed health systems early this year [1] and many European countries are now facing the second wave of the pandemic [2] . In the first wave, many public health systems faced the severe challenge of medical capacity shortages. For instance, unexpected critical shortages of hospital beds and medical staff occurred in many countries during the COVID-19 outbreak. Such limited medical capacity imposes an upper bound on the number of patients of being promptly diagnosed and properly treated. Infections without timely diagnosis or treatment may further facilitate the stealth transmission and spread of the virus.

Today, despite the importance of medical capacity, it is unclear to public health decision makers how the abovementioned shortages would exacerbate the spreading of diseases during pandemics such as the COVID-19. On the basis of existing research on the transmission pattern of the epidemic [e.g., 3, 4-7], we developed a dynamic susceptible-exposed-infected-recovered (SEIR)-based inference framework to estimate the impact of medical capacity shortage on the spread of COVID-19 during the pandemic. We used the data in the first wave of COVID-19 pandemic in Wuhan city, New which assures its robustness to some degree. We defined the loss function as the sum of squared errors by day:

where ‫ݕ‬ a n d ‫ݕ‬ ො

denote the real and predicted numbers of infected cases, respectively.

In the case of COVID-19 transmission in China, we denoted January 1, 2020, as the starting point of our model ‫ݐ(‬ = 1). The end point for the hospitalization fraction recovery (i.e., ܶ ଵ

) was fixed at t = 60 (i.e., March 1, 2020) because almost all identifiable patients had been hospitalized by then. In late January and early February 2020, Wuhan faced a more severe threat from medical capacity shortages than other regions in China. Specifically, before Hubei Province announced its Level 1 emergency response on January 24, the highest level for a public health emergency, Wuhan only had 7,500 hospital beds available to treat infected patients, which was well below the peak number of 35,000 COVID-19 patients in this city. In comparison, because of efficient mobilization, strict quarantine measures and a policy of accepting all patients, the epidemic outside Hubei Province was controlled to a relatively mild level with the sufficient capacity. According to epidemic statistics, there were about 10,000 patients at the peak and 32,717 total infections out of the population of 1.33 billion in non-Hubei regions in China by April 2, 2020, far below the 600,000 beds available outside of Hubei Province 1 . Fig. 1 summarizes the bed shortage situation in Wuhan in February 2020. It shows that the hospitals in Wuhan increased the number of available beds from 7,500 in late January to 25,000 in late February. During the process, the bed occupation rate decreased from 100% to 80%.

This dramatic drop occurred between t = 45 (February 14, 2020) and t = 55 (February 24, 2020).

Insert Fig. 1 here

Because there was clearly no bed shortage outside of Hubei Province, we fixed ݀ ଶ in eq. (1) at 10 for regions outside of the province; thus, the hospitalized rate in non-Hubei regions was near one, meaning that all infected patients in these places could be hospitalized immediately and none would further infect others in the system. The estimated parameters were ߚ , ݀ ଵ , a n d ݀ ଶ

in Wuhan and ߚ , ݀ ଵ , a n d ܴ outside of Hubei Province.

1 Data were collected from the daily information announced by provincial health commissions in China during the COVID-2019 pandemic. The data of bed numbers in the whole country were obtained from City Statistics Yearbook.

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The copyright holder for this preprint this version posted November 7, 2020. (i.e., February 9) for Wuhan when the hospitalized rate was approximately 0.37 (i.e., 1/e). This is because it was the period of the most rapid increase in medical capacity in Wuhan with the construction of mobile field hospitals and quarantine zones.

Model estimation confirmed the situation in Wuhan: Fig.2 shows that the hospitalized rate for infected patients increased from 0.005 on February 5 to 0.51 on February 10 and to 0.83 on February 13 before it finally exceeded 0.99 after February 21 (see Fig. 2 ). In contrast to Wuhan, other regions outside of Hubei Province did not face challenges of medical capacity shortage, because the abundant number of beds in hospitals always exceeded the number of locally confirmed cases.

Insert Fig.2 here.

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The decay in transmission rate, ߚ ሺ ‫ݐ‬ ሻ

, also applies to both Wuhan and all other regions in China. If the 12-day recovery period is considered, which means a recovery rate of 8.33% of patients per day, then the total number of unhospitalized people was 8,873 in that month-long period until February 15, 2020.

We conducted two sensitivity analyses in the context of Wuhan, with respect to the hospitalized rate and transmission rate.

First, we simulated the number of infections in Wuhan due to the different levels of medical capacities. Specifically, we varied the hospitalized rate to be 1.5 times, 1.75 times, or twice of the original rate estimated by our model presented in Fig. 2 . As illustrated in Fig. 5 , the sensitivity analysis revealed that a 50% increase in medical capacity compared with the original rate would lead to a 27% decrease in the peak number of patients, which dropped from over 36,327 to 28,505 in

Wuhan. In addition, 75% and 100% increases in the hospitalized rate would lead to 34% and 39% fewer patients in peak number, respectively. 2 The calculation of average treated fraction: use arithmetic averageሺ݂

, where ݂ is the treated fraction at day i, and k is the total number of days we take into consideration.

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The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint Insert Fig. 5 here

We also conducted a sensitivity analysis on how the transmission rate may worsen or attenuate the effect of reaching the capacity limit. We varied the speed at which the original transmission rate decreased by assuming 0.5, 0.75, 1.25, 1.5, 1.75 times, or twice of the original ݀ ଵ value. Fig. 6 illustrate the results. First, we find that, with the given capacity limit in Wuhan on February 19, a 50% slower decay rate d 1 in transmission would lead to a 175% increase in the number of infected patients and a 25% decrease in the decay rate (i.e., 75% of the original level) would lead to a 26% increase in the number of infected patients. The further sensitivity analysis reveals that a 25%, 50%, 75%, or 100% increase in decay rate d 1 would lead to 47%, 59%, 66%, or 70% fewer infected patients, respectively.

By contrast, Fig. 7 demonstrates that the change in decay rate in regions outside of Hubei Province,

where there were no shortages in medical capacity, had a smaller impact on the epidemic compared with in Wuhan. Specifically, a 50% or 25% smaller decay rate ݀ ଵ would lead to increases of 34.19% or 9.63% in the number of infected patients respectively, while increases of 25%, 50%, 75%, and 100%

in the decay rate would lead to 9.00%, 15.24%, 18.98%, and 21.75% fewer patients respectively.

These results indicate the influence of hospitalization capacity on the transmission rate when all control measures are equal; that is, a lower capacity would intensify the influence of different transmission-decay levels, thus influencing the epidemic progression.

Insert Fig. 6 , Fig. 7 and Fig. 8 here Capacity has also affected the total number of deaths throughout the epidemic. From data provided by the Centers for Disease Control in Wuhan, we estimated the death rate in Wuhan to be 0.05. Moreover, we found that with 1.5 times, 1.75 times, and twice the original rate, the number of deaths would decrease from 4430 to 3474, 3309, and 3179, respectively (see Fig. 8 ).

With the outbreak of COVID-19 epidemics in the North America and Europe, medical capability shortages were reported in New York State in the United States and in Italy. We used the situation at . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint these two locations to demonstrate the generalizability of the model with capacity limits at the state and country levels.

To estimate the situations, we collected the numbers of infected and hospitalized patients in New York State between March 8 and April 27, 2020, from the US Centers for Disease Control and Prevention 3 and those in Italy between February 23 and April 24, 2020, from the country's Civil Protection Department. 4 Because of the lack of individual recovery records in the New York state, we used the reported average recovery period, namely 12 days (Guan et.al, 2020) .

We also collected their tested numbers to validate our starting point, turning points and ending points for the change of beta and fraction (i.e., to 0.08 and 0.25, respectively, which were derived from the model using Wuhan data. We also set N in New York State and Italy at the respective population numbers.

The R 2 values of the models for New York State and Italy were 0.996 and 0.972 respectively, indicating a good fit within the data set. The fitted ݀ ଵ a n d ݀ ଶ

were 0.075 and 0.349 for New York State and 0.040 and 0.375 for Italy, respectively, which are close to the fitted parameters for Wuhan.

The higher ݀ ଶ

for Italy indicates that it improved its capacity more quickly than other regions did. , which is higher than the initial transmission rate of 0.334 in Italy at ‫ݐ‬ = 60. This difference suggests more frequent contact between people in New York State before control measures were introduced. 3 The data were collected from https://covidtracking.com/api 4 The data were collected from https://github.com/pcm-dpc/COVID-19

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The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint Insert Fig. 9 and Fig. 10 We also conducted sensitivity analyses in the cases of New York State and Italy. Specifically, we varied the speed at which the transmission rate decreased by multiplying the original d 1 by a ratio ranging between 0.75 and 1.5. The results, as illustrated in Fig. 11(a) , indicate that a 25% slower decrease in the original transmission rate in New York State would lead to a 238.88% increase in the peak number of infected patients, which is much higher than that in Wuhan. In addition, a 25% or 50% faster decrease in the original transmission rate would lead to 52.08% or 69.46% smaller peak number of infected patients, respectively. As shown in Fig. 11(b) , In Italy, a 25% slower decrease in the original transmission rate would lead to a 228.32% increase in the peak number of infected patients, whereas a 25% or 50% faster decrease in the transmission rate would lead to a 57.73% or 76.11% decrease in the peak number of infected patients, respectively. A possible reason for why slowed transmission rates had a greater influence in New York State and Italy than it did in Wuhan is the higher starting transmission rates and longer time before the decline in transmission rate (ߚ) in New York State and Italy.

Insert Fig. 11 and Fig. 12 here

For the sensitivity analysis on medical capacity, we varied the hospitalized rate to 0.25, 0.5, 0.75, 1.5, 1.75, and 2 times of their original levels, respectively, and Fig. 12 presents the results.

Because the change in rate would influence the time point of the peak number of infected patients as well as the rate at which the infection rate slows, we evaluated not only the peak number of infected . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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patients but also the speed at which it decreased. Regarding the peak in New York State, 75%, 50%, and 25% decreases in the hospitalized rate would lead to increases in the peak number of infected patients from 11,497 to 115,049, 115025, and 115,001, respectively. Moreover, 50%, 75%, and 100% increases in the rate would reduce the peak number to 114,929, 114,905, and 114,881 respectively. For Italy, 75%, 50%, and 25% decreases in the hospitalized rate would lead to increases in the peak number from 110,982 to 117,108, 113,578, and 115,001, respectively. Moreover, 50%, 75%, and 100% increases in the hospitalized rate would reduce the peak number of infected patients to 109,649, 109,121, and 108,774, respectively.

To determine the effects of different hospitalized rates on the speed of decline in the infection rate, we also examined the time at which the number of infected patients would decrease to half of the peak value. The time point at which the peak number in New York State would decrease to below 57,500 (i.e., approximately half of its estimated peak number) would be May 3 based on the original rate, and it would be delayed to May 10, May 7, and May 4 for 75%, 50%, and 25% decreases in the hospitalized rate, respectively. Increasing the hospitalized rate in New York State by 50%, 75%, and 100% would move the time point for reaching 50% of the peak forward to April 30, April 29, and April 29, respectively. For Italy, the original time point for the number of infected patients to decrease to below 55,500 (i.e., by approximately half of the peak number) would be May 7. This would be delayed to July 28, July 14, and May 17 if the hospitalized rate were 75%, 50%, and 25% smaller respectively. Increasing the hospitalized rate by 50%, 75%, and 100% would cause the half-peak level to arrive on April 28, April 27, and April 26, respectively. Furthermore, changes in the hospitalized rate would influence the total number of deaths in New York State and Italy. From the concluded cumulative total numbers of positive cases and deaths, we were able to estimate the death rate to be 0.084 in New York State and 0.135 in Italy. Accordingly, we found that 75%, 50%, and 25% decreases in the hospitalized rate in New York State would lead to increases in the number of deaths from 28,817 to 35,785, 33,003, and 30,712, respectively (see Fig.   13 ). Furthermore, 50%, 75%, and 100% increases in the hospitalized rate would lead to decreases in the number of deaths to 25,919, 25,346, and 25,088, respectively. Moreover, 75%, 50%, and 25% decreases in the rate in Italy would lead to increases in the number of deaths from 34,913, to 69,223, 52,799, and 42,034, respectively; furthermore, 50%, 75%, and 100% increases in the hospitalized rate would lead to decreases in the number of deaths to 26,783, 25,635, and 25,179, respectively.

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The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint Insert Fig. 13 here 

We conducted three robustness checks in this study. The first one tested the influences of different is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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In addition, changes in U would also influence the total number of deaths. Fig. 15 China outside of Hubei Province) were affected by cases exported from the center (such as Wuhan) [3, 4] , and such human mobility would increase the exposure rate in cities outside of the central area.

Thus, eq. (4) can be rewritten as follows: We applied the same parameter settings as those adopted in the main analysis. Human mobility data were collected from the Baidu Migration Index in 2020, which measures travel flow through changes in mobile phone locations. The performance of the new model in terms of accuracy and explanatory power was largely consistent with that displayed in Fig. 4 . Therefore, accounting for mobility did not affect the main findings.

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In the last robustness check, we compared Nelder-Mead method, which is used in our analysis, with Conjugate Gradient (CG) method, Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, and Limited-memory BFGS (L-BFGS). CG is a modified gradient descent method based on conjugate directions of gradient descent. It avoids the computation of Hessian Matrix and its inverse, which leads to higher efficiency and robustness. BFGS is a type of Quasi-Newton method, which avoids the computation of Hessian through approximation. L-BFGS limits history size of iteration compared with BFGS, and it uses a relatively sparse implicit representation of Hessian approximation. All these methods are widely used in nonlinear optimization problems. Table 1 summarizes the R-Squared values when using these methods in our analysis, which demonstrate that the Nelder-Mead method performs significantly better than other three methods.

Insert Table 1 here The major difference between these methods is that the Nelder-Mead method is a direct search method that does not need to calculate derivatives, and thus its performance on non-linear functions is better than derivative-based methods, especially when the derivatives are hard to compute. In our model, the Gompertz functions in the fraction and β equations have brought in some type of non-linearity and made it more difficult to calculate the derivatives, and thus it is natural that the Nelder-Mead method performs better in our problem.

Medical capacity shortages are a considerable challenge faced by many public health systems during the COVID-19 pandemic and other epidemics that will likely arise again in the future. Through the development of a novel SEIR-based model, this study investigated the impact of medical capacity shortages and empirically estimated their severity in Wuhan, New York State, and Italy during the outbreak and first wave of COVID-19 pandemic. Among these locations, Italy faced the most severe medical capacity shortages given its lower hospitalization fraction in the rising phase of the pandemic.

Using observable infections and medical capacity information, this study demonstrates that the shortage in medical capacity significantly increased the infected number; with Wuhan as the example, the infection number would be 39% lower than the actual number if the capacity were twice of the . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint original size. This is the first quantified evidence to show that bed shortages facilitate the spread of COVID-19. To reduce the impact of this type of shortage, public health systems should be flexible in increasing their medical capacity. Increased recruitment of retired doctors and nurses and the establishment of mobile field hospitals [17] [18] [19] have been implemented to compensate for deficiencies in medical capacity and slow the spread of COVID-19. We believe it is still critical to manage the medical capacity in the coming second wave of COVID-19 pandemic.

If the shortage cannot be resolved promptly and efficiently, the infection curve of the pandemic will inevitably steepen. While affected countries are making efforts to produce or import medical equipment, chronic global shortages of various medical equipment and medical staff remain one of the most urgent threats to numerous countries. Uniting to confront the pandemic is necessary. Instead of fighting alone, different countries and regions should combine their efforts through a more coordinated supply chain and resource sharing with international or interregional cooperation.

Our robustness check on U revealed the importance of medical system and patient treatment strategies during the pandemic. A small U could represent a lax attitude to COVID-19, whereas a large Further studies should account for more factors associated with medical capacity.

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Note: The blue, orange, and green lines denote the daily number of used beds, total number of beds, and occupancy ratio of beds, respectively. The bed occupancy ratio could exceed one in cases of temporary expansion, such as the placement of beds in hallways.

Note: The blue and orange lines denote the hospitalized rate in Wuhan and outside of Hubei province, respectively. The capacity outside of Hubei Province is always more than the infection number; thus, the rate is one.

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Note: The blue, green, red, and orange lines denote the predicted number of infected patients in Wuhan with the original hospitalized rate, a 50% increase in the hospitalized rate, a 75% increase in the hospitalized rate, and a 100% increase in the hospitalized rate.

Note: The blue, orange, green, red, purple, brown, and pink lines denote the number of infected patients predicted in Wuhan with the original , a 50% lower , a 25% lower , a 25% higher , a 50% higher , a 75% higher , and a 100% higher , respectively.

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Note: The blue, orange, green, red, purple, brown, and pink lines denote the predicted number of infected patients in non-Hubei regions with the original , a 50% lower , a 25% lower , a 25% higher , a 50% higher , a 75% higher , and a 100% higher , respectively. Note: The blue, green, red, and orange lines denote the predicted number of deaths in Wuhan with the original hospitalized rate, a 50% increase in the hospitalized rate, a 75% increase in the hospitalized rate, and a 100% increase the hospitalized rate, respectively.

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The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint Note: The blue, orange, green, red, purple, and brown lines denote the number of infected patients with the original , a 25% lower , a 25% higher , a 50% higher , a 75% higher , and a 100% higher , respectively.

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The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint Note: The blue line denotes the number of infected patients with the original hospitalized rate. The orange, green, and pink lines denote the number of infected patients with 75%, 50%, and 25% lower hospitalized rate, respectively. The red, purple, and brown lines denote the number of infected patients with 50%, 75%, and 100% higher hospitalized rate, respectively.

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The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint Note: The blue line denotes the number of deaths with the original hospitalized rate. The orange, green, and pink lines denote the number of deaths with 75%, 50%, and 25% decreases in the hospitalized rate, respectively. The red, purple, and brown lines denote the number of deaths with 50%, 75%, and 100% increases in the hospitalized rate, respectively.

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The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint (a) Hospitalized rate in New York State and Italy (b) Number of infected patients in New York State . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.05.20226530 doi: medRxiv preprint (c) Number of infected patients in Italy . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

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