key: cord-0861348-zf8stj0q
authors: Wang, Xia; Li, Qian; Sun, Xiaodan; He, Sha; Xia, Fan; Song, Pengfei; Shao, Yiming; Wu, Jianhong; Cheke, Robert A.; Tang, Sanyi; Xiao, Yanni
title: Effects of medical resource capacities and intensities of public mitigation measures on outcomes of COVID-19 outbreaks
date: 2020-04-21
journal: nan
DOI: 10.1101/2020.04.17.20070318
sha: 15ea7f055f682d920fa4f56ffa23b1385805018a
doc_id: 861348
cord_uid: zf8stj0q

The COVID-19 pandemic is complex and is developing in different ways according to the country involved. To identify the key parameters or processes that have the greatest effects on the pandemic and reveal the different progressions of epidemics in different countries, we quantified enhanced control measures and the dynamics of the production and provision of medical resources. We then nested these within a COVID-19 epidemic transmission model, which is parameterized by multi-source data. We obtained rate functions related to the intensity of mitigation measures, the effective reproduction numbers and the timings and durations of runs on medical resources, given differing control measures implemented in various countries. Increased detection rates may induce runs on medical resources and prolong their durations, depending on resource availability. Nevertheless, improving the detection rate can effectively and rapidly reduce the mortality rate, even after runs on medical resources. Combinations of multiple prevention and control strategies and timely improvement of abilities to supplement medical resources are key to effective control of the COVID-19 epidemic. A 50% reduction in comprehensive control measures would have led to the cumulative numbers of confirmed cases and deaths exceeding 590000 and 60000, respectively, by 27 March 2020 in mainland China. The proposed model can assist health authorities to predict when they will be most in need of hospital beds and equipment such as ventilators, personal protection equipment, drugs and staff.

The COVID-19 pandemic is complex and is developing in different ways according to 27 the country involved. To identify the key parameters or processes that have the greatest 28 effects on the pandemic and reveal the different progressions of epidemics in different 29 countries, we quantified enhanced control measures and the dynamics of the production 30 and provision of medical resources. We then nested these within a COVID-19 epidemic 31 transmission model, which is parameterized by multi-source data. We Using information such as the number of beds per thousand people in each country 83 and differences in increasing volumes of medical resources (closely related to medical 84 staff numbers) that can be provided by each country during public health emergencies 85 (9-14), we modeled the number of beds provided by each country during the 86 development of a COVID-19 epidemic with the logistic growth function using country-87 specific varying growth rates and carrying capacities (section SM1 of Supplementary 88 material (SM)). In order to represent the limitation of hospital beds we divided 89 confirmed cases into two groups in terms of severity of symptoms: non-hospitalized 90 The multiple data sources including the numbers of newly reported cases and the 97 cumulative numbers of reported deaths for all six countries were used to estimate the 98 unknown parameters and to fit the data (Figs.1 and S2, Table S2 ). The parameter values 99 associated with the intensity of disease transmission in each country are compared and 100 discussed in SM3. Like China, the epidemic in South Korea is almost stable, and their 101 respective effective reproduction numbers have, by mid-April 2020, both been less than 102 1 for six weeks ( Fig.1 (B, C) . The COVID-19 epidemic in Japan has been fluctuating 103 on a small scale with a lot of random fluctuations. However, since 25 March, the 104 epidemic has rebounded, the numbers of newly reported cases and deaths have 105 continued to increase (Figs.1(D) and S2(C)). The Italian and Spanish epidemics seem 106 to be about to peak and they are approaching their turning points, but their cumulative 107 death rates will continue to rise, and there is no sign of stabilization in the short term 108 (Figs.1(E, F) and S2(D, E)). Finally, the epidemic in Iran has a strange trend, with 109 repeated and huge fluctuations (Figs.1(G) and S2(F)). 110

In order to reveal the complex patterns and huge differences in the COVID-19 111 epidemics among the various countries shown in Figs.1 and S2, we compared the 112 effectiveness and timeliness of the continuously strengthened comprehensive 113 prevention and control strategies in various countries (Fig.2) , with a view to increasing 114 our understanding and making suggestions for future prevention and control strategies. 115

To do this, we quantified the intensities of the control measures against COVID-19 116 epidemics for each country by estimating the evolution of contact rate (c(t)), quarantine 117 rate (q(t)), detection rates ( (t) and δ ( )) and medical resource capacity ( ( )) (see 118 sections SM2 and SM3). 119

It follows from Fig.2 that five of the six countries, but not Japan, are constantly 120 increasing their numbers of beds available ( ( ), green curves) for COVID-19 patients 121 with the development of the epidemic in accordance with each country's medical 122 capacity. The rates of increases in the numbers of beds are in the order South Korea, 123

China, Italy, Spain and Iran. South Korea and China would soon be able to reach the 124 maximum number of medical beds needed after their control intensity improvements 125 ( Fig.2(A) and (B) ). Due to the low rate of increase of infected individuals in Japan, so 126 far there is no urgent need to supplement the number of beds for high-risk patients there 127 (shown in Fig.2(C) ). The contact rate function (blue curve in Fig.2 Table 1 ). If the two parameters 153

δ If (related to the detection ability) and 3 were reduced at the same time to 1/3 of the 154 estimated values, then the duration of the run on medical resources would increase 155 significantly (from 12 days to 37 days) and consequently the cumulative number of 156 deaths would increase rapidly, up to 317.6% by 26 April (Fig.3 (A-B) ). If the detection indicates that rapidly increased supplies of medical resources and disease detection 160 effectively reduced the mortality in China. 161

Increasing the provision of beds (3 ℎ here) threefold in Italy, Spain and Iran will 162 only alleviate the shortage of resources for a short time, and then the run on medical 163 resources will happen again soon afterwards (green curves in Fig.3 (C,E,G) ). Italy and 164

Spain began to recover slowly, after almost 25 days and 15 days, respectively, with zero 165 beds remaining. Iran began to recover at a faster speed after a long period with zero 166 beds remaining. Nevertheless, Iran had the largest reduction in the number of 167 cumulative deaths (a reduction of 20%), followed by Spain (12.8% reduction) (Table  168 1). If the maximum number of beds is only increased to 3 , the results shown in Fig.3  169 clarify that there is little impact on the death toll in Spain and Iran ( Fig.3(F, H) ). 170

Increases in the detection rate in Italy, Spain and Iran greatly reduces the cumulative 171 number of deaths (red curves in Fig.3 (D, F, H). This is because increasing the detection 172 rate leads to significant declines in the numbers of new infections, due to strict 173 quarantine and isolation strategies, which not only decreases the number of deaths but 174 also avoids runs on medical resources (red curves in Fig.3(C, E) ). Furthermore, in Iran 175 increasing the detection rate still induces a run on resources in the early stage of the 176 epidemic but leads to recovery at a later stage due to reduced numbers of new infections 177 (black curves in Fig.3 represented by the four rates 1 , 2 , 3 and ℎ : the contact rate declines, quarantine rate 182 increases, decreasing periods for detection and increasing rates of medical resource 183 production, respectively (see SM for explanations). Reducing these rates by 10%, 20%, 184 30%, 40% and 50% simultaneously would have resulted in increased fractions in the 185 cumulative numbers of confirmed cases and deaths (Table 2) the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is Detection of infections is a key process that significantly affects the numbers of 207 confirmed cases and deaths. This is especially so for an increasing detection rate, which, 208 while increasing the number of confirmed cases in the short term, leads to declines in 209 the number of new infections. This is due to strict contact tracing followed by 210 quarantine and isolation, and consequently reductions in the number of confirmed cases 211 and deaths in the long term. Moreover, increasing the detection rate may result in runs 212 on medical resources, depending on their initial capacities. As illustrated in Fig.3 (C, E 213 and G) merely increasing detection rates in Italy or Spain did not induce runs on medical 214 resources but these did occur in Iran (red curves). Hence the synergistic effect of 215 improving medical capacity and production with enhancing detection is essential to 216 mitigating the COVID-19 pandemic as well as avoiding runs on medical resources. 217

We suggest that Japan should pay more attention to increasing medical resources as 218 its detection rate has increased since 25 March, otherwise the numbers of confirmed 219 cases and deaths will increase quickly as the intensity of its control measures is not as 220 high as in South Korea or even in Iran. If Iran had medical conditions equivalent to 221 those of South Korea, the effects of its control measures would be far more effective 222 and the current situation would be less severe. Comparing the estimated rate functions 223 for Italy, Spain and Iran indicates that a low detection rate is a key process that 224 significantly affects the epidemic, while Iran is mainly affected by its limited medical 225 resources. Regardless of other factors, improving the detection rate can effectively and 226 rapidly reduce the mortality rate, even after runs on medical resources. Therefore, in 227 order to effectively reduce the numbers of new infections and mortality in COVID-19 228 All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.04.17.20070318 doi: medRxiv preprint the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.04.17.20070318 doi: medRxiv preprint Note that 1 , 2 , 3 , and ℎ are the estimated values for corresponding countries, and for 333

South Korea 3 = 0 due to its constant diagnosis rate in Case 1 . For Cases 2 , 3 , 4 , 334 5 and 6 , the four rates 1 , 2 , 3 , and ℎ were simultaneously reduced by 10%, 20%, 335 30%, 40% and 50% respectively. 

In this model, , , , , , , 1 , 2 , represent the populations of susceptible ( ), 375 quarantined susceptible with contact tracing ( q ), exposed ( ), quarantined suspected 376 with contact tracing ( ) including patients visiting fever clinics, infected ( ) with 377 symptoms, infected (A) but asymptomatic, people after a first medical visit but 378 without a confirmed COVID-19 diagnosis and who are requested to quarantine at 379 home (H 1 ), hospitalized and confirmed (H 2 ) and recovered (R). denotes the total 380 population, and H c (t) represents the capacity of hospital beds at time t which is used 381 to describe the medical resource capacity. The detailed definitions can be found in 382 section SM2. 383 All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.04.17.20070318 doi: medRxiv preprint

In model (1), through contact tracing a proportion, q, of individuals exposed to the 384 virus is quarantined, and can either move to compartment or , depending on 385 whether they are infected or not. The other proportion, 1q, consists of individuals 386 exposed to the virus who are missed from contact tracing and move to the exposed 387 compartment when they become infectious, or else they stay in compartment . 388

Further, we denote the transmission probability by β and the contact rate by c. Then, 389 the quarantined individuals, if infected (or uninfected), move to compartment (or 390 S q ) at a rate of (or (1 -) )). Those who are not quarantined, if infected, will 391 move to compartment at a rate of βc(1 − q). We denote by constant the transition 392 rate from the susceptible class to the suspected compartment via general clinical 393 medication due to fever or other symptoms. Meanwhile, the transmissibility of 394 asymptomatic patients is lower than that of symptomatic patients, thus < . 395 the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.04.17.20070318 doi: medRxiv preprint where ℎ indicates the country-specific production capacity of medical resources in response to 418 emerging infectious diseases and f denotes the country-specific maximum number of beds that can 419 be provided during the disease outbreak. Therefore, these two parameters reflect the capacity of 420 medical resources of each country in response to COVID-19 outbreaks. In the early stage of an 421 outbreak, due to sufficient medical resources or insufficient understanding for the hospital bed the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is As the definition of the number of confirmed cases from the population waiting to 475 be tested (i.e. the class) has not considered the process of passing the incubation 476 period, the baseline parameter values of ( ) in some countries are greater than those 477 of ( ), as shown in Table S2 . The detection rates of Japan, Italy and Spain are 478 relatively lower than those for China and South Korea. However, Japan did not 479 gradually improve its detection rate until 25 March, while the detection rate for Iran 480 was increasing and finally tended to a level almost similar to that for China, which 481 indicates that Iran is constantly improving its detection rate. 482

Quarantine intensity or ( ) 483

The isolation rate q in Japan has been very high since the outbreak, which fully 484 reflects the high intensity of self-isolation in Japan, with the strong self-discipline of 485 its citizens being one of the important factors resulting in the low level of the 486 outbreak. The final quarantine rates of China, South Korea and Iran tend to be close to 487 those of Japan with a relatively high growth rate r 2 . In contrast, the baseline values of 488 quarantine rates for Italy and Spain are relative low, and the growth rate for Spain is 489 smaller than those of all other countries. 490

There is no doubt that early in the outbreak in China, the number of contacts with 492 susceptible persons per infected person was the largest. The final contact numbers of 493

Italy, Spain and Iran are relatively low, which indicates that these countries have 494 escalated social distancing measures in the later period. If they continue to maintain 495 this level of measures for a long enough period, the outbreak can be halted. However, 496

Japan has always adopted a relatively mild prevention and control strategy, and its 497 exposure number has been maintained at a high level, while the limit value of 498 South Korea is relatively large. This reveals that although the cumulative number of 499 reported cases in these two countries is not large at present, the number of newly 500 reported cases may increase repeatedly in the near future. This could be particularly 501 serious for Japan. 502

Due to the low cumulative number of confirmed cases and the low number of 504 newly reported cases, there is no problem of limited medical resources in Japan so far, 505 but with the development of the epidemic, whether there will be a run on medical 506 resources or not remains to be seen. The production capacity ℎ of medical resources 507 in Italy is the largest except for South Korea, and then China. Compared with the 508 cumulative number of reported cases in China and Italy, as well as the capacity to 509 provide medical resources, i.e. the number of beds, it is clear that there is a run on 510 medical resources or a shortage of medical resources in Italy, which is much more 511 serious than that in China. Spain and Iran are the slowest in terms of capacity to 512 supplement medical resources, which may also be one of the reasons for the high 513 All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.04.17.20070318 doi: medRxiv preprint cumulative number of reported deaths in the two countries. It is also closely related to 514 the recovery rate discussed below. 515

Recovery rate and disease-induced death rate of isolated cases at hospital 2 and 2 516

As for the recovery and mortality rates, since the epidemic data only report the 517 number of confirmed or in-hospital cases, we can only compare the recovery and In order to analyze the influence of the data randomness on parameter estimation 531 and model prediction, we assume that the epidemic data of each country follows a 532

Poisson distribution, and we randomly generate 1000 columns of datasets for fitting. 533

We then obtain the 95% confidence intervals for the curves generated by the real data 534 estimations in Fig.1 the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is Quarantined rate of exposed individuals at the initial time Maximum quarantined rate of exposed individuals under the current control strategies 2 Exponential increasing rate of quarantined rate of exposed individuals Constant quarantined rate of exposed individuals the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is All rights reserved. No reuse allowed without permission.

the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.04.17.20070318 doi: medRxiv preprint

The effectiveness of quarantine and isolation determine the 539 trend of the COVID-19 epidemics in the final phase of the current outbreak in China

Analysis of COVID-19 epidemic traced data and 542 stochastic discrete transmission dynamic model (in Chinese)

Statement on the meeting of the International Health 545

Emergency Committee regarding the outbreak of novel coronavirus 546 (2019-nCoV

NHCC: National Health Commission of the People's Republic of China

MSPC: Ministero della Salute

WHO: World Health Organization