key: cord-0970023-doqqzcc3 authors: Alvarez, M. M.; Trujillo-de Santiago, G. title: Only a combination of social distancing and massive testing can effectively stop COVID-19 progression in densely populated urban areas date: 2020-06-24 journal: nan DOI: 10.1101/2020.06.23.20138743 sha: 54ee7c053b838a3e2b1f1b7edd3717d6b156f75f doc_id: 970023 cord_uid: doqqzcc3 We present a simple epidemiological model that includes demographic density, social distancing, and efficacy of massive testing and quarantine as main parameters to model the progression of COVID-19 pandemics in densely populated urban areas (i.e., above 10,000 hab km2). Our model demonstrates that effective containment of pandemic progression in densely populated cities is achieved only by combining social distancing, widespread testing, and quarantining of infected subjects. This finding has profound epidemiological significance, and sheds light on the controversy regarding the relative effectiveness of widespread testing and social distancing. Our simple epidemiological simulator can also be used to assess the efficacy of a governmental/societal response to an outbreak. This study has also relevant implications on the concept of smart cities; densely populated areas are hot spots highly vulnerable to epidemic crisis. The first equation of the set (equation 1) states that the rate of accumulation of infected 98 habitants (symptomatic and asymptomatic) in an urban area (assumed to be a closed 99 system) is proportional to the number of infective subjects (X-R) present in that population 100 at a given point and the fraction of the population susceptible to infection ((P o -X)/P o ). Note 101 . 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 June 24, 2020. 136 As with any epidemiological model, this model relies on some basic assumptions that must 137 be sustained in clinical or epidemiological data. We now briefly discuss the assumptions 138 that were made and the rationale behind the relevant values of the parameters of the model: 139 the fraction of asymptomatic infected, the average time to recover, the fraction of 140 symptomatic patients that would require hospitalization, and the average time of bed 141 occupancy per hospitalized patient. 142 The fraction of asymptomatic infected is one of the critical inputs to the model; it 143 determines the final and maximum feasible threshold of symptomatic infected. However, 144 the current evidence is not yet sufficient to support a conclusive value for this parameter. 145 Nevertheless, a recent serological study conducted in New York City (NYC) found anti-146 SARS-CoV-2 IGGs among 21.2% of the population (www.360dx.com; www.cnn.com ), 147 and this result is consistent with previous information related to massive epidemic episodes. 148 . 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 June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint population in urban areas (i.e., Monterrey, México, and Pittsburgh, USA) (7, 8) exhibited 150 specific antibodies regardless of experiencing symptoms, while the fraction of confirmed 151 symptomatic infections was lower than less than 10%. This serological result based 152 exclusively on information from NYC suggests that more than 90% of exposed New 153 Yorkers (~91.4%) were asymptomatic or exhibited minor symptoms. Based on this (still 154 unpublished) data, we assumed a symptomatic fraction of only 10% in the calculations and 155 forecasts presented here. 156 In addition, the average time of sickness was set at 21 days in our simulations, as this is 157 within the reported range of 14 to 32 days(9), with a median time to recovery of 21 158 days(10). Viral shedding can last for three to four weeks after the onset of symptoms, with 159 a peak at day 10-11.(11) Therefore, we assume that all those infected not quarantined . 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 June 24, 2020. Definition of representative scenarios 182 We aimed to reproduce representative settings for COVID-19 progression; therefore, we 183 selected two hypothetical but realistic urban scenarios. Figure 1 shows the most densely 184 Based on this analysis, we centered our estimates of COVID-19 progression in these two 193 classes of "representative" cities (3.5 million inhabitants, 5,000 hab km 2 ; and 10 million 194 citizens, 10,000 hab km 2 ). 195 . 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 June 24, 2020. We also based our estimates of µ o , the intrinsic rate of COVID_19 propagation, on data 206 extracted from the local dynamics of the pandemics in Madrid (a city in our first category) 207 and New York City (a city in our second category). These two cities also belong to a 208 limited number of cities that have generated reliable datasets on the local progression of the 209 . 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 June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint number of COVID-19 positive cases over time. We calculate the value of µ o (i.e., the 210 intrinsic rate of infectivity of SARS-CoV2 before interventions) by assuming that the initial 211 subjects. We then simply calculate the intrinsic rate of infection from the initial slope of a 213 plot of ln [X] vs time, which is a usual procedure for calculation of intrinsic growth rates in 214 cell culture scenarios under the assumption of first order rate growth dependence. 215 Following this rationale, we set µ o for all our simulations. Consistently, we noted that the 216 initial rate of propagation observed in NYC, a city with twice the demographic density of 217 Madrid, doubles this µ o value (Table 1) . Therefore, we take the demographic density of 218 Madrid as a reference (5,185 hab km 2 ) and assume that multiplying µ o by the normalized 219 demographic density (with respect to that in Madrid) is a reasonable procedure for adapting 220 the model to any urban area. 221 222 Effect of social distancing and massive testing 223 Social distancing has been regarded as the one of the most effective buffering measures for 224 containment of local COVID-19 epidemics(24, 25). However, the effectiveness of massive 225 testing, either alone or in combination with social distancing, has not been evaluated 226 First, we conducted simulations in which we evaluated the independent impact of different 228 degrees of social distancing and massive testing in a Type I city (3.5 million inhabitants and 229 medium demographic density). Figure 2a shows the impact of different degrees of social 230 distancing at a fixed and basal value of massive testing. In this simulation, a basal value of 231 social distancing (α=0.1) means that only 10% of the infected patients are diagnosed and 232 . 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 June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint quarantined, while the rest of the infected subjects continue active until recovery. This 233 strategy is consistent with that adopted by countries that diagnosed essentially only those 234 subjects who were symptomatic and asked for medical assistance (i.e., México, Chile, and indicated with grey curves for a reference scenario with no social distancing and basal level 238 of testing. Higher degrees of enforcement of social distancing (i.e., such that the 239 demographic density is effectively reduced by 20, 40, and 60%) are presented with blue, 240 green, and red lines, respectively. Levels of social distancing of 20% and 40% delay the 241 pandemic curve by 15 and 30 days, whereas the pandemic progression is successfully 242 buffered only when social distancing effectively reduces demographic density (and 243 therefore activity) by 60% for extended times (i.e., for 6 months). 244 distancing and testing renders better results than any one of the two strategies 254 . 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 June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint independently applied. When social distancing is elevated to a 40% and combined with 255 more intensive testing efforts, the epidemic peak is dramatically delayed. . 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 June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint day 75, and lowers the highest demand of beds from 75,000 to fewer than 30,000. Increased 273 testing at 40% social distancing further contributes to extinguish the epidemic peak. 274 We also estimated the pandemic progression under the same set of scenarios for a densely 275 populated city (Type II: 5×10 6 citizens and 10,000 hab km 2 ). The results similarly indicate 276 that only a combined strategy of social distancing and scaled-up testing and quarantine may 277 effectively control the pandemic progression due to "selective social distancing". However, 278 the higher population leads to increases in the number of cases in the same time frame (let 279 us say, the first 120 days from pandemic onset) and in the maximum threshold of 280 symptomatic cases. The higher demographic density also causes a higher rate of transition. 281 Therefore, the containment strategies need to be stronger than those required for Type I 282 cities. For example, in the absence of intensified testing, the degree of social distancing 283 required to buffer the pandemic is much higher in a Type II city (α=0.75) than in a type I 284 city (α=0.60). Similarly, only aggressive social distancing interventions combined with 285 intensified testing, i.e., (σ=0.6, α=0.3) or (σ=0.7, α=0.5) can mitigate the pandemic 286 progression in larger or denser cities (Type II). A summary of the results for different 287 combinations of scenarios is presented in Tables 2 and 3. We present scenarios for both 288 moderately and densely populated cities (Type I and II). Four different indicators are 289 calculated for each scenario, including the day of the epidemic peak, the number of new 290 infection cases at the epidemic peak, the cumulative number of symptomatic infections 291 after 120 days of the local pandemic onset (4 months), and the maximum bed occupancy. 292 293 . 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 June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint 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 June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint Table 2 . Effect of social distancing and testing in a city with a demographic density of 5,500 inhabitants/km 2 and a population of 3.5 × 10 6 307 persons these three cities has been made available by government officials. Interestingly, the 317 demographic characteristics of these major cities exhibit important differences, as well as 318 the types of counter-measures adopted to contain COVID-19. 319 Madrid (a Type-I city) and NYC (nearly a Type-II city) have practically extinguished the 320 pandemic. Therefore, the position and magnitude of the pandemic peak offers valuable 321 information to estimate values of the magnitude of social distancing (σ) and diagnostic 322 effort (α). In contrast, Mexico City has not reached the pandemic peak yet, and struggles to 323 contain COVID-19 in a challenging demographic situation. We found sets of parameters 324 that properly describe the evolution of COVID-19 in each of these cities, despite the 325 obvious differences in the behavior of each progression curve (Figure 4 ). For Madrid, our 326 simulations suggest that social distancing measures have achieved a degree of 58% of 327 reduction in population density (α=0.58). However, even considering these relatively 328 higher values of social distancing, an aggressive testing program (α=0.50) was needed to 329 bend the curve at a cumulative number of ~70,000 cases and reduce the emergence of new 330 cases to the current levels (less than 10 per day). This implies that overall approximately 331 50% of the active infected subjects were found and quarantined through testing. 332 We also fitted the model to the pandemic progression observed in NYC. NYC is a densely 333 populated area with a population mark of 8,400,000 inhabitants (i.e., nearly a Type-II city). 334 Therefore, only a combination of social distancing and intensified testing can stop 335 progression effectively (Table II) . Our results suggest that NYC has applied a strategy 336 mostly based on aggressive testing. 337 . 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 June 24, 2020. . 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 June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint effective reduction of 30% in demographic density) and a massive testing effort (α=0.98) is 345 the combination that better recapitulates the actual pandemic evolution in NYC. NYC is, 346 therefore, a remarkable example of the efficacy of massive diagnosis and quarantine, as a 347 city that was able to stop COVID-19 progression at a cumulative count of ~250,000 348 symptomatic subjects, which is about 25% of the maximum expected. In perspective, with 349 an effective distancing of 27% and no aggressive testing (i.e., α=0.50 instead of α=0.98), 350 the peak of bed occupancy in the city would have been three-fold higher, causing a total 351 collapse of the hospital system. Our results also show that demographic density is a key 352 factor in COVID-19 progression. Note that the testing effort in NYC was more intense than 353 in Madrid. However, NYC has double the demographic density of Madrid, resulting in a 354 higher number of those infected than in Madrid (250,000 versus 70,000). houses 25,000,000 inhabitants. From the scenarios simulated before (Figure 3) , we may 366 readily infer that only a combination of aggressive social distancing and massive testing 367 . 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 June 24, 2020. Here we introduce a mathematical model, based on demographic and clinical data that 381 enables evaluating the relative benefit of social distancing and massive testing. Using this 382 simple model, we investigate scenarios of COVID-19 evolution in two types of 383 representative cities (i.e., 3,500,000 inhabitants and 5,000 hab km 2 , and 5.0 X 10 6 384 inhabitants and 10,000 hab km 2 ). 385 Our modeling simulations show that for Type-I cities, extreme and sustained social 386 distancing (i.e., effectively decreasing the demographic density by 60% or more) may design/redesign of urban areas. The concept of sustainability and cost-effectiveness of 392 densely populated urban areas has to be revisited. Our results make explicit that large cities 393 are highly vulnerable to epidemic crisis. 394 In principle, this model can be adapted to any urban area by setting the population and 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. (which was not certified by peer review) The copyright holder for this preprint this version posted June 24, 2020. . https://doi.org/10.1101/2020.06.23.20138743 doi: medRxiv preprint based on a simple differential model, epidemiological data reported in literature (as detailed 416 in the text of the manuscript) and the local demographical density. 417 First Case of 2019 Novel Coronavirus in the United States Countries test tactics in "war" against COVID-19 COVID-19 case fatality rate: estimate using a fixed-effects model Allergy and Immunology Immune responses 428 in COVID-19 and potential vaccines: Lessons learned from SARS and MERS 429 epidemic Two-Year Prospective Study of the Humoral Immune Response of 431 Patients with Severe Acute Respiratory Syndrome H1N1 Influenza in Positive RT-PCR Test Results in Patients Recovered From COVID-19 SARS-CoV-2 Viral Load in Upper Respiratory Specimens of Infected 444 Presumed Asymptomatic Carrier Transmission of COVID-19 Global spread of COVID-19 and pandemic potential Severe acute respiratory 450 syndrome coronavirus 2 (SARS-CoV-2) The epidemic and the challenges Real-Time Estimation of the Risk of Death from Novel Coronavirus 453 (COVID-19) Infection: Inference Using Exported Cases Pathological findings of COVID-19 associated with acute respiratory 455 21 Clinical characteristics of COVID-19 patients with digestive symptoms 469 in Hubei, China: A descriptive, cross-sectional, multicenter study Facing Covid-19 in Italy -Ethics, Logistics, and Therapeutics on the Epidemic's Front Line How will 474 country-based mitigation measures influence the course of the COVID-19 epidemic? 475 Isolation, quarantine, social distancing and community containment: pivotal role for 477 old-style public health measures in the novel coronavirus (2019-nCoV) outbreak | 478