key: cord-0687892-gksv01nd
authors: Bandyopadhyay, A.; Schips, M.; Mitra, T.; Khailaie, S.; Binder, S.; Meyer-Hermann, M.
title: COVID-19 in Italy: targeted testing as a proxy of limited health care facilities and a key to reducing hospitalization rate and the death toll.
date: 2020-10-14
journal: nan
DOI: 10.1101/2020.10.12.20211169
sha: 09febc379eec8852d6dc9301b27e275208d9ec64
doc_id: 687892
cord_uid: gksv01nd

The novel Coronavirus SARS-CoV-2 (CoV) has induced a worldwide pandemic, notably in Italy, one of the worst-hit countries in Europe, which witnessed a death toll unseen in the recent past. There are potentially many factors, such as infections from undetected index cases, early vs late testing strategies, limited health care facilities etc., that might have aggravated the COVID-19 situation in Italy. We developed a COVID-19 specific infection epidemic model composed of susceptible (S), exposed (E), carrier (C), infected (I), recovery (R) and dead (D) (SECIRD), specifically parameterized for Italy to disentangle the impact of these factors and their implications on infection dynamics to help planning an effective control strategy for a possible second wave. Our model discriminates between detected infected and undetected individuals who played a crucial role in the disease spreading and is not well addressed by classical SEIR-like transmission models. We first estimated the number of undetected infections through a Bayesian Markov Chain Monte Carlo (MCMC) framework, which ranges from ~7 to ~22 fold higher than reported infections, depending upon regions. We exploited this information to evaluate the impact of the undetected component on the evolution of the pandemic and the benefits of an enhanced testing strategy. In high testing regions like Veneto, 18% of all infections resulted in hospitalization, while for Lombardia and Piemonte, it is 25% and 27%, respectively. We investigated the impact of an overwhelmed health care system upon death toll by applying hospital and intensive care unit (ICU) capacities in the SECIRD model, and we estimated a 10% reduction in death in Lombardia, the worst hit region, if a higher number of hospital facilities had been available since the beginning. Adopting a combined strategy of rapid early and targeted testing (~10 fold) with increased hospital capacity would help in avoiding bottlenecks affecting the health care system. Our results demonstrate that the early testing would have a strong impact on the overall hospital accessibility and, hence, upon death toll (~20% to 50% reduction) and could have mitigated the lack of facilities at the crucial middle stage of the epidemic.

The novel Coronavirus SARS-CoV-2 (CoV) has induced a worldwide pandemic, notably in Italy, one of the worst-hit countries in Europe, which witnessed a death toll unseen in the recent past. There are potentially many factors, such as infections from undetected index cases, early vs late testing strategies, limited health care facilities etc., that might have aggravated the COVID-19 situation in Italy. We developed a COVID-19 specific infection epidemic model composed of susceptible (S), exposed (E), carrier (C), infected (I), recovery (R) and dead (D) (SECIRD), specifically parameterized for Italy to disentangle the impact of these factors and their implications on infection dynamics to help planning an effective control strategy for a possible second wave. Our model discriminates between detected infected and undetected individuals who played a crucial role in the disease spreading and is not well addressed by classical SEIR-like transmission models. We first estimated the number of undetected infections through a Bayesian Markov Chain Monte Carlo (MCMC) framework, which ranges from ∼ 7 to ∼ 22 fold higher than reported infections, depending upon regions. We exploited this information to evaluate the impact of the undetected component on the evolution of the pandemic and the benefits of an enhanced testing strategy. In high testing regions like Veneto, 18% of all infections resulted in hospitalization, while for Lombardia and Piemonte, it is 25% and 27%, respectively. We investigated the impact of an overwhelmed health care system upon death toll by applying hospital and intensive care unit (ICU) capacities in the SECIRD model, and we estimated a 10% reduction in death in Lombardia, the worst hit region, if a higher number of hospital facilities had been available since the beginning. Adopting a combined strategy of rapid early and targeted testing (∼ 10 fold) with increased hospital capacity would help in avoiding bottlenecks affecting the health care system. Our results demonstrate that the early testing would have a strong impact on the overall hospital accessibility and, hence, upon death toll (∼ 20% to 50% reduction) and could have mitigated the lack of facilities at the crucial middle stage of the epidemic.

October 12, 2020 1/38

The COVID-19 outbreak created a worldwide pandemic causing more than 750,000 deaths and 2 over 21 million total cases worldwide as of August 15 th [1] . Until now, COVID-19 has killed more 3 people than SARS and MERS. Developing and deploying a safe and effective vaccine is a lengthy 4 process, and thus controlling the severity of coronavirus disease through a vaccine or targeted 5 therapy-though a major medical concern-is not envisioned in the short term. Alternatively, 6 non-pharmaceutical interventions (NPIs) are recommended in order to control the spread of 7 the disease and have been implemented by several governments, despite the huge economic loss 8 predicted by experts which might lead to a global recession [2] . From the experience of Wuhan, 9 strict measures can be effective in reducing the spread of the virus. How much these NPIs 10 help in the containment of the virus spreading is of high political and academic interest and 11 entirely depends upon the objectives of mitigation [3, 4] . Though different models of NPIs and 12 their implementation methods have been proposed, their impact and effectiveness on disease 13 dynamics are under scrutiny and remain a matter of global discussion [3, [5] [6] [7] [8] . On the contrary, 14 Singapore and Hong Kong were able to contain the virus by aggressive testing [9] , while South 15 Korea adopted a trace, test, treatment strategy [10] . Both strategies are effective and are equally 16 essential but not necessarily economically optimal. Differently, Japan avoided both lockdown and 17 extensive testing by isolating the whole contact clusters and by heavily relying on self-awareness 18 and discipline of the population to avert high-risk situations [11] . 19 The COVID-19 outbreak originated in Wuhan, People's Republic of China, in early December 20 2019. Within two months, it had erupted and unfolded with tremendous speed in Italy, which 21 became the European epicenter of the disease spreading, forcing the government to impose 22 a lockdown on March 9 th . On March 19 th , 3405 people had already died in Italy, thereby 23 surpassing China, while 35731 people were diagnosed as COVID-19 positive. This induced Italy 24 to shut down all non-essential businesses on March 21 st . Despite the strict measures applied, a 25 total of 32178 symptomatic people were hospitalized by April 8 th in Lombardia, accounting for 26 12976 hospital admissions, followed by Emilia Romagna (4130), Piemonte (3196), and Veneto 27 (1839) [12] . This led to the complete collapse of the health care system within a few weeks of 28 the first detection of COVID-19 cases, most notably in Lombardia where even funeral homes 29 had been overwhelmed and were incapable of responding in reasonable time [13] . Even though 30 the state expanded the hospital and intensive care unit (ICU) capacity, it could not prevent 31 a bottleneck of the health care system which may have caused a high number of deaths for a 32 prolonged time period. 33 There are potentially many reasons that might have aggravated the COVID-19 situation 34 in Italy, in particularly the distinct demographic structure of Italy when compared to other 35 European nations. In 2019, nearly 23% of the Italian population were aged 65 years or older [14] . 36 Moreover, the average household size and the prevalence of three-generation households are 37 larger in Italy compared to Germany [15] . Limited hospital and ICU capacity might also have 38 contributed to the high number of deaths and, hence, the high case fatality rate (CFR) when 39 compared to other countries. One of the major contributions to the infection spreading came from 40 the asymptomatic and mildly symptomatic infected groups, which mostly remained undetected. 41 At the beginning of the pandemic, Italy focused on testing symptomatic patients only, which 42 resulted in a high proportion of positive tests and high CFR compared to other countries [16] . 43 This left in the society a high proportion of undetected cases, which became a major driver of 44 new positive infections because of their unawareness, while the detected symptomatic cases were, 45 in general, systematically isolated. A different study estimates that in Italy the true number of 46 total infections is around 30 fold higher than that reported, while for Germany it is in the range 47 of six fold [17] (data up to March 17 th ). 48 The current study focuses on analyzing the impact of the targeted testing and limited hospital 49 and ICU capacity on the evolution of the pandemic in different Italian regions. Estimates of the 50 surge capacity of Italian ICUs are available [13, 18, 19] . Here, we developed a COVID-19 specific 51 October 12, 2020 2/38 infection epidemic model composed of susceptible (S), exposed (E), carrier (C), infected (I), 52 recovery (R), and dead (D) (SECIRD). In order to evaluate the COVID-19 situation in Italy in 53 a realistic framework, we first estimated the undetected fraction across different regions of Italy. 54 We used this undetected fraction to parameterize the SECIRD model for describing observed 55 infections, hospitalized, ICU and death dynamics. We studied the influence of undetected and 56 NPIs installed on the time-dependent reproduction number, R t . We analyzed the impact of the 57 overwhelmed health care system upon death toll by limiting hospital and ICU bed availability 58 in the SECIRD model and estimated that an extra 10% people died in Lombardia due to such 59 difficult circumstances. We estimated that the impact of a strategy combining targeted testing 60 with home quarantine (∼ 10 fold more isolation of infected) and a hospital capacity at its current 61 elevated state would have significantly reduced the death toll by circa 20% to 50%. 62 Methods

Data preprocessing 64 Demographic and mortality data are available from the Italian Institute of Statistics' (ISTAT) 65 website [20, 21] . ISTAT collects mortality data from the Italian National register office for 66 the resident population (ANPR). Daily deaths from 2015 to 2019 are available stratified by 67 gender and age. For 2020, data are available up to April 15 th , listing 6866 municipalities and 68 covering 86% of the Italian population. For each region, the municipalities listed include those 69 for which the death data set is complete and we, accordingly, extracted demographic data for 70 these municipalities. Here, we considered seven age groups: 0-20, 21-40, 41-50, 51-60, 61-70, 71 71-80 and 81+. For each region and for each age range, we counted the daily deaths for the 72 period January to April 15 th 2015-2020. We then summed up daily deaths of municipalities by 73 age groups. Similarly, from the demographic data we calculated the population size of each age 74 group. Due to the unavailability of demographic data for 2020, we used 2019 data as a proxy 75 of 2020. To calculate the Infection Fatality Rate (IFR) for Italy, we considered mortality and 76 demographic data of municipalities across all regions for which data are complete and followed 77 the same procedure.

Bayesian estimation of COVID- 19 IFR 79 To estimate IFR, we implemented maximum likelihood estimation for the binomial distribution 80 of the mortality rate under a Bayesian framework. Our model is adopted from [22] and modified 81 accordingly. The model assumes that the observed number of deaths in the COVID-19 period 82 (February 20 th to April 15 th ) of each year is binomially distributed according to: where a denotes the seven age groups, mentioned in the previous section and y denotes the 84 year. D a,y and N a,y denote total death and population of age a in year y, respectively. δ a is the 85 baseline death rate of age a and is heterogeneous across age groups. To model deaths in 2020, 86 in addition to δ a , we considered a COVID-19 death rate, δ Covid a multiplied with the exposed 87 fraction, θ. δ Covid a is the IFR of age a and it is assumed to be absent in the previous years. δ Covid a 88 is sampled from a uniform distribution with range between 0 and 0.2. The upper bound has been 89 chosen considering that the IFR, by definition, is equal or less than the CFR. For COVID-19, the 90 reported CFR is within the range of 5% to 15%. θ is the infection rate (IR) or attack rate and 91 denotes the fraction of the population that is exposed. As supported by a recent seroprevalence 92 October 12, 2020 3/38 study [23] it is assumed to be constant across all age groups. Moreover, seroprevalence studies 93 indicate that population-wide immunity is, in general, less than 50% [23] [24] [25] , thus we sampled 94 θ from a beta distribution for which the density peaks between 20% and 40%. In a nutshell, 95 we are estimating fifteen parameters (considering seven age groups), δ a , δ Covid a , and θ from the 96 observation of death data of previous years (2015-2020) classified by age groups (42 data points) 97 given the age distribution of population (2015-2020, 42 values). 98 We used the following priors to estimate the δ a , δ Covid a and θ: 99 δ a ∼ Uniform(0, 0.1) δ Covid a ∼ Uniform(0, 0.2) θ ∼ Beta (3, 5) For each region, the model was evaluated using the Markov Chain Monte Carlo (MCMC) 100 sampling method. We used 30 independent chains; each drew 50,000 samples from the joint 101 posterior distribution. We discarded the first 5000 as burn-in periods from each chain. We 102 merged the results of all 30 independent chains and calculated the 95% credible interval by using 103 the 95 th quantile of the posterior distribution. Trace plots of MCMC and posterior distribution 104 are available in the Supplementary Material (Fig. S3 ). The total number of infections for each 105 region was calculated from the definition of IFR, which is death over total infection. Here we 106 considered the number of deaths as the excess deaths of February 20 th to April 15 th with respect 107 to the average of the previous years (2015-2019). Simulation results are reproducible and were 108 carried out using R version 3.6.2 [26] [27] [28] [29] . 109 

To understand the impact of potential aggravating factors, namely infections from undetected 111 index cases, early vs late testing strategy, and limited heath care facilities on disease progression, 112 we adapted a COVID-19 specific SECIRD-model from [30, 31] and specifically parameterized 113 it for Italy. The SECIRD-model distinguishes healthy individuals without immune memory 114 of COVID-19 (susceptible, S), infected individuals without symptoms but not yet infectious 115 (exposed, E) and infected individuals without symptoms who are infectious (carrier, C I , C R ). 116 The carriers are distinguished into asymptomatic (C R ) and pre-symptomatic infected (C I ), 117 determined as α and (1 − α) portion of the exposed, respectively. The pre-symptomatic infected 118 are categorized into detected symptomatic (I H and I R ) and undetected mild-symptomatic (I X ), 119 determined as µ and (1 − µ) portion of the carrier (C I ). Out of the C I , ρ fraction required 120 hospitalization (I H ) and (1 − ρ) fraction are symptomatic but recover without hospitalization 121 (I R ). Further, compartments for hospitalization (H) and intensive care units (U ) were introduced 122 to monitor the load on the healthcare system. Similarly, ϑ and (1 − ϑ) represent the fraction of 123 H that requires ICU (H U ) or recovered from hospital (H R ), respectively. δ and (1 − δ) represent 124 the fraction of ICU who subsequently die (U D ) or recover (U R ). The recovered compartment (R) 125 consists of recovered patients from different states of the infection. The model is summarized 126 in SECIRD Model (Reference) Fig. 1 , with parameters in Table S1 . The model equations are 127 outlined in the Supplementary Material.

In order to understand the the number of secondary infections per primary case, we measured 129 time-varying reproduction number (R t ) [32] and how it is altered by different measures adopted 130 by society, we opted for fitting the data in one week shifting time windows. This approach has 131 two advantages: first, the reproduction number R t is determined as a time-dependent variable 132 and thus it will reflect the impact of NPIs on the infection dynamics; second, the moving-window 133 helps smoothing the evaluation of sudden jumps in the data, which most likely reflects reporting 134 delays. We further fine-tuned this approach by including the history of the viral spreading in 135 each time window, which is stored in the state space of the model in the previous window. In 136 each time window, a best fit of the model parameters was chosen based on the cost function 137 value (squared difference between data and simulation). In the next window, the state of the 138 model of the previous time window is used as initial condition for the subsequent fitting inside 139 the time window.

Testing Model but not yet infectious (exposed, E) and infected individuals without symptoms who are infectious (carrier, C R,I , asymptomatic and pre-symptomatic respectively), infected (I X,H,R ), hospitalized (H U,R ) and ICU (U D,R ) patients, dead (D) and recovered (R X,Z ), who are immune from reinfection. The data analysis of the clinical state of all infected cases (up to June 22 nd ) by ISS showed ∼ 30% asymptomatic cases, with an increasing tendency over time [33] [34] [35] . Moreover, in a study performed in Vo' Euganeo, Veneto, the percentage of asymptomatic cases was found to be ∼ 40% [36] . Therefore, we set the asymptomatic fraction α = 0.4 in the model. The previously October 12, 2020 5/38 estimated fraction of undetected cases,μ (see Estimation of undetected in Results section, Table  1 ) is by definition:μ

The R t formula at time window k reads [30] :

To generate confidence intervals for R t , we created an ensemble of altered systems by a random 141 modification of the parameters from their reference value such that the total parameter variation, 142 κ, defined as log(κ) = L n=1 |log kn

, is within 20% of its reference value. k n , k 0 n and L 143 represent the parameters of the altered system, the reference system and the total number of 144 parameters, respectively. We generated 30 perturbed parameter sets that can quantitatively 145 reproduce the observed data; and all statistical analysis were performed considering these 146 parameter sets. Parameter variations are reported in Fig. S4 and S10.

Testing model

In order to understand the influence of extra testing on infection dynamics, we adopted a model where a fraction of the undetected infected cases (I X ) is detected (I XD ) via testing and, hence, contained. The infectivity power of I XD decreases to β (β < 1) but the infectious period remains unaltered (1/R 4 ) (Testing Model in Fig. 1 and Table 2 ). We introduced a time-dependent undetected fraction µ , which decreases daily by 2%, starting fromμ and up to a fixed percentage, 60%. The asymptomatic fraction was fixed as in the Reference model (α = 0.4); the undetected portion of symptomatic is instead modified so that the fraction of undetected cases, µ 1 (t), and the fraction of newly detected cases, µ 2 (t), satisfy the following:

The parameters obtained by fitting the data with the Reference model were transferred into the Testing model. Transferring parameters maintains the compartmental flow as in the Reference model and thus ensures that the result reflects the sole effect of isolating a fraction of undetected infection. Correspondingly, the R t formula is modified as follows:

To estimate the impact of capacity limitations of the health care system, we implemented time-150 varying capacity constraints on the hospital (H lim (t)) and ICU (U lim (t)) accessibility (Capacity 151 Model in Fig. 1 and Table 2 ) in the SECIRD model, using the available data on the number of 152 hospital and ICU beds in the different regions (Table 3) .

153 Table 3 reports the pre-pandemic capacity and the increased capacity, specifically allocated 154 to COVID-19 patients, with the installation dates. Some regions doubled their capacity and, 155 presumably, this extension of infrastructure has been implemented in a stepwise manner. We 156 assumed a linear increase of the hospital (H lim (t)) and ICU (U lim (t)) capacity from three days 157 prior to their exhaustion until the installation date, so that it reached the maximum allowed 158 capacity on the installation date. This new limit is available thereafter. The exhaustion date is 159 determined from the data and refers to the day at which the number of hospitalized and ICU 160 patients overcomes the initial capacity. In addition, it was reported that pre-pandemic, overall, 161 85% hospital beds and 50% ICU beds are occupied [38] . In the Capacity model, the remaining 162 percentage of the pre-pandemic capacity (Table 3) has been considered as the baseline capacity 163 of hospital and ICU beds, i.e. the starting values of H lim (t) and U lim (t), respectively.

In the model we introduced the I D compartment, where the flux from I H is directed when the hospital capacity is reached. Access to the hospital or ICU of the patients is driven by sharp exponential functions:

f Hlim (t) drives the flow of the infected population into I D when the hospital capacity is reached, 165 while f Ulim (t) drives a fatal outcome for patients in need of ICU when the ICU reaches its 166 capacity. We assumed that inaccessibility of hospital or ICU leads to faster death. In particular, 167 when the ICU capacity is reached, people in the hospital compartment (H U ) die after 1/R 7 days 168 which is less than hospital-ICU-dead route (1/R 7 + 1/R 10 ). Similarly, when the hospital capacity 169 is reached, people in the infected compartment (I H ) die after 1/R 6 + 1/R 7 days, satisfying 170 1/R 6 < 1/R 6 + 1/R 7 < 1/R 6 + 1/R 7 + 1/R 10 (see SECIRD models in the Supplementary).

The MaxCap model is defined by the same equations as the Capacity model, but the 172 parameters, U lim and H lim are set at the maximum ICU and hospital limits, respectively, from 173 the beginning of the simulations to represent a health care system not overwhelmed.

The parameters in the model are classified in physiological and fractional parameters. Physiologi-176 cal parameters are those whose value mainly depends on the nature of the virus (R x , x = 2, . . . , 10). 177 We first determined the range of the physiological parameters, except death rate (R 10 ), based 178 on a literature search [39, 40] (Table S1 ) and then estimated their value by considering the first 179 two weeks' data points, representative of the exponential growth phase. In the course of the 180 pandemic, factors like NPI installation, change in detection and treatment strategies, public 181 awareness and self-isolation,and hospital accessibility substantially alter the disease dynamics by 182 impacting the transmission probability, the amount of undetected infected in the system and 183 the death rate. Fractional parameters (ρ, ϑ, δ), together with R 1 and R 10 , are the parameters 184 affected by these contingent factors. The parameters α and µ have been previously discussed 185 (see SECIRD-model and basic reproduction number section in Methods). 186 We estimated model parameters by minimizing the sum of squared differences between 187 the observed data (infected, hospitalized, ICU patients and death numbers (Italy Data on 188 Coronavirus 2020 [41])) and model simulation using Matlab's nonlinear least-squares optimizer. 189 The method was repeated separately for each region in Italy. We opted for a moving time window 190 with the size of 7 days to account for temporal changes in disease transmission. The values of 191 R x , (x = 2, . . . , 9) were kept constant throughout the window fitting. Fractional parameters 192 (ρ, ϑ, δ), R 1 and R 10 were fitted in each window. 

Estimation of undetected cases 197 The severity of an epidemic can be characterized by the case fatality rate (CFR), defined 198 as the percentage of deaths among the total number of diagnosed infections, and has been 199 of high interest since the very beginning of the COVID-19 outbreak [44, 45] . On the other 200 hand, infection fatality rate (IFR) is defined as the percentage of deaths among all infections, 201 including the undiagnosed infections. For COVID-19, the true number of cases is unknown 202 as a substantial portion of the infections are either asymptomatic or mildly symptomatic and 203 remained undetected [46, 47] . At the beginning of the pandemic, testing was limited only to the 204 symptomatic patients due to clinical findings suggesting that symptomatic cases are the major 205 source of disease spreading [48] [49] [50] [51] [52] . It is, therefore, very difficult to get a reliable estimate of 206 the true number of infections. A few methods have already been proposed to quantify the true 207 number of infections and, hence, a realistic IFR [53] [54] [55] . [56] . In Fig. S1 we show region-wise, weekly deaths from January 1 st to 215 April 15 th 2020. For the Italian regions where the pandemic started, like Lombardia, Veneto, 216 Piemonte, the observed mortality of this year was substantially higher than previous years. For 217 these regions, we estimated the total infection and associated IFR by implementing a Bayesian 218 framework by adapting a standard binomial model (see Methods and [22] ).

After the first identification of a COVID-19 case on February 20 th 2020 in Codogno Hospital, 220 near Lodi, Lombardia [19] , the number of reported positive cases increased to 36 in the next 24 221 hours and, interestingly, the new cases were not linked to the first case, suggesting that the virus 222 was circulating before its first identification. This is reflected in our estimation of undetected 223 cases (Table 1) . High increases in death over this year were observed in some cities, like Bergamo 224 (568%), Cremona (391%), Lodi (371%), Brescia (291%), Piacenza (264%), Parma (208%) [56] . 225 In the northern regions of Italy, especially where the initial outbreak occurred, for example in 226 Emilia Romagna, Piemonte and Veneto, undetected infections were nearly 10 fold higher than 227 the reported cases; and in Lombardia more than 21 fold. We observed substantial heterogeneity 228 of the IFR across different age groups. For the age ranges below 60, it was determined as low as 229 0.05%. IFR was substantially higher in the 81+ age group (9.5% to 20%) and very stringent 230 across the regions (Fig. S2 ). Despite Italy having the highest COVID-19 deaths in Europe, 231 estimated infection rates (IR) were relatively low (highest in Lombardia ∼ 13%) across all 232 regions, and hence the population was far from reaching the herd immunity threshold (∼ 70%, 233 assuming no previous immune memory). Our estimated total infections (detected + undetected) 234 are close to the numbers reported in [55, 57] .

Correlation between undetected cases and test frequency 236 Despite being hit hardest by COVID-19, some of the Italian regions handled this crisis situation 237 better and managed to contain the virus. For instance, in Veneto, CFR was 6.4%, 3 fold lower 238 when compared to Lombardia at 18.3%. This is also reflected in the IR, 2.61% in Veneto while in 239 Lombardia it was 13% despite their geographical proximity. The testing strategy implemented by 240 these two regions was completely different. Most regions, like Lombardia and Piemonte, followed 241 the World Health Organization (WHO) and central health authority indications by mainly testing 242 the symptomatic cases, while Veneto implemented a much more extensive population testing. 243 Toscana followed a testing strategy very similar to Veneto by ramping up its testing capacity 244 October 12, 2020 8/38 . We opted for a moving time window of 7 days to smooth out the reporting delays that 264 might induce artificial fluctuations (see Methods). We then shifted the window by one day and 265 evaluated the current window by using the result of the previous window as the initial state. We 266 followed the same procedure for 30 different parameter sets. Parameter variation for Italy is 267 shown in Fig. S4 . 268 We then used the fitted parameters to obtain the time-varying reproduction number, R t 269 (Fig. 3B) . The sudden increase in reported cases resulted in an overshoot in the R t curve at the 270 beginning. As nationwide NPIs were installed, public awareness increased and people started 271 self-isolation and social distancing measures, the reproduction number continuously decreased, 272 approaching unity at the end of April. In the regions with many undetected infections, like 273 Emilia Romagna, Lombardia and Piemonte, the reproduction number reached unity in the first 274 week of May, while in Veneto and Toscana it reached unity in the middle of April and was 275 substantially lower by the first week of May. As R t functionally depends upon many factors (see 276 R t formula in the Methods section), we opted for a sensitivity analysis to find the important 277 factors that regulate R t . Sensitivity analysis revealed that R t is highly sensitive towards the 278 changes in R 1 andμ (Fig. S7 ). The impact of installed NPIs and, hence, R 1 is embedded within 279 the decreasing proclivity of R t across the different regions. The impact of the undetected cases 280 on the R t evolution can as well be inferred through the SECIRD model by comparing the R t of 281 October 12, 2020 9/38 . CC-BY-NC 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 October 14, 2020. the Reference model with a model having lower undetected cases. With this aim, we defined the 282 Asymptomatic model by imposingμ = α, µ = 1.

In the Asymptomatic model, all symptomatic infections are detected and, hence, their 284 infectivity is reduced (β < 1). The lack of the higher infectivity power compartment, I X , 285 causes a lower turnover from susceptible to exposed. This effect is apparent in the initial phase 286 October 12, 2020 10/38 . CC-BY-NC 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 October 14, 2020. . of the pandemic, when R t curves resulting from the Asymptomatic are much lower than the 287 R t curves resulting from the Reference model (blue boxplot and red boxplot, respectively, in 288 Fig. 3 ). On the long term, instead, the R t curves from the two models converge, despite the 289 fraction of undetected cases being constant throughout the simulations:μ for the Reference 290 and α for the Asymptomatic. This is consistent with the effect of the restriction measures, 291 limiting the spreading through undetected cases. The difference in the R t curves of these two 292 models is higher in the pre-lockdown period and it vanishes over time. Thus, the influence 293 of undetected infections on R t wanes (Fig. 3B) , most likely as a result of restricted mobility 294 following nationwide lockdown. This illustrates the effectiveness of lockdown in the containment 295 of the disease. 

Quantify the effect on hospital rates and death toll of reduced amount of undetected fraction As the impact of undetected cases on R t faded with time, we aimed at identifying and quantifying 298 the benefit of track, test, and isolate (TTI) at early and late phases of the pandemic. We simulated 299 three hypothetical situations where a TTI strategy begins one week before the lockdown (March 300 2 nd ), the day after the lockdown (March 10 th ), and one week post lockdown (March 15 th ). In 301 each scenario, we assumed that enhanced testing resulted in a 2% daily decrease of the undetected 302 fraction starting from its estimated value (Table 1) to 60%. In the SECIRD model, we considered 303 that a fraction (µ 2 (t)) of symptomatic undetected cases, I X , is detected (I XD ) , and hence is less 304 infectious (β, see Methods, Fig. 1 , Testing model in Table 2 ). To ensure that the altered infection 305 dynamics is due to the reduction of undetected cases, we maintained the compartmental flow of 306 the SECIRD model by using the parameter set of the Reference model complemented with a 307 sequential decrease of the fraction of undetected cases µ (t) starting from the estimated fraction 308 µ (Table 1) . This setting will help to elucidate the impact of isolating undetected infections that 309 could be achieved by targeted testing and home quarantine of contact clusters around identified 310 infections. This in silico experiment resulted in a substantial increase in the number of detected 311 infections but reduced the number of infected people that subsequently require hospital access. 312 The early detection scenario showed up to 27% reduction in the hospitalized compartment, which 313 reduced death numbers by up to 41% ( Fig. 4A -B) depending upon the region and how early 314 testing starts. The increase in the total infected is due to the extra detection of undetected 315 infections and not new infections. This can also be recognized in R t (Fig. S8 ): though the 316 total number of infections is drastically higher than the actual reported infections, R t falls 317 sharply and for Italy it reaches unity three weeks earlier. This result implies that track, test 318 and isolation of suspected positives can be an effective strategy to substantially decrease disease 319

October 12, 2020 11/38 . CC-BY-NC 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 October 14, 2020. propagation. South Korea mounted a targeted testing strategy to contain the disease spreading 320 without imposing strict measures, like lockdown, immigration control etc [10] .

Having established from the model that increasing detection and isolation lowers hospital-322 ization rates, we investigated whether the same relation can be inferred from the data. We 323 October 12, 2020 12/38 . CC-BY-NC 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 October 14, 2020. . calculated the correlation between the median hospitalization rate, defined as the ratio of the 324 sum of the hospital plus ICU patients to the total reported cases, and the total number of 325 tests performed per capita up to May 21 st , 2020 (Fig. 4C ). This data analysis confirms a 326 lower hospitalization rate in high test performing regions. High testing regions, like Veneto or 327 Friuli, exhibited hospitalization rates of 15% and 7%, respectively, in contrast to Lombardia 328 and Piemonte with 25% and 27%. Of note, Veneto performed about twice more tests per head 329 than Lombardia which reduced new cases from undetected index cases and subsequently their 330 hospital access, and was sufficient to induce the significant drop in the hospitalization rate. 331 This qualitative behavior indicates that testing substantially confined the COVID contagion by 332 undetected cases. Our in silico experiment shows the cumulative effect of decreasing undetected 333 cases, which is seen in the decreased peak of hospitalization depending upon how early testing 334 begins.

Capacity model and excess dead due to the shortage of hospital beds 336 Besides installing NPIs and recommending social distancing and self-isolation, strengthening 337 the health care system is also an inevitable part of the government response. According to the 338 data published by the Italian Ministry of Health, before the pandemic started Italy had 3.18 beds 339 per 1000 people with an average occupancy of 75-90% [38], while Germany had 8 beds per 1000 340 people with ∼ 77% occupancy [14] . During this crisis, between March 1 st and March 11 th , 2020, 341 9-11% infected people were daily admitted to ICU. Out of ∼ 5200 ICU beds (pre-pandemic) in 342 Italy, 2500 were already filled by March th . To cope with this critical situation, each region had 343 planned to boost the hospital and ICU facilities (Table 3) . Despite the considerable increase 344 in hospital and ICU capacity, the unexpected huge wave of patients and the necessary time to 345 adapt the facilities presumably complicated the crisis management.

October 12, 2020 13/38 . CC-BY-NC 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 October 14, 2020. Adapting SECIRD, we developed the Capacity model by imposing limits on the hospital 347 and ICU accessibility (Capacity Model in Fig. 1 and Table 2 ). Considering the occupancy of 348 hospitals and ICUs (85% and 50%, respectively [38]), the baseline number of hospital and ICU 349 beds was set at 15% and 50%, respectively, of the total number of beds pre-crisis (Initial hosp. 350

October 12, 2020 14/38 . CC-BY-NC 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 October 14, 2020. . https://doi.org/10.1101/2020.10.12.20211169 doi: medRxiv preprint q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q and Initial ICU in Table 3 ).

To represent the increase of capacity during the crisis, we used a linear function with a daily 352 increment so that the capacity reaches its target value in the simulation at the same date as in 353 each region (ICU installed and Date and Hosp. installed in Date in Table 3 ). In addition to 354 imposing the new day-wise capacity onto the SECIRD model, we considered a sharp exponential 355 function (see Methods) to stop the inflow into the hospital and ICU compartments on reaching 356 capacity. We assumed that the unavailability of hospital or ICU beds leads to faster death. We 357 estimated the parameters describing the data with the Capacity model using the same protocol 358 applied to estimate parameters for the Reference model (Fig. 5) . By perturbing the parameters 359 and refitting the data, we generated 30 different parameter sets (Parameter variability is shown 360 in Fig. S10 for Lombardia).

To quantify the impact of the limited hospital capacity on COVID-19-associated deaths, we 362 defined the MaxCap model where the hospital and ICU capacities were fixed at their maximum 363 from the very beginning. The compartmental flow in both models was kept identical by using 364 the same parameter set as for the Capacity model. We quantified the impact of the limited 365 capacity on COVID-19-associated deaths by subtracting the death numbers of the MaxCap 366 model from the Capacity model. This difference represents the number of people that would have 367 benefited from a system with a substantially higher capacity at the beginning of the epidemic. 368 The effect of limited health care facilities was dramatic in Lombardia with a ∼ 10% difference in 369 the number of deaths, corresponding to ∼ 1500 people. 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 October 14, 2020. In a realistic scenario, many regions adopted parallel strategies: they ramped up facilities to test 372 the immediate contacts of an identified infection (tracking and testing, e.g., Veneto [59] ); and 373 also planned expansions of health care facilities to accommodate more patients. In light of the 374 reduction in hospitalization and death numbers by extending the track, test, and isolate (TTI) 375 strategy (result of the Testing model, Fig. 4A ,B) and the reduction in fatalities by increasing the 376 number of hospital facilities (result of the Capacity model, Fig. 5B) , we aimed at quantifying 377 effects of combining increased hospital capacities with the TTI and considered four scenarios: Thereby, earlier/later was assumed one week before/after the lockdown. To simulate scenarios 383 1 and 2, we transferred the Capacity model parameters into the TestCap model (Table 2) to 384 keep the compartmental flow intact. To simulate scenarios 3 and 4, we reevaluated the TestCap 385 model assuming the hospital and ICU capacity at their maximum levels from the beginning. In 386 all scenarios, improved TTI was simulated as step-wise reduction of the fraction of undetected 387 cases by 2% of the symptomatic undetected cases per day (µ (t), Testing model in Methods). 388 Given the data, this decrease would be equivalent to ∼ 10-fold increased detection. 389 Fig. 6 reveals several interesting facets. Previously, we had estimated that in Lombardia 390 a 10% reduction of deaths could be achieved by improved hospital infrastructure (Fig. 5B) . 391 Boosting hospital capacity with early TTI further reduced death numbers by a significant 392 amount, which ranged from ∼ 19% to 51% across different regions ( Fig. 6 and S11). Early TTI 393 with ∼ 5 fold more testing reduced hospitalization up to ∼ 12%, with a subsequent decrease of 394 death toll up to ∼ 22% (Fig. S12) . This supports the importance of early TTI in controlling the 395 pandemic. Moreover, TTI proved more potent than increasing hospital capacities in limiting the 396 death toll. Even in the late TTI scenario, our simulation shows a decrease in the death number 397 up to 30% (Fig. 6 ) depending on the region. Of note, adopting an early TTI strategy brings 398 the frequency of hospitalizations down close to the initial hospital capacity before extending 399 the infrastructure (Fig. 6 ). An exception is Lombardia, where adopting an early TTI strategy 400 led to ∼ 18% reduction in the necessity of hospitalizations, while the late TTI strategy did not 401 decrease the simulated peak number of hospitalizations and led to a situation similar to what 402 actually happened. Though the peak size remained unchanged in Lombardia in the late TTI 403 scenario, simulations showed a reduction in the number of deaths of ∼ 18%, reaching ∼ 26% 404 when combined with an increased hospital capacity.

More testing reduced the frequency of hospitalizations in all regions as is evident from Fig. 4C . 406 These results indicate the importance of early detection and isolation of suspected cases, which 407 substantially reduce the hospitalization rate and could partially compensate for limited health 408 care facilities at the crucial middle stage of the epidemic. On the other hand, despite the strong 409 reduction of hospitalizations and the peak number of deaths, such an early TTI strategy would 410 not suffice to contain the needed number of hospitalizations within the initially available facilities 411 (purple line, Fig. 6 ). This finding emphasizes the urgent need of extending hospital infrastructure 412 to prevent an overwhelmed health care system.

Herd immunity projection 414 In order to prepare for a putative second wave of the epidemic, it is helpful to estimate our 415 current standing in terms of immunization of the population. Previously, considering the death 416 data provided by ISTAT up to April 15 th 2020, we showed by IFR calculation that the IR was 417 October 12, 2020 16/38 . CC-BY-NC 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 October 14, 2020. ∼ 13% and 10% in Lombardia and Italy, respectively. The fraction of infected people can also 418 be inferred from the SECIRD model. Considering 93% and 95% undetected cases for Italy and 419 Lombardia, respectively, it can be shown from the SECIRD model that the fraction of the people 420 infected up to April 15 th , 2020 is close to the range of estimated IR through our Bayesian MCMC 421 framework (vertical black line in Fig. 7 ). This calibration ensures that a reliable projection of 422 total infected people can be made using the SECIRD model. To this end, we considered two 423

October 12, 2020 17/38 . CC-BY-NC 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 October 14, 2020. . https://doi.org/10.1101/2020.10.12.20211169 doi: medRxiv preprint hypothetical scenarios. First, the undetected fraction is fixed throughout the epidemic. Second, 424 the fraction of undetected cases decreases slowly starting 7 days post lockdown. Considering 425 constant 90% undetected cases, only Lombardia is close to the herd immunity threshold of 70%; 426 in Italy and Veneto only 13% and 10% of the population was infected, respectively. Considering 427 the more realistic scenario where the fraction of undetected cases fades away with time by 428 lockdown measures or public awareness, our model estimated a fraction of 4%, 10%, and 2% of 429 infected people in Italy, Lombardia, and Veneto, respectively. The nationwide predicted total 430 number of infected people is close to the reported number of a recent nationwide seroprevalence 431 study carried out on 64660 people by ISTAT and the Ministry of Health [23] . 432 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q (Table 1 ).

The COVID-19 pandemic placed a huge social and economic burden on the Italian government 434 and thus confronted policymakers with a dilemma in setting the main objectives of mitigation, 435 e.g., minimizing morbidity and contingent mortality, avoiding an epidemic peak that overwhelms 436 health-care services, minimizing economic loss, and flattening the epidemic curve before a 437 vaccine is made available. Achieving everything by a single intervention is likely to over-promise, 438 especially for the COVID-19 pandemic. One unique feature of COVID-19 is that its serial interval 439 is shorter than its median incubation period and it is shorter than SARS. Thus, substantial 440 secondary infections may occur prior to disease onset [46] . This leads to the rapid spread of 441 the disease by asymptomatic carriers. In order to control the undetected fraction and the 442 spreading through asymptomatic and pre-symptomatic carriers, a rigorous and effective testing 443 strategy is required. The assumption of central health authorities that symptomatic patients 444 are the dominant disease spreaders [60] and the decision of focused testing of symptomatic 445

October 12, 2020 18/38 . CC-BY-NC 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 October 14, 2020. . patients only has proven to be an insufficient and ineffective strategy as it puts the whole society 446 at risk by reducing the effectiveness of the containment measures imposed at the beginning. 447 Besides implementing NPIs, improving health care facilities is also a part of the government 448 response. Demographically, the Italian population is different than other EU member states, 449 with a substantially older age population, more households containing multiple generations, and 450 a higher occupancy of hospital and ICU beds. COVID-19 is most lethal in older patients and 451 aggravated the health of patients with pre-existing conditions. Moreover, historically, hospital 452 beds per 1000 inhabitants have decreased by 16% since 2010 in Italy, compared to only 3% [14] 453 in Germany. This shortage of hospital beds might also have exacerbated the COVID-19 situation 454 in Italy.

Our retrospective study reveals many lessons that can be learned from the COVID-19 situation 456 in Italy. Though containment measures are necessary to reduce the exponential growth of the 457 pandemic and flatten the infection curve as early as possible, lockdown alone is not sufficient to 458 control the pandemic and cannot be a long-term plan; neither is it recommended by economists, 459 especially in low and middle-income countries [61] . The power of lockdown lies in restricting the 460 mobility and contacts, reducing the spreading from the mainly asymptomatic undetected infected 461 cases, which results in a general containment of virus spreading. Alternatively, the outcome of 462 the extensive targeted testing strategy adopted by Veneto and Toscana has shown the efficacy 463 in containing the COVID-19 contagion: these two regions contained the undetected fraction and 464 managed to flatten the infection curve one month earlier than Lombardia and Piemonte. Many 465 other countries like Hong Kong, South Korea, Taiwan have successfully flattened the infection 466 curve and controlled regional outbreaks without implementing a strict lockdown. This confirms 467 the effectiveness of a screening strategy and maintaining social distancing. Importantly, we 468 showed that a massive increase in testing significantly reduces the infection transmission and 469 would ultimately reduce the infection to hospitalization rate, which consequently helps easing 470 the pressure on the health care facilities. We showed that ∼ 10 fold more testing would release 471 enormous pressure from health care facilities, which in turn significantly reduces the death toll. 472 However, the ∼ 10 fold increased testing demands huge testing facilities and is not an economic 473 strategy. Moreover, successful detection depends upon the subject getting tested, and their 474 previous travel and contact history. Alternatively, tracking and targeted testing with home 475 quarantine of possible cases significantly reduce infection transmission and could be adopted 476 instead of rapid mass testing. A more effective strategy would be to put the whole contact 477 cluster into isolation, which Japan adopted [11] . It has to be emphasized that the impact of 478 testing on the spreading of infections is based on the isolation of positively tested individuals. 479 This implies that contact tracing and quarantine without testing would have a similar effect and 480 might be an efficient strategy when sufficient test capacities are not available.

In the middle of the crisis, many health care workers were infected with COVID-19 while 482 treating COVID-19 patients, and the voluntary participation of interns and retired personnel 483 was required. Moreover, delays in testing of health care personnel led to the spread of infection 484 through health care workers. Regular testing of healthcare workers in hospitals and in retirement 485 homes is mandatory to avoid the spread of infection. Improvements in the capacity of hospital 486 and ICU beds is urgent given the aging population [62] . In our model, we have shown that a 487 substantial portion of the death toll could have been prevented by targeted testing and this 488 could have mitigated the effects of limited health care facilities at the crucial middle stage of 489 the pandemic, though it would not have contained the hospitalization within its pre-pandemic 490 limit. Hence, the bottleneck of health care facilities could hardly have been avoided by adopting 491 massive testing alone. We have estimated that we are far from reaching the herd immunity 492 threshold. Thus we believe that the combination of increased detection and isolation of suspected 493 cases, together with improved health care facilities, could reduce mortality in a possible second 494 wave without implementing a strict lockdown.

October 12, 2020 19/38 . CC-BY-NC 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 October 14, 2020. Prevenzione Sanitaria presso Ministero della Salute, for responding to our requests in time and for 500 sharing data of hospital and ICU capacities. We thank Rebecca Ludwig for thoughtful discussion 501 and comments on the manuscript. This project has received funding from the European Union's 502 Horizon 2020 research and innovation programme under grant agreement No 101003480 and the 503 Initiative and Networking Fund of the Helmholtz Association. The funding bodies had no role 504 in the design of the study, collection, analysis, and interpretation of the results, or writing the 505 manuscript. . CC-BY-NC 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 October 14, 2020. 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 October 14, 2020. , θ, we used following priors: Uniform(0,0.1), Uniform(0,0.2), Beta (3, 5) . Of note, heterogeneity in δ Covid a distribution is increasing with age.

October 12, 2020 26/38 . CC-BY-NC 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 October 14, 2020. . CC-BY-NC 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 October 14, 2020. Table S1 were used and the transmission rate, R 1 , death rate, R 10 and fractional parameters (ρ, ϑ, δ) were varied in each time window (see Methods); dots: data; continuous lines: simulation results.

October 12, 2020 28/38 . CC-BY-NC 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 October 14, 2020. Vertical lines correspond to the Lockdown imposition (green) and release (magenta). Black dotted horizontal line represents R t = 1.

October 12, 2020 29/38 . CC-BY-NC 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 October 14, 2020. . https://doi.org/10.1101/2020. 10.12.20211169 doi: medRxiv preprint R t Sensitivity Fig S7: R t sensitivity. Sensitivity of R t is performed by perturbing each parameter 30% of its reference value and by simulating the Reference model up to three months. Boxplot represents the variation in R t from its reference point. R t is highly sensitive to R 1 andμ.

October 12, 2020 30/38 . CC-BY-NC 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 October 14, 2020. October 12, 2020 31/38 . CC-BY-NC 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 October 14, 2020. . CC-BY-NC 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 October 14, 2020. . CC-BY-NC 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 October 14, 2020. . CC-BY-NC 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 October 14, 2020. . https://doi.org/10.1101/2020.10.12.20211169 doi: medRxiv preprint q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 8.21%

1.19% q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 2.9% 0.55% q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 12.15% 2.62%

Emilia Romagna Lombardia Piemonte Early Late q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 15.08% 6% q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 18.45%

6.02% q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q is reduced starting one week before the lockdown (Early, green) or one week post lockdown (Late, light blue), resembling ∼ 5 fold more testing than the average tests performed per day.

Hospitalized is the sum of hospital and ICU patients. The reduction in Hospitalized peak and Dead number with respect to the data (red dots) has been reported as percentage. The purple horizontal line is the capacity (Hospital + ICU) before the pandemic. 5 times more testing with highest hospital beds would have decreased hospitalised at later stage of epidemic and would have saved ∼ 15% − 23% of infected people.

October 12, 2020 35/38 . CC-BY-NC 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 October 14, 2020. . https://doi.org/10.1101/2020.10.12.20211169 doi: medRxiv preprint SECIRD models Reference model equations: Equations of the Reference model used to fit the data ( Fig.  3A and Fig. S9 ) and to evaluate R t (Fig. 3B and Fig. S6) .

dR X dt = R 9 C R + R 4 I X (13)

Testing model equations: Equations of the Testing model used to quantify the impact of the undetected reduction on the Hospitalised and Dead compartments (Fig. 4A ,B) and on the R t curve (Fig. S8 ). It includes an additional compartment (I XD ) with respect to the basic Reference Model which represents the additional Detected Infected.

October 12, 2020 36/38 . CC-BY-NC 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 October 14, 2020. . https://doi.org/10.1101/2020.10.12.20211169 doi: medRxiv preprint dS dt = −R 1 (t) (C I + C R + I X + β(I H + I R + I XD )) N S dE dt = R 1 (t) (C I + C R + I X + β(I H + I R + I XD )) . CC-BY-NC 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 October 14, 2020. . https://doi.org/10.1101/2020.10.12.20211169 doi: medRxiv preprint dS dt = −R 1 (t) (C I + C R + I X + β(I H + I R + I XD )) N S dE dt = R 1 (t) (C I + C R + I X + β(I H + I R + I XD )) . CC-BY-NC 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 October 14, 2020. . https://doi.org/10.1101/2020.10.12.20211169 doi: medRxiv preprint

COVID-19: Socio-economic impact

Mitigation strategies for pandemic influenza A: balancing conflicting policy objectives

Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand. Imperial College preprint

The effect of multiple interventions to balance healthcare demand for controlling COVID-19 outbreaks: a modelling study

Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions

Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe

The Common Interests of Health Protection and the Economy: Evidence from Scenario Calculations of COVID-19 Containment Policies. medRxiv

How will countrybased mitigation measures influence the course of the COVID-19 epidemic?

Information Technology-Based Tracing Strategy in Response to COVID-19 in South Korea-Privacy Controversies

Japan ends its COVID-19 state of emergency

Covid-19 Italy situation report

COVID-19 and Italy: what next?

Organisation for Ecnomic Co-operation and DEvelopment (OECD)

More than 10% of households in Romania, Latvia and Bulgaria were three-generation in 2008

Estimates of the severity of coronavirus disease 2019:a model-based analysis. University of Goettingen

COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability. medRxiv

Critical Care Utilization for the COVID-19 Outbreak in Lombardy, Italy: Early Experience and Forecast During an Emergency Response

An empirical estimate of the infection fatality rate of COVID-19 from the first Italian outbreak

Primi risultati dell'indagine di sieroprevalenza sul SARS-CoV-2; 2020

High SARS-CoV-2 Seroprevalence in Children and Adults in the Austrian Ski Resort Ischgl. medRxiv

SeroTracker: a global SARS-CoV-2 seroprevalence dashboard. The Lancet Infectious Diseases

R: A Language and Environment for Statistical Computing

MCMCvis: Tools to visualize, manipulate, and summarize MCMC output

CODA: Convergence Diagnosis and Output Analysis for

R2WinBUGS: A Package for Running WinBUGS from R

Estimate of the development of the epidemic reproduction number Rt from Coronavirus SARS-CoV-2 case data and implications for political measures based on prognostics

Complete and up-to-date analysis of Germany and all federal states

A new framework and software to estimate time-varying reproduction numbers during epidemics

Sorveglianza Integrata COVID-19 in Italia

Sorveglianza integrata COVID-19: archivio

Aggiornamento nazionale 15 settembre 2020

Suppression of a SARS-CoV-2 outbreak in the Italian municipality of Vo'

Clinical features of patients infected with 2019 novel coronavirus in Wuhan

Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia

Estimates of the severity of coronavirus disease 2019: a model-based analysis

COVID-19: Recovering estimates of the infected fatality rate during an ongoing pandemic through partial data. medRxiv

How deadly is COVID-19? A rigorous analysis of excess mortality and age-dependent fatality rates in Italy

Using mobility to estimate the transmission intensity of COVID-19 in Italy: a subnational analysis with future scenarios

Ministero della Salute

Materia: Sanità e igiene pubblica

Impact of lockdown measures on the informal economy A summary

Intensive care management of coronavirus disease 2019 (COVID-19): challenges and recommendations