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COVID-19 vs. MoMoThe COVID-19 official deaths and MoMo ED time series overlaped for the period from 3 March 2020 to 1 January 2021 for Spain and its 19 regions (Fig. 2). In general, there was good agreement between both datasets, meaning that most of MoMo ED were related to COVID-19 deaths. During the first wave, the most important differences were observed in Spain, Madrid, Cataluña, Castilla-La Mancha, and Castilla y León. Before 22 June in Spain, MoMo ED showed 15,445 accumulated deaths more than the official COVID-19 deaths, which is beyond the error band. That difference comes basically from the four regions with the largest numbers of deaths (Madrid, Cataluña, Castilla-La Mancha, and Castilla y León). Table 1 shows the accumulated values before 22 June, which were used to estimate the CFR for Spain and its 19 regions according to the third phase of the National Seroprevalence Study4,5. For all regions, the CFR estimated from MoMo ED was larger than the CFR estimated from COVID-19 deaths. In particular, Asturias, Canarias, and Murcia were twice as large. Ceuta and Melilla dramatically increased their CFR from MoMo ED, although that may be biased due to their small populations and numbers of deaths.Similarly, the same variables for the period from 23 June to 29 November 2020 are reported in Table 2. In Spain, MoMo ED showed 6173 accumulated deaths more than the official COVID-19 deaths. This difference is a third of the difference observed prior to 22 June; because this is within the error band, there was a significant improvement in the detection of COVID-19 deaths in this period. Figure 2 also shows a general agreement between MoMo ED and official COVID-19 deaths time series after the first wave, with the exception of late July and early August. These differences were due to two heat waves that were responsible for at least 25% of the MoMo ED16.Infections estimated from COVID-19 deathsTo illustrate the delay between official daily infections data and REMEDID estimated daily infections, we applied REMEDID from COVID-19 deaths assuming CFR = 100%. Figure 3 shows the current IO21 and the infections associated with COVID-19 deaths for the first wave. The latter in Spain reached a maximum on 13 March 2020 (Table 3), the day before the national government decreed a state of emergency and national lockdown. Thus, the adopted measures had an immediate effect, which was observed in the official data IO21 7 days later (20 March). This delay is similar to the incubation period (mean 5.78 days2), which could be explained because official infections were reported when symptoms appeared. This delay reached 16 days when we compared with earlier version IO20 (not shown), which highlights the usefulness of the methodology to reinterpret official data from very early stages of the pandemic. On the other hand, the maximum number of deaths was reached on 1 April, which was 19 days after the inferred infection maximum, bringing this delay close to the 20 days expected between infection and death (Figs. 1, 3).Figure 3Official COVID-19 infections and deaths, and estimated infections with case fatality ratio (CFR) of 100% in Spain during the first wave. Left y-axis: COVID-19 daily infections IO21 (blue curve). Right y-axis: COVID-19 deaths (orange curve) and its REMEDID-estimated infections with CFR = 100% (red curve). All curves are for Spain. Thin blue and orange curves are daily data, and thick curves are smoothed by 14-day running mean. Arrows show delays between the maximum of inferred infections and maxima from COVID-19 deaths (orange arrows) and COVID-19 infections (blue arrows). Solid arrows are expected delays, dotted while arrows are observed delays.Full size imageTable 3 Date of first infection for REMEDID estimated daily infections from COVID-19 deaths (IRO) and from MoMo Excess Deaths (ED) (IRM), and for official COVID-19 daily infections released on June 2020 (IO20) and on February 2021 (IO21).Full size tableWe applied REMEDID to the official COVID-19 deaths with the corresponding estimated CFRs (see “Data” section) to obtain the time series of estimated daily infections, hereafter referred to as IRO. Figure 4 shows IRO and the accumulated infections for Spain and its 19 regions. Note that in Spain, IRO are amplified versions of inferred infections in Fig. 3. In Spain, the first infection, according to IRO,, is on 8 January 2020 (Table 3), 43 days before the first infection was officially reported on 20 February 2020 according to IO20. By contrast, IO21 places the first infection on 1 January 2020. Spain reached the maximum number of IRO on 13 March, a day before the state of emergency and lockdown were enforced (Table 4). On 14 March, IO20 = 1832, and IO21 = 7478; however, IRO = 63,727 (CI 95% 60,050–67,403), 35 and 9 times IO20 and IO21, respectively (Table 5). This implies that on that day, IO20 and IO21 only reported 2.9% (CI 95% 2.7–3.1%) and 11.7% (CI 95% 11.1–12.5%) of new infections, respectively. Although detection of infections clearly improved from IO20 to IO21, almost 90% of the infections are still not documented in the peak of the first wave. The situation is similar for the accumulated infections before 22 June 2020, as reported by the National Seroprevalence Study4,5.Figure 4Daily and accumulated infections for official COVID-19 daily infections (IO21), and daily infections estimated from COVID-19 deaths (IRO). Lines are daily infections and refer to the y-axis on the right; bars are accumulated infections and refer to the y-axis on the left. Red lines and cyan bars are official COVID-19 data; orange lines and blue bars are inferred infections with case fatality ratio (CFR) in Table 1. Thin orange lines correspond to the CFR confidence interval.Full size imageTable 4 Date of the most prominent relative maxima, for Spain and the 19 regions, of the REMEDID estimated daily infections from COVID-19 deaths (IRO) and from MoMo excess deaths (ED) (IRM), and official COVID-19 daily infections (IO21).Full size tableTable 5 REMEDID estimated daily infections from COVID-19 deaths (IRO) and from MoMo excess deaths (ED) (IRM) on 14 March, and for official COVID-19 daily infections released on June 2020 (IO20) and released on February 2021 (IO21).Full size tableIn almost all regions, IO20 showed a delay of 1 month or more between the first infection and IRO (Table 3). No delay in IO21 occurred in Islas Baleares, Castilla-León, and Galicia, while in three regions (Cataluña, Madrid, and La Rioja), the first case occurred earlier than the first case of IRO. However, 6 regions had delays of 15 days and other 6 regions had delays of 1 month. According to IRO, all regions except Ceuta and Melilla had some infections in January, but in IO21 only 6 regions had infections in that month. In all scenarios, the first infections were in Madrid and Cataluña.During the first wave, according to IRO most of the regions had maximum daily infections around 14 March. In Madrid, the maximum was reached on 11 March, coinciding with the educational centres closing and an official warning by the regional government (Table 4). Asturias was the last region to reach peak infections (25–26 March). The maximum percentage of documented cases (12.6%, CI 95% 9.2–18.4%) occurred in Asturias on 14 March, but in the other regions, only between 1.2 and 8% of the infections were documented (Table 5).Figure 4 shows how the IO21 and IRO curves of Spain and the 19 different regions fluctuated following the same pattern until the middle of June 2020, but thereafter, they showed different patterns. This reflects the fact that the Spanish government had decreed the control measures for the whole nation until June, but thereafter, each regional government implemented its own control measures. For example, some regions (e.g., Aragón, Islas Baleares, Cantabria, Comunidad Valenciana, Extremadura, Galicia, Murcia, País Vasco, and La Rioja) had two peaks, but others had only one. An apparent maximum on 22 June in Islas Baleares is an artifact produced by the interpolation for transition from the two CFRs. Although beyond the scope of this work, it would be very interesting to investigate the effects of the different control measures implemented on the corresponding IRO for the 19 regions.The Spanish COVID-19s wave reached a maximum of daily infections on 22 October from IRO and on 26 October from IO21. The delay of 4 days is similar to the mean incubation period (5.78 days2). The estimated number of new infections is still larger than the documented cases, but the shapes of the two curves are more similar in the second wave than in the first wave (Fig. S1). The same is true for the 19 regions, most of which had the largest peak around 22–26 October, with the exceptions of Canarias and Madrid, which reached maxima in late August and early September, respectively.Infections from MoMo excess deathsAssuming that MoMo ED accounts for both recorded and non-recorded COVID-19 deaths, negative deaths are meaningless, and they were set to zero. Then, the associated daily infections can be estimated, as in “Infections estimated from COVID-19 deaths” section, with a CFR of 100% from MoMo ED for Spain (Fig. 5). Note two main differences between this time series and that estimated from official COVID-19 deaths: (1) MoMo data present an error band that was inherited by the estimated infections; (2) MoMo ED estimated infections reached a maximum of 1443 (CI 99% 1329–1547), doubling the 776 inferred daily infections from official COVID-19 deaths in Fig. 3. This is because maximum MoMo ED was 1,584 (CI 99% 1468–1686) and maximum COVID-19 official deaths was 828, both estimated from the 14-day running mean time series. The maximum of inferred infections was reached on 13 March, just one day prior to the state of emergency and lockdown. The expected and observed delays with respect to official infections and MoMo ED were similar to those observed for estimated infections from official COVID-19 deaths. Error bounds of the estimated infections in Fig. 5 were computed from the MoMo ED error bounds. However, it should be highlighted that the combination of the error bounds from MoMo ED and the estimated CFRs might lead to unrealistic error estimates. To avoid this, the error estimates in Fig. 6 were estimated from the MoMo ED time series (no error bounds) and the error bounds of the estimated CFRs.Figure 5Official COVID-19 infections, MoMo Excess Deaths (ED), and estimated infections with case fatality ratio (CFR) of 100% in Spain during the first wave. Left y-axis: COVID-19 daily infections IO21 (blue curve). Right y-axis: MoMo ED (orange curve) and its REMEDID-estimated infections with CFR = 100% (red curve). All curves are for Spain. Thin blue and orange curves are daily data, and thick curves are smoothed by 14-days running mean. Dashed curves represent the error estimate of MoMo ED (orange) and inferred infections (red). Arrows show delays between the maximum of inferred infections and maxima from MoMo ED (orange arrows) and COVID-19 infections (blue arrows). Solid arrows are expected delays, dotted while arrows are observed delays.Full size imageFigure 6Daily and accumulated infections for official COVID-19 daily infections (IO21), and daily infections estimated from MoMo Excess Deaths (ED) (IRM). Lines are daily infections and refer to the y-axis on the right; and bars are accumulated infections and refer to the y-axis on the left. Red lines and cyan bars are for official COVID-19 data; and orange lines and blue bars are for inferred infections with case fatality ratio (CFR) in Table 1. Thin orange lines represent the error estimate of inferred infections.Full size imageThe REMEDID was applied to the MoMo ED with the corresponding CFRs (see “Data” section) to obtain the estimated daily infections, which will be referred hereafter as IRM. The IRM were calculated for Spain and its 19 regions and are depicted in Fig. 6, as well as the accumulated IRM. In Spain, the first infection shown by IRM happened on 9 January, with an error estimate from 9 to 10 January, 41 to 42 days before the first documented infection of IO20 on 20 February 2020 (Table 3). The maximum IRM was 77,855 (CI 95% 73,364–82,347) reached on 13 March. On 14 March, IRM showed 14,128 infections more than IRO (Table 5). Notice that the CFR used with MoMo ED data was larger than the one used with official COVID-19 deaths data, which makes this difference even more remarkable, because the larger the CFR the lower the estimated infections. Therefore, if the true CFRs, which are unknown, were used in both cases, IRM would double IRO on 14 March, as happened when a CFR of 100% was used (Figs. 3, 5). Notice that with the CFRs used, the IRM and IRO resulted in the same accumulated infections on 22 June and 29 November, matching the results of the seroprevalence study. Nevertheless, IRM showed 42 times more cases than IO20 and 10 times more than IO21 on 14 March, detection of official cases of only 2.4% (2.2–2.5%) and 9.6% (9.1–10.2%), respectively.Table 3 shows the estimated date of first infection for Spain and by region. Note that the first cases of IRM in Spain were on 9 January and in Aragón, Canarias, and Navarra on 8 January, which is possible because significant excess deaths in a region may not become significant for the whole country. In general, the maxima of daily infections were closer to those on 14 March in IRM than in IRO. During the first wave, all regions showed a single maximum, except for Ceuta, Melilla, and Murcia, which showed two maxima (Fig. 6). In general, the IRM time series in all regions were similar during that period. The official data clearly under-detected infections during the first wave. On 14 March, IRM were comparable to IRO, overlapping CI in all regions, but not in Spain as a whole (Table 5). During the second wave, there was improved detection of cases with differences among regions. More