We conducted a cross-sectional study to characterize and compare the first, second, and third waves of COVID-19 in each region of Peru. Peru’s territory encompassed 25 regions (“departamentos”), which are subdivided into 196 provinces (“provincias”) and 1,869 districts (“distritos”). For this study, we grouped all the provinces of Lima as the Lima region and included the constitutional province of Callao as an independent region. Consequently, we used the same classification of regions used by the study data sources in our analysis.

We used the weekly mortality rate as the study outcome. At the national and regional levels, we calculated the weekly mortality rate by multiplying the accumulated death counts per epidemiological week by 100,000 and dividing the product by the estimated annual population. We obtained the death counts, population estimates, variants distributions, and region's geographical boundaries using open data curated from the government of Peru. We described the metadata and links from each of these sources in Table 1. We obtained the death counts from all causes from the National System of Deaths (SINADEF), which is updated daily at the Unique National Health Information Repository (REUNIS) ¹⁵ . We obtained the annual estimated population at the regional and national level from the National Institute of Statistics and Informatics (INEI) ¹⁶ , registering Peruvian citizens and accurately allocating their residence region. We obtained the weekly distribution of SARS-CoV-2 variants circulating in Peru from the Peruvian National Institute of Health (INS) ¹⁷ . Finally, we got the map shapefiles from the Peruvian Ministry of the Environment (MINAM) ¹⁸ .

We performed a descriptive analysis to characterize the COVID-19 waves by calculating the weekly mortality rates at the national and regional levels. We used the epidemiological week in which the Peruvian Ministry of Health confirmed the first COVID-19 death to set the beginning of each first wave, and the end of the third wave as the point at which the weekly mortality rate returned to pre-pandemic levels. We performed a graphical analysis of the weekly mortality rates at the national and regional levels by using the “ggplot2” package ¹⁹ . We fit a segmented regression model with unknown break-points to assess the end of the first and second waves, which we defined as the point where the trend in the weekly mortality rates changed from negative to positive. For this purpose, we used the methodology developed by Muggeo VM ²⁰ and the package "segmented" designed by the same author. Next, we calculated and described the mortality variability between women and men and among the age groups of 0 to 19, 20 to 59, and 60 years old and older to assess whether the demographics affected the comparability of the mortality among regions. After this verification, we compared the unstandardized mortalities instead of the standardized mortalities adjusted by age and gender. To compare the duration of each wave, we quantified the "time from the beginning to the peak" and the "total duration" of each wave, both in epidemiological weeks. Also, we compared the peak of each wave (measured as the higher weekly mortality rate), the wave onset week, and the wave last week, which we tabulated as a heat map. Finally, we characterized the pattern of each regional wave and performed a K-means clustering analysis to assess typical patterns during Peru's first, second, and third waves separately using the regional weekly mortality as the study outcome. During the K-means clustering analysis, we used the elbow method to determine how many clusters minimized the intra-cluster variance and maximized the inter-cluster variance. And, to confirm the findings of this analysis, we used the silhouette method, which measures the quality of clustering by calculating the average silhouette, which was used to graphically identify the optimal number of clusters by plotting the highest value of the average silhouettes. We used R 3.6.1 (R Foundation for Statistical Computing, Vienna, Austria) and R Studio 1.2.5001 (Free Software Foundation, Inc., Boston, MA) for the statistical analysis and the QGIS program 3.22 to elaborate the maps with the clustering analysis results.

The Ministry of Health confirmed the first death by COVID-19 at the epidemiological week 10 of 2020, and up to the epidemiological 13-2022, Peru suffered three COVID-19 waves ( Figure 1A). Based on our segmented regression analysis ( Figure 1B), this first wave most likely lasted 39 weeks ending at the epidemiological week 48 of 2020, which consequently was the epidemiological week with the lowest weekly mortality rate before the second wave started. On the other hand, we found that the second wave was the deathlier and the longest among the three waves, with 41 weeks from the epidemiological week 49-2020 until the epidemiological 36-2021. The end of the second wave coincides with the epidemiological week in which delta became the predominant SARS-CoV-2 variant in Peru, representing over 50% of them ( Figure 2). However, the weekly mortality rate increment was minimal until it became explosive when omicron displaced delta and became the predominant variant in the epidemiological week 52-2022. Regardless, the third wave was the less deathly and the shortest one, with an overall duration of 29 weeks from the epidemiological week 37-2021 to the 13-2022. Consequently, the epidemiological week 13-2022 was when the weekly mortality rates returned to pre-pandemic levels.

In the first three waves of the COVID-19 pandemic and for 109 weeks, Peru accumulated 514,006 deaths from all causes. Given that the pandemic started in the 10th epidemiological week and the first epidemiological week included the last three days of 2019, we calculated the weekly baseline mortality before the first wave as the mean mortality per week during epidemiological weeks two to nine, which was 7.21 ± 0.22 deaths per 100,000 people. Consequently, we calculated the excess deaths during the first three waves as 258,106 deaths, including 88,273 in the first wave, 145,401 in the second wave, and 24,432 in the third one. Based on these counts, we calculated that the excess deaths represented 49%, 60%, and 26% of all the deaths in the first, second, and third waves, respectively. On the contrary, we observed that the mortality ratio between the adults 60 years old and older and the adults 20 to 59 years-old progressed from 13.1 to 13.4 and 16.2 in the first, second, and third waves. Overall, the second wave was deathlier than the first one, and the first wave was deathlier than the third one ( Table 2).

Overall, at the national level, higher mortality was recorded during the second wave (743 deaths per 100,000 inhabitants), followed by the first wave (553 deaths per 100,000 inhabitants) and the third wave (284 deaths/per 100,000 inhabitants). At the regional level, we observed that during the first waves, the three regions with the highest mortality overall were Callao (750 deaths per 100,000 inhabitants), Lima (750 deaths per 100,000 inhabitants), and Moquegua (681 deaths per 100,000 inhabitants). During the second wave, the regions with the highest mortality overall were Ica (1035 deaths per 100,000 inhabitants), Arequipa (927 deaths per 100,000 inhabitants), and Lima (894 deaths per 100,000 inhabitants). And during the third wave, the regions with the highest mortality overall were Madre de Dios (395 deaths per 100,000 inhabitants), Ica (349 deaths per 100,000 inhabitants), and Arequipa (341 deaths per 100,000 inhabitants). Furthermore, we observed high variability of the weekly mortality weeks among waves and, within each wave, across regions ( Figure 3). Nevertheless, it was consistently higher among men than women and adults 60 years old and older compared to other age groups ( Table 3). At the regional level, we observed that during the first, second, and third waves, the mortality rate among men was higher than among women in all regions except for Arequipa during the third wave. Likewise, the mortality among the people 60 years old and older was higher than those aged 20 to 59 years old and 0 to 19 years old in all three waves, with the elders' age group consistently having the highest mortality rates. During the first wave, the region of Huancavelica had the most increased mortality among people 60 years old and older, with 4,413 deaths per 100,000 inhabitants. During the second wave, Ica was the region with a higher mortality rate, with 6,131 deaths per 100,000 inhabitants. And during the third wave, Huancavelica was again the region with a higher mortality rate, with 2,673 deaths per 100,000 inhabitants. Madre de Dios had a higher mortality rate among the people 20 to 59 years old age group, with 361 deaths per 100,000 inhabitants during the first wave. During the second wave, Ica registered the higher mortality, with 544 deaths per 100,000 inhabitants, and during the third wave, Madre de Dios reported the higher mortality, with 313 deaths per 100,000 inhabitants. Among people in the 0 to 19 years old age group, Madre de Dios had the higher mortality rate during the first, second, and third wave, with 161,226, and 161 deaths per 100,000 inhabitants, respectively.

In our cluster analysis, we observed that the spread of COVID-19 across the regions of Peru followed different wave patterns ( Figure 4) in both mortality ( Table 4) and duration ( Table 5). We found six clusters of regions with varying wave patterns in the first wave, either by using the Elbow method ( Figure 4A) or the Silhouette method ( Figure 4B). During the first wave, the regions of Lima and Callao had two of the deathlier and early waves, both beginning in epidemiological week 10. In contrast, Moquegua was the region with the latest onset with a first wave that started at the epidemiological week 16. During the second wave, we characterized two clusters with different region wave patterns ( Figure 4C and Figure 4D). As for the third wave, we also found that the regions of Peru could be classified into two different clusters ( Figure 4E and Figure 4F).

The first wave of Peru started in Lima, the region that reported the first COVID-19 cases and the first COVID-19 death in the country. Lima showed a similar wave pattern to its surrounding regions, including Ancash in the North, Callao in the East, and Ica in the South. Another region that showed a similar wave pattern to Lima was Tumbes on the northern border of Peru, frontier with Ecuador, which implies that COVID-19 cases may also have entered Peru from Ecuador at the beginning of its first wave ( Figure 5A). During the first wave, the regions of Peru exhibited six different wave patterns ( Figure 6). Overall, all the regions from "cluster one" exhibited a first wave characterized as the earliest and longer lasting, with a mortality rate that did not exceed 40 deaths per 100,000 inhabitants. The first wave spread from Tumbes to Piura, Piura to Lambayeque by the Panamericana highway, and from Lima to Loreto and Ucayali by air traffic. All from "cluster two," these regions exhibited an early and short duration first wave, with a peak weekly mortality rate of 39 deaths per 100,000 inhabitants. Then, the first wave seems to have spread to the nearby regions, including Arequipa from Ica, La Libertad from Ancash, and Madre de Dios from Ucayali. All the regions from "cluster three" exhibited a short duration and intermediate first wave, with a maximum mortality rate of 43 deaths per 100,000 inhabitants. Then, the first wave moved to the highlands, impacting the regions of Amazonas, Apurímac, Ayacucho, Cajamarca, Huánuco, Pasco, and San Martín. The "cluster four" showed a moderate first wave with peaks that did not exceed a mortality rate of 23 deaths per 100,000 inhabitants. Finally, the first wave spread to the southern regions of Peru, impacting the regions of Cusco, Huancavelica, Junín, Puno, and Tacna; all these regions from cluster three had the latest and shorter first waves, with a maximum mortality rate of 37 deaths per 100,000 inhabitants. Among the southern regions of Peru, Moquegua behaves as a stand-alone cluster (cluster six). Despite having one of the latest first waves, Moquegua had the higher peak among all the regions of Peru, with a weekly mortality rate of 78 deaths per 100,000 inhabitants. Moquegua's peak during the first wave was also the highest across all regions and the three waves.

During the second wave, the regions of Peru exhibited two different wave patterns ( Figure 5B and Figure 7). The first cluster was composed by the regions of Ancash, Arequipa, Callao, Ica, Junín, La Libertad, Lima, and Tumbes. During the second wave, these regions had deathlier second waves with higher weekly mortality rates (peak mortality range: 27 to 40 deaths per 100,000 inhabitants). Callao and Ancash had the earliest onset (epidemiological weeks 46 and 47 of 2020, respectively) and Ica the deathlier second wave, with a peak of 40 deaths per 100,000 inhabitants. The second cluster included the regions of Amazonas, Apurimac, Ayacucho, Cajamarca, Cusco, Huancavelica, Huánuco, Lambayeque, Loreto, Madre de Dios, Moquegua, Pasco, Piura, Puno, San Martin, Tacna, and Ucayali. Overall, this cluster had some regions with the faster peak second waves (Pasco, Tacna, Loreto Huánuco, and Moquegua, all with a time to peak below 10 weeks) and some regions with the lower mortality (Amazonas, Pasco, Loreto, and Cajamarca, all with mortalities at the wave peak bellow 20 deaths per 100,000 inhabitants).

The third wave started when delta became the most predominant variant in Peru. However, during the third wave, omicron displaced delta and spread violently across the country, starting in most regions simultaneously. Overall, we differentiate two wave patterns ( Figure 5C and Figure 8). The first cluster included all the regions from the coast of Peru except for Lambayeque and Cajamarca, and all the regions with highlands, except for Pasco, plus the southern regions of the jungle Ucayali and Madre de Dios. Among them, Arequipa, Ancash, and Ucayali were the regions with the faster peak (4, 5, and 5 weeks, respectively); Ancash, Huánuco, La Libertad, and Tumbes were the regions with the longest waves (23, 20, 20, and 20 weeks of durations, respectively). At the same time, Madre de Dios, Ucayali, and Puno were the regions with the higher peak mortality (23, 23, and 21 deaths per 100,000 inhabitants at the wave peak, respectively). The second cluster included the regions of Amazonas, Cajamarca, Lambayeque, Loreto, Pasco, and San Martín. These waves were significantly less mortal than cluster one (mean peak mortality: 9.5 ± 2.8 vs. 16.2 ± 3.5 deaths per 100,000 inhabitants; p <0.05).

Geographically speaking, the spread of COVID-19 during each of Peru's waves had Lima as the epidemic epicenter and followed the coastal roads (trough the Panamericana highway) to spread to the nearby regions. During the first wave, the epidemic was reported as exported from Lima to Iquitos by over 100 Chinese tourists that traveled early in the wave, including the first case confirmed in Iquitos city ²¹ . On the other side, pretty much all the regions along the Andes had the latest first waves in the country ( Figure 5A). However, with the introduction of more transmissible and infectious variants, such as alpha, gamma, and lambda, the second wave spread from the coastal regions to the highlands and jungle at once ( Figure 5B). Finally, the introduction of delta started the third wave, which spread violently with the introduction of omicron across the country, and only a few regions of the eastern jungle and northern highlands had late waves ( Figure 5C). Statistically, the first and second wave's clusters distribution correlates significantly (Spearman rho = 0.5468; p = 0.0047), but the second and third wave's clusters do not (Spearman rho = 0.3430; p = 0.0932).