A modelling study across the Italian regions: Lockdown, testing strategy, colored zones, and skew-normal distributions. How a numerical index of pandemic criticality could be useful in tackling the CoViD-19
AA modelling study across the Italian regions:Lockdown, testing strategy, colored zones, andskew-normal distributions. How a numericalindex of pandemic criticality could beuseful in tackling the CoViD-19.A modelling study across the Italian regions:Lockdown, testing strategy, colored zones, andskew-normal distributions. How a numericalindex of pandemic criticality could beuseful in tackling the CoViD-19. A s Europe is facing the second wave of the CoViD-19 pandemic, each country shouldcarefully review how it dealt with the first wave of outbreak. Lessons from the firstexperience should be useful to avoid indiscriminate closures and, above all, to determineuniversal (understandable) parameters to guide the introduction of containment measuresto reduce the spreading of the virus. The use of few (effective) parameters is indeed ofextreme importance to create a link between authorities and population, allowing the latterto understand the reason for some restrictions and, consequently, to allow an active particip-ation in the fight against the pandemic. Testing strategies, fitting skew parameters (as mean,mode, standard deviation, and skewness), mortality rates, and weekly CoViD-19 spreadingdata, as more people are getting infected, were used to compare the first wave of the out-break in the Italian regions and to determine which parameters have to be checked beforeintroducing restrictive containment measures. We propose few universal parameters that,once appropriately weighed, could be useful to correctly differentiate the pandemic situationin the national territory and to rapidly assign the properly pandemic risk to each region. Stefano De Leo and Manoel P. AraújoStefano De Leo and Manoel P. Araújo
Department of Applied Mathematics, Campinas State University, [email protected]@ime.unicamp.br
I. IntroductionI. Introduction
Let’s begin this article by analysing the data of deathsper million of inhabitants in the world as of Decem-ber 31, 2020. In Figure 1, we find the data for theworldwide countries with a population greater than 10million people and a number of deaths per million ofinhabitants (DpM) over 100. In the attached Table,we also find the explicit data (absolute numbers of con-firmed deaths, populations and DpM) for the countrieswith a DpM greater than 240. The data can be lookedup at the
Coronavirus Source Data by Our World inData [1]. Italy appears on the second place among thecountries with the highest mortality rate with 1226.6DpM, the number is obtained by dividing the absolutenumber of CoViD-19 confirmed deaths at December31, i.e. 74159, by the Italian population (60.46 millionof inhabitants). The highest DpM number, 1684.9,belongs to Belgium. For this country, it is importantto spend some words regarding this. In the beginning of the pandemic, for most countries around the world,the CoViD-19 death toll was tallied from patients inthe hospitals who tested positive for CoViD-19. Bel-gian authorities have gone further than that, by alsoincluding the deaths of non-hospitalized people whoare suspected of having the virus, in particular thedeaths in nursing (elderly) homes. Since the beginning,Belgium is one of the few countries in Europe thathave strictly followed and, maybe even extended thecriteria for the CoViD-19 death classification, givenby the World Health Organization: “A death due toCoViD-19 is defined for surveillance purposes as adeath resulting from a clinically compatible illness, ina probable or confirmed CoViD-19 case, unless thereis a clear alternative cause of death that cannot berelated to CoViD disease (e.g. trauma). There shouldbe no period of complete recovery from CoViD-19between illness and death. A death due to CoViD-19may not be attributed to another disease (e.g. cancer)and should be counted independently of pre-existing Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] a r X i v : . [ q - b i o . P E ] F e b onditions that are suspected of triggering a severecourse of CoViD-19” [2]. For example, when Belgiumreported 6262 deaths, 52% of those fatalities were innursing homes. Of these, only 4.5% were confirmed tohave had CoViD-19, with the rest just being suspectedcases. It led Belgian CoViD-19 task-force spokesmanand virologist Steven van Gucht to suggest that whenwe compare Belgium with other countries the Belgiandeath rate should be divided by two [3]. In Italy, thepositivity to Sars-Cov-2 alone is not sufficient to con-sider death as due to CoViD-19, the presence of allthe following four conditions is also necessary: Deathoccurred in a patient definable as a microbiologicallyconfirmed case (molecular swab) of CoViD-19; Pres-ence of a clinical and instrumental picture suggestingCoViD-19; Absence of a clear cause of death otherthan CoViD-19; Lack of full clinical recovery periodbetween illness and death [4]. Looking at the rank-ing of countries by DpM on June 28, Belgium, Spain,United Kingdom, Italy and France appear, respectively,with 830, 606, 593, 574, and 456. Considering the ratioof the reported CoViD-19 mortality and the excessmortality, the adjusted deaths per million became 755(Belgium), 1010 (Spain), 742 (United Kingdom), 857(Italy), and 470 (France) [5]. Clearly showing that,during the first pandemic wave, the CoViD-19 deathtoll was significantly underestimated in Spain ( − − − Protezione Civile Italiana [6] are available fordownload at GitHub [7]. The regions of North-WesternItaly (Val d’Aosta, Lombardia, Liguria, Piemonte) ap-pear in the top 4, with a 36315 total deaths, whichwith a total population of 16.11 M implies 2254.2DpM. Immediately after these regions, we find the 3regions (Emilia-Romagna, Friuli-Venezia Giulia, Ven-eto) and the 2 autonomous provinces (Bolzano, Trento)of North-East Italy with 17600 total of deaths whichwith a total population of 11.66 M leads to 1509.4 DpM.Going down the table, we find the 4 Central regions(Marche, Toscana, Umbria, Lazio) and one of South-ern regions (Abruzzo) with 10850 deaths which with atotal population of 13.3 M implies 815.8 DpM. Finally,the remaining Southern regions (Molise, Puglia, Cam-pania, Basilicata, Calabria) and the two islands (Sicilia,Sardegna) count 9405 total deaths, which with a totalpopulation of 19.15 M leads to 491.1 DpM. The geo-graphical DpM difference amongst the Italian regionscan be shown by using the red color for the regions witha DpM ≥ ≤ DpM < ≤ DpM < ≤ DpM < < Decretodel Presidente del Consigli dei Ministri (DPCM) ofthe 1st of March, DPCM200301 at [8]. Seven dayslater, the measure to avoid any movement of per-sons to and from these territories, as well as withinthe same ones, except for movements motivated byproven work needs, situations of necessity or healthreasons were extended to the whole Lombardia andsome provinces of Emilia-Romagna (Modena, Parma,Piacenza, Reggio Emilia, and Rimini), Marche (Pesaroand Urbino), Piemonte (Alessandria, Asti, Novara,Verbano-Cusio-Ossola, Vercelli), and Veneto (Padova,Treviso, and Venice), DPCM200308 at [8]. One daylater, the measurements concerned the entire nationalterritory, DPCM200309 at [8]. A sequence of decreesin just a few days that clearly shows the panic of theItalian authorities. Panic probably due to the lack ofan adequate pandemic plan to deal with the outbreak.After January 11, when the first CoViD-19 victimin China was confirmed, after January 13, the day onwhich the virus caused the first death outside China(Thailand), after January 24, when the first cases inFrance were confirmed, after January 30, the dateon which the WHO declares the CoViD-19 a global Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] ealth emergency [9], Italian authorities should haveimmediately activated the pandemic plan by worrying,for example, about having a large supply of personalprotective equipments, the careful monitoring of lungdiseases compared to previous years and the control ofintensive care units in the country.In the excellent report [10] prepared by the CoViD-19 Emergency Team at the WHO European Officefor Investment for Health and Development in Venice(Italy), the authors discussed why the first phase ofItaly’s response to the CoViD-19 brought its healthsystem to near collapse creating a panic in the popula-tion. In February, life in Italy had not changed much:carnival festivities, tourists in the cities, people in theski resorts and football fans at the stadium. A scary ex-ample was the UEFA Champions League match playedat the Giuseppe Meazza stadium of Milano between theItalian team of Bergamo,
Atalanta , and the Spanishone of
Valencia with 45792 spectators. According toan analysis conducted by INTWIG [11], in collabora-tion with Report [12] and BergamoNews [13], amongthe 3400 (of 36000) Atalanta fans interviewed morethan 20% had symptoms compatible with CoViD-19in the 15 days following the match. This footballmatch was a clear pandemic bomb that then madeBergamo become a symbol of the epidemic that dev-astated Lombardia between February and March 2020.A study of the Institute
Mario Negri (Bergamo) andof the Deparment of Biomedical and Clinical Science,University of Milano [14] estimated the cumulativeprevalence of SARS-CoV-2 infection in Bergamo ina group of workers who returned to the workplaceafter the end of the Italian lockdown on 5th May 2020.Performing an enzyme-linked immunosorbent assay(ELISA) to detect the humoral response against thespike and nucleocapsid proteins of SARS-CoV-2, aswell as nasopharyngeal swabs to assess the presenceof SARS-CoV-2 using real-time reverse transcriptionpolymerase chain reaction (rRT-PCR), the researchersobserved the prevalence of SARS-CoV-2 infection inthe province of Bergamo reached 38.5%, significantlyhigher than has been reported for most other regionsworldwide. By using the result of this study, we canalso calculate the real
Infection Fatality Rate for theoutbreak in Bergamo. The IFR is one of the import-ant numbers alongside the herd immunity threshold,and has implications for the scale of an epidemic andhow seriously we should take a new disease. Assum-ing that the 38.5% of the Bergamo population wasinfected by the virus, the IFR in this area reducesfrom 20% (comfirmed deaths over confirmed infectedpeople) to almost 1% in perfect agreement with theinterval between 0.5% and 1% calculated across differ-ent countries [15]. Observe that for a common flu, theIFR is around 0.1%. Just a factor 3 (i.e. 0.3% insteadof 0.1%) without a vaccine is sufficient to lead to acollapse of the health systems of most countries in theworld. The study we aim to present in this report is basedon the analysis of 45 pandemic weeks. The centralday of the weeks, around which we will calculate our7-day averages is Thursday, with the first week centredon February 27 and the last one on December 31.Before presenting the analysis of pandemic data, itis convenient to spend a few words on the situationof the intensive care units (ICUs) in Italy before thefirst and second pandemic waves. Intensive care units,providing treatment for people who are in a very criticalsituation, are staffed with specially trained healthcareprofessionals, and contain sophisticated monitoringequipment. Due to the fact that some people infectedby CoViD-19 may be unable to breathe on their own,they need to use a machine that helps with breathing(a ventilator) and monitoring equipment to measureimportant body functions, such as heart rate, bloodpressure and the level of oxygen in the blood. Thecollapse of the intensive care units surely was and stillis the main preoccupation in facing this pandemic. Weobserve that the collapse of the health system is notonly due to the lack of intensive care beds but also tothe lack of trained healthcare professionals (this wasone of the main problems in Italy). The total numberof beds in ICUs at the beginning of the outbreak was5179. In Summer, the commissioner (Domenico Arcuri)responsible for the implementation and coordinationof the measures necessary for the containment andcontrast of the epidemiological emergency CoViD-19prepared a plan to create 3553 additional ICUs. OnOctober 13, the call for companies closed, and thestart of the implementation work was scheduled forthe end of October. Too late, because at that timethe second wave in Italy had already arrived. In themeantime, the regions added a total of 1279 stablebeds to their initial 5179 and so the current dowryis 6458 places [16]. This implementation was donewith significant regional differences also due to theaccumulated delays: The regional plans were expectedat the end of June and instead were only approved atthe end of July. The situation of intensive care bedsfor the Italian regions at the beginning of the firstand second pandemic waves is shown in the followinggraphicsThe number of ICUs suggested by the World Health Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] rganization is 150 per million of inhabitants. To un-derstand the critical situation in Italy at the beginningof the first pandemic wave, we will highlight with thered color the regions with a number of intensive carebeds less than 75, with orange those with a numberof beds greater than or equal to 75 but less than 100,with yellow greater than or equal to 100 but less than125, with green greater than or equal to 125 but lessthan 150, and, finally, with cyan greater than or equalto 150.Even after the implementation of new intensive carebeds, only 4 regions, Friuli Venezia Giulia (144.5 ICUsper million), Basilicata (131.1), Liguria (135.5), andLazio (127.3), appear in green and 2, Veneto (168.1)and Val d’Aosta (158.7) in cyan. Campania presentsthe most critical situation with 73.8 ICUs per millionof inhabitants. Notwithstanding this critical situation(red zone), at December 31, Campania with a DpMof 491.2 (green zone) appears in the lower part ofthe regional DpM Table and at the beginning of theinfographic shown in Figure 2. II. Delayed action and lockdownII. Delayed action and lockdown
As observed in the Introduction, the Italian govern-ment, in an attempt to stop the spreading of the firstwave of the pandemic, adopted strict containmentmeasures (lockdown) throughout the whole nationalterritory starting from March 9. For the second wave,on the other hand, the Italian authorities applied theregional division into colored zones of pandemic risk.In Table 1, we find, region by region, the numberof the daily averages for positive (column A), hospit-alized (B), hospitalized in ICUs (C) and deaths (D).In this Table, we also find the population (P) of eachregion and the numbers of daily averages for positive(A ∗ ), hospitalized (B ∗ ), hospitalized in ICUs (C ∗ ), anddeaths (D ∗ ) per million of inhabitants. The data ofTable 1 were used to prepare Figure 3. To facilitatethe understanding of data and tables, we will analysesome specific cases. Let us consider the situation ofLombardia in the second pandemic week (centred atMarch 5). In this week, the daily average of posit-ives, hospitalized, hospitalized in intensive care, and deaths was 1971.3, 1505.1, 259.1, and 34.7. To com-pare Lombardia with the other regions, we normalisethese number by its population (10.104 M) obtaining:195.1, 149.0, 25.6, 3.4. One of the most importantpandemic parameter (often underestimated during thefirst pandemic wave) is the ratio of hospitalized overpositive people. Indeed, when a minimum thresholdof hospitalized (20 per million) is reached, the hospit-alized/positives ratio is the first indicative number ofthe gravity of the disease. The more advanced thestage of infection is the more diffusion we have, soit becomes more likely that weaker groups will be af-fected and more people will need hospitalization. Themore people are hospitalized the more people couldcomplicate their clinical status with the possibility ofneeding intensive care. In the second pandemic week,Lombardia had 149.0 hospitalized per million of inhab-itants and 195.1 positives to CoViD-19 leading to ascary 76.4%. In Figure 3, we have chosen the cyancolor when this ratio is less than 10%, green between10% and 20%, yellow between 20% and 30%, orangebetween 30% and 40%, and, finally, red when the ratiois greater than 40%. Other indicators such as hospital-ized in ICUs/number of ICUs and deaths per millionclearly confirm the Italian government’s responsibilityin the lack of firmness and determination in curbingthe spreading of the pandemic in the Northern regions,in particular Lombardia. The CoViD-19 occupancy ofICUs is another important indicator. In Figure 3, wehave chosen the cyan color when this ratio is less than15%, green between 15% and 30%, yellow between 30%and 45%, orange between 45% and 60%, and, finally,red when the ratio is greater than 60%. For the dailydeaths per million, the colored zones were fixed at 2, 4,6, and 8. At this stage of the outbreak, due to the lackof pandemic planning and territorial monitoring theCoViD-19 deaths are obviously underestimated. Allthe regions appear in the cyan zone (the only one ingreen is Lombardia).On March 8, the Italian authorities imposed restric-tions to Lombardia and some provinces of Emilia Ro-magna, Marche, Piemonte, and Veneto on March 8 and,24 hours later, the restrictions were extended to theentire national territory on March 9. An incomprehens-ible way of handling the first wave of the pandemic andleading to panic in the Italian population. From thedata of the second pandemic week (Table 1) graphic-ally shown in Figure 3, it is clear that the containmentmeasures for regions such as Lombardia (9), EmiliaRomanga (5), Marche (10), Piemonte (14), and Veneto(21) should have been taken much earlier. This is con-firmed 3 weeks later (fifth pandemic week centred atMarch 16), when the situation precipitated not only forthe mentioned regions but for all the other Northernregions. For some regions the 7-day averages of deathsper million reached scary values: 9-Lombardia (41.1),20-Val d’Aosta (38.5), 13-P.A. Trento (24.7), 5-EmiliaRomagna (20.1), 8-Liguria (19.1), 10-Marche (19.0), Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] quarantine has its origin in Venice in the14th century during the Black Death. The city decidedto extend the quarantine period for ships and peoplefrom 30 to 40 days. This was a very important (fortu-itous) decision. The incubation period for the bubonicplague was estimated to be 37 days [17]. The nationalquarantine was the only answer found by the Italiangovernment. The toll that a 10-week block during thefirst pandemic wave took on the Italian people wasa very costly one, both from an economic and socialpoint of view. The Central, Southern regions and Is-lands were forced to a strict lockdown notwithstandingthe virus had practically arrived not yet entered theirterritory (we shall come back to this point later whenwe model the pandemic curves of the first wave byskew-normal distributions). The panic created in thepopulation led people with CoViD-19 to aggravatetheir health before seeking medical treatment and alsocreated disastrous effects in the prevention of otherdiseases.The deaths in the first half of 2020 could at least havebeen honoured if the second wave of the pandemic wasaddressed properly. But even when facing the secondwave, the Italian authorities have shown a poor abilitynot only in communicating with the population but,above all, in fighting the pandemic. III. The 21 pandemic parametersIII. The 21 pandemic parameters
In the absence of a vaccine or effective drugs treatment,and because of the still low level of immunity inthe population, a rapid resumption of sustainedtransmission may occur in the community (secondwave) once we reduce the containment measures, adopted to tackle the first pandemic wave. Tryingto avoid this, the Minister of Health with a decreeof April 30 [18] indicates the monitoring criteriathat must be followed in order to promptly classifythe pandemic risk and to be able to adopt localcontainment measures to face a new outbreak wave.The monitoring included the following indicators:6 indicators of data collection capacity (IA);6 indicators of diagnostic control, investigation andcontact tracing (IB);9 indicators of transmission stability and resilienceof the health system (IC).The 21 indicators are explicitly given in Appendix. Anexcessive number of indicators, typical of the Italianbureaucracy, is clearly, independent of their validityor not, an additional difficulty in monitoring the dis-ease. The regions can probably (but always with greatdifficulty) monitor these indicators when the outbreakgives a respite but clearly 21 indicators cannot be mon-itored and even more understood by the populationduring the worst phase of the pandemic. To under-stand the great confusion generated in the populationby the Italian authorities population, we recall some ofthe incomprehensible decisions taken by the authoritiesthrough dozens and dozens of decrees each of one witha number of pages between 100 and 150. During theCoViD-19 crisis, it is necessary to communicate withthe population in a simple, clear, and effective wayexactly the opposite of what the Italian authorities did.After the first Summer months with open discothequesand without the need to use personal protective equip-ment outdoors (in many European countries the useof mask outdoors was imposed in the beginning of thereopening period) the Minister of Health on August16 decides to impose the use of mask outdoors. But,only from 6pm to 6am of the day later and only whenagglomerations could not be avoided [18]. Certainly aconfused and unclear way of communicating with thepopulation who clearly do not understand why at 6pmthe use of the mask is triggered and 5 minutes beforeit is not. A good example of how authorities shouldn’tcommunicate with their own population. Only twomonths later, the use of the mask outdoors is compuls-ory during the whole day, DPMC201013 [8]. The useof the mask also has a psychological effect, keeping theattention of the user higher.Before analysing the measures taken by the Italiangovernment to face the second pandemic wave, let usobserve the current situation in the pandemic weeknumber 36 (centred on October 29). In this week theItalian 7-day average of daily positives and hospitalizedwas 761615.0 and 37259.4, respectively, leading to anhospitalized/positives ratio of approximatively 5% anda (7-day average) daily deaths per million of 3.5 (theabsolute number was 212.6), see Table 1 and Figure 3.The daily hospitalized/positives ratio (5%) confirms Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] hat we are already in the second pandemic wave andthe daily deaths near to 4 that we should have alreadytaken containment measures. In the final sections, weshall discuss in detail the numerical pandemic criticalityindex which permits to correctly classify the risk of eachregion. For the moment, let us have a look at the (7-dayaverage) daily deaths per million of inhabitants. Atweek 36: 1-Abruzzo (4.4), 8-Liguria (8,3) , 9-Lombardia(5.0), 11-Molise (5.7), 12-PA Bolzano (5.1), 13-PATrento (4.2), 14-Piemonte (4.4), 16-Sardegna (3.8), 18-Toscana (3.9), 19-Umbria (4.9) and 20-Val d’Aosta(23.8) overcome the national mean, with two regions(Liguria and Val d’Aosta in a very critical situation).At November 4, The Minister of Health gave the firstcolored classification of the Italian regions [18]. Fourregions appear in the red zone (Lombardia, Piemonte,Val d’Aosta, and Calabria), two in the orange one(Puglia e Sicilia), and the remaining regions andBolzano and Trento in the yellow zone.Why the yellow color was assigned to Liguria and to Ca-labria the red one? In the week before the classification(week 36), Liguria had a ratio of hospitalized/positiveinhabitants of 976.1/7754.3 ≈ ≈ ≈ ≈ ≈ ≈ IV. Skew normal distributionsIV. Skew normal distributions
In studying the CoViD-19 data, we must use two dis-tinct approaches [19,20]. First, until reaching the curvepeak, we have to model the data by a Gaussian distri- Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] ution [21]. Once the peak has been reached, we haveto introduce a parameter which models the asymmetry of the curve. In this case the skew-Gaussian distribu-tions [22–25] come into play. The explicit analyticalformula of the skew probabilities density functions,used in this paper to fit the Italian pandemic curvesof the pandemic first wave, is given by PDF a ( x ) = T a exp " − ( x − µ a ) σ a √ π σ a × Erfc (cid:20) − s a ( x − µ a ) √ σ a (cid:21) (1)where a = confirmed cases per Million of Inhabitants (pMoI) , = positives pMoI , = hospitalized pMoI , = hospitalized in ICUs pMoI , = deaths pMoI , and Erfc is the complementary error function,Erfc( z ) = 2 √ π Z ∞ z d t exp[ − t ] . The skewness of the distribution, defined by γ = (cid:16) − π (cid:17) (cid:18) δ √ − δ (cid:19) (2)where δ = r π s √ s , has a value in the interval ( − , µ + σ δ . (3)The mode (maximum) has not an analytic expressionbut, as shown in [26], an accurate closed form is givenby mode = µ + σ δ − γ √ − δ − sign( s ) exp[ − πs ] (cid:19) . (4)For total confirmed cases and deaths, we used thecumulative skew-normal distributions, CDF a ( x ) = Z x − ∞ d e x PDF a ( e x ) . The four parameters, T , µ , σ , and s , were calculated byusing the 7-day averages data and by fitting them by the NonlinearModelFit of the computational programWolfram Mathematica [27]. The fitting parameters fortotal confirmed cases and deaths, for daily positives,hospitalized, and hospitalized in ICUs are found inTable 2.In order to optimize the graphical presentation ofthe pandemic data, we have decided to normalise thetotal confirmed cases and deaths to those of Lombardia.At the sixteenth pandemic week (centred on June 6),Lombardia (number 9 in the plots) reached 90979.7(7-day average) total confirmed cases and 16374.9 (7-day average) total deaths. Numbers that, consideringthe population of 10.104 M, lead to 9004.3 confirmedcases per million of inhabitants and 1620.6 deaths permillion. For Lombardia, we used the scale factor 1000.For total confirmed cases and deaths, all the otherregions have been then normalised to the Lombardiavalues. The regional scale factor appears in the lowerleft corner of each regional plot, see Figure 4 and 5.Let us explain how the scale factors have to be used.In the pandemic week 16, Calabria (num. 3), Puglia(num. 15), and Veneto (num. 21) had 1160.4, 4513.4,and 1920.1 (7-day averages) confirmed cases and 97.0,529.4, 1966.1 (7-day average) deaths. By consideringtheir populations, 1.925 M, 4.008 M, and 4.907 M, wefind 602.8, 1126.1, and 3912.8 total confirmed casesper million of inhabitants and 50.4, 128.6, and 400.7deaths per million. By using the scale factor appearingin the corresponding plots (Figure 4 and 5), we canobtain the total confirmed cases and total deaths foreach region. In particular, for the regions cited above,we findCalabria : 9 . ×
67 = 603 , . ×
31 = 50 , Puglia : 9 . ×
544 = 1125 , . ×
82 = 131 , Veneto : 9 . ×
435 = 3915 , . ×
247 = 395 . The scale factors can also be used to determine theregional colors for the total confirmed cases and deathsof the first pandemic wave: cyan at 150, green at 300,yellow at 450, orange at 600, red at 1000, with a propor-tional color gradation between two colors. Looking atthe total confirmed cases per million of inhabitants: 7regions appear in the cyan zone, 5 of which (Basilicata,Calabria, Campania, Sardegna, and Sicilia) with ascale factor of deaths per million less than 100 and twoof which (Lazio and Puglia) with a number between100 and 150, and 2 regions (Molise and Umbria) inthe green zone. For the total deaths per million ofinhabitants, we have 9 regions in the cyan zone, all ofthem (Basilicata, Calabria, Campania, Lazio, Molise,Puglia, Sardegna, Sicilia, and Sardegna) with a scalefactor less than 100, and 4 regions in the green zone(Abruzzo, Friuli Venezia Giulia, Toscana, and Veneto).From Figure 4 and 5, it is clear that the critical num-bers belong to the Northern regions with the exceptionof Friuli Venezia Giulia and Veneto. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] he skew-Gaussian distributions (blue, gray, andwhite lines) show an excellent agreement with thepandemic data (colored, gray, and white histograms).The fitting parameters can then be used to comparedifferent regions and, for the same region, to comparepositives, hospitalized, and hospitalized in the intensivecare units data. It is also important to note that thegradation of colors in the pandemic curves of confirmedcases and deaths gives us an idea of the temporalevolution in each region. Normalisation is always donewith respect to Lombardia.In Lombardia, for the first pandemic wave, the mor-tality rate seems to be 1.6/9=17.8%. It is obviousthat this rate cannot be the real infection fatality rate(IFR) of Sars-CoV2 because 17.8% is calculated byusing the number of known confirmed cases and notthe number of real infected people. In an interestingstudy done in a small German town, of 919 individuals15.53% were infected. By applying this infection rateto the total population in the community, i.e. 12597,we can estimate 1956 (real) infected people. Having 7Sars-CoV2 deaths reported by the local authorities, the real IFR can be estimated to be 7/1956 =0.36% [28].By using the infection rate of 15% in Lombardia, weshould have, during the first wave, 1.5 million of infec-ted people. This means a factor 16.7 with respect tothe number of confirmed cases reported by the localauthorities. In this case, the real
IFR for Lombardia isfound around 1%. Lower than 17.8% but still greaterthan 0.36%. Observe that a factor 2.5 in the totaldeaths implies 16000 instead of 6400 deaths. This highIFR, very close to the one found for Bergamo [14], isclearly due to the confusion generated in the popula-tion and to the lack of a national pandemic plan. Ina panic situation, people to do not seek medical helpat the right time and, in many cases, this aggravatestheir health conditions generating a difficult situationto be managed by the medical staff. We also remem-ber that during the first wave, the Lombardia elderlyhomes were even used to accommodate patients withCoViD-19. An incomprehensible choice that broughtthe the virus to the most fragile age range with obviousdramatic consequences. In the Northern regions thecontainment measures were adopted too late, but thiswas not the only cause of the disaster. The enormousdifficulties in which health professionals worked clearlyshow, as observed in the excellent report by Zambonet al. [10], the lack of a pandemic plan. The WorldHealth Organization was accused of conspiring withthe Italian authorities to remove the Zambon’s reportrevealing the mismanagement of Italian governmentat the beginning of the CoViD-19 pandemic. In the102-page report, the authors observed that the nationalpandemic plan had not been updated since 2006 andthat, due to being unprepared, the initial responsefrom hospitals was improvised , chaotic , and creative .For the Southern regions, where the virus had not yetarrived or had only reached a minimum extent and therefore could be controlled with targeted measures,the lockdown was identical to that adopted for theNorthern regions. As we will see later, things havenot changed much when the second pandemic wavearrived. A shame for the Italian government and asadness for its population who certainly did not de-serve such treatment and who, contrary to what thenational authorities did, responded with discipline anddetermination in the months of March, April, and May.The pandemic curves were controlled by the disciplineand determination of the Italian population and by theheroic work of health professionals which compensatedfor the confusion and the incompetence and the lackof programming of the Italian authorities which foundin a medieval lockdown the only answer to the firstwave of pandemic. V. The four pandemic parametersV. The four pandemic parameters
In this Section, we turn our attention on 4 pandemicparameters: New confirmed cases over new testedpeople, hospitalized and hospitalized in ICUs per mil-lion of inhabitants, and ,finally, daily deaths. The firstparameter is the one used to determine the infectionreproduction number, but this cannot be the only para-meter to be observed, as the other 3 parameters canbe more effective in understanding the real situationof the pandemic.CoViD-19 tests can be useful to reduce the virusdiffusion by using timely preventive isolation measuresand by monitoring close contacts of infected people.Before discussing the importance of a massive testingstrategy, let us see which types of tests are currentlybeing used [29]. The most effective test to detect thepresence of the Sars-CoV-2 virus is the one based onthe molecular analysis. This test has been used inItaly to identify people who have contracted the virus.Once a person carrying the virus has been identified,it is clear that a first measure is the isolation of thesame and, once isolated, the local authorities have tocheck his close contacts. Digital proximity trackingtools are used to widen the network of possible con-tacts. The effectiveness of such digital tools clearlydepends on a high coverage and utilization rate amongthe population. National lockdown during the firstpandemic wave, lack of a pandemic plan, confusion,bad communication, and questionable choices in thereopening period (such as the non-obligation to weara mask outdoors) led the population to underestimatethe possibility of a second pandemic wave. The contacttracing app suggested by the Italian government was,due to the very low acceptance within the population,practically useless. The lack of an effective networkof regional contact tracing led to the collapse whenthe pandemic began to spread within the territory.Without a massive testing strategy and without aneffective contact tracing is clear that many asympto-matic people will never be identified. In addition to Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] he molecular test, other tests should have been em-ployed: The quick swab antigen test, the classic andrapid serological test, and the salivary test. For thequick swab antigen test, the sample collection methodsare similar to those of molecular tests (nasopharyngealswab). This test has a lower sensitivity but it allowsto identify the antigens of the SARS-CoV-2 virus in avery short time (about 15 minutes). The serological (orimmunological) test detects the presence of specific an-tibodies that the immune system produces in responseto infection (IgA, IgM and IgG) and their quantity inthe blood. They tell us if we have contracted the virusand for how long. This test requires a venous bloodsample, and is carried out in specialized laboratories.The rapid serological test is based on the same prin-ciple as the classic one, but it only tells us whether ornot specific antibodies for the virus are present in thebody. The average response time is about 15 minutesand can also be done outside the laboratories. Serolo-gical tests, by their nature, are unable to tell whetherthe patient has an ongoing infection, but only whetheror not he has come into contact with the virus. Theycan therefore provide useful information to understandhow many people have come into contact with thevirus (stratify them by age and geographical region)and to determine if a natural (herd) immunity hasbeen achieved. Salivary collection is simpler and lessinvasive than nasopharyngeal swab or blood sampling.This type of test assesses the presence of the virus inthe body and it could be very useful for screening largenumbers of people. So, when performed on a recurringbasis (every 72 hours), it could allow for rapid isola-tion and outbreak control decisions. This test is, forexample, very important in reopening schools.The choice to do not prioritize a massive use of testsfor screening was certainly one of the problems regard-ing the territorial pandemic control, unfortunately, itwas not the only mistake. In the beginning of a pan-demic, having a few number of infected, the differencesbetween new tests done and new people tested is sosmall to be practically insignificant. Once the pan-demic is spreading enough in the territory, the rate ofnew cases over new tests done (see the regional whitehistograms in Figure 6) can lead to wrong conclusions.What is to be considered, it is the number of new casesover the number of new people tested (blue histogramsin Figure 6).Let us consider an explicit example to understandthe great confusion created by Italian authorities whenlooking at the pandemic data and in the communic-ation with the population. First of all, let us showthe importance of using weekly averages instead ofdaily data. At November 29, Puglia had the follow-ing daily numbers: 907 (53218-52311) new confirmedcases and 8285 (780364-772079) new tests done. Fromthese data, the daily infection rate communicated tothe population was 10.9%. On day later, Puglia had1102 (54320-53218) new cases with 4151 (7845515- 780364) new tests done and, consequently, an infectionrate of 26.5%. This frightening leap get into panicmidia and population. It is clear that a 7-day average,it is a more appropriate way to treat the pandemicdata. By using, the 7-day averages, the rate passesfrom 15.9%, (53218-43507)/(780364-719303), to 16.0%,(54320-44487)/(784515-61434), see the Puglia whitehistogram at the week 40 in Figure 6. After understand-ing that in the communication with the population isbetter used 7-day average, let us now analyse whichwas the mistake done by the Italian authorities in fa-cing the second pandemic wave. As observed before,to calculate the real infection rate, we have to use thenumber of new tested people and not the number ofnew tests. By using the number of new tested people,we find 30.2%, (53218-43507)/(538195-506049), and29.3%, (54320-44487)/(541174-507599), see the Pugliablue histogram at the week 40 in Figure 6. The estim-ation of the correct infection rate is fundamental tounderstand in which stage the pandemic is. An artifi-cial reduction in the infection rate not only creates theproblem of not having the real picture of the infectedin the territory but also creates another even moreserious problem which is the artificial reduction of thepandemic reproduction factor, obtained by analysingthe growth of the infection rate.Looking at Figure 6, the difference between whiteand blue histograms is evident for 5-Emilia Romagna,6-Friuli Venezia Giulia, 9-Lombardia, 8-Liguria, 12-P.A. Bolzano, 13-P.A. Trento, 20-Veneto, and 21-Vald’ Aosta: 8 of the 9 regions (with deaths per milliongreater than 1300) which appear in the top of the tablegiven in Figure 2. Piemonte local authorities used, inaddition to molecular tests, serological tests. Thisobviously reduces the infection rate. As previouslyobserved such tests do not give information on thepatient’s current state of infection. The number of ser-ological tests was removed later, see the Piemonte plotin Figure 6 at the pandemic week number 43 (centredat December 17). Once again an incomprehensiblechoice, in this case done by the local authorities whichdid not follow the indication given by the national ones.The difference between the white and blue histogramsis almost non-existent for 2-Basilicata, 3-Calabria, 4-Campania, 11-Molise, and 16-Sardegna, very smallfor 17-Sicilia, and small for 7-Lazio and 15-Puglia.A minimal difference between the two curves clearlyshows the local capacity to control the spreading ofthe pandemic.Studying the pandemic reproduction factor is cer-tainly one of the main objectives in facing an outbreak,but a correct analysis requires to know the number ofnew people tested by a molecular analysis. Looking atFigure 6, it is incomprehensible how Veneto was alwaysplaced in the area of low pandemic hazard zone (yel-low) and Calabria placed, at November 4, in the one ofgreatest pandemic danger (red) and then, at Novem-ber 27, in the medium risk (orange) never reached the Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] ellow classification. The infection rate is surely oneof the first parameter to be investigated and it couldplay a fundamental role in a timely anticipation of theterritorial spreading of the virus. Nevertheless, threeothers parameters are of great importance when facingthe outbreak: Hospitalized per Million of Inhabitants(pMoI), hospitalized in ICUs pMoI, and, finally deathspMoI. The detailed study of these 3 pandemic para-meters is the subject matter of the next section andleads, together with the confirmed over tested ratio,to the introduction of a numerical pandemic criticalityindex.When discussing the relationship between new con-firmed cases and new tested people, we used 5 coloredzones: up to 10% (cyan), between 10% and 20% (green),between 20% and 30% (yellow), between 30% and 40%(orange), and, finally, greater than 40% (red), see Fig-ure 5. Let us now determine the criticality of thecolored areas for hospitalized and hospitalized in ICUs.For the hospitalized in ICUs, the pandemic criticalareas have been determined by taking into accountthe total number of ICU beds available in each region.Observing that part of the beds must be reserved fornon CoVid-19 patients, the begin of the red zone wasfixed at 60% of occupancy. The least criticality areasare then found between 45 % and 60% (orange), 30%and 45% (yellow), 15% and 30% (green), and, finally,below 15% (cyan). In facing the second pandemic wave,regions have increased their capacity for ICU beds: 3-Calabria 152 ICUs (an increase of 4.8%), 9-Lombardia983 (14.2%), 15-Puglia 366 (20.4%), and 21-Veneto825 (67.0%). Considering their different populations(1.925 M, 10.104 M, 4.008 M, and 4.907 M) we thushave 79.0, 97.3, 91.3, and 168.1 ICUs per million ofinhabitants. The colored zone of criticality are thenfound at (11.9, 23.7, 31.6, and 47.4) for Calabria, (14.6,29.2, 39.9, and 58.4) for Lombardia, (13.7, 27.4, 36.5,and 54.8) for Puglia, and (25.2, 50.4, 67.2, and 100.9)for Veneto, see Figure 8.During the first pandemic wave the most affectedregion showed a factor 10 of proportionality betweenhospitalized and hospitalized in ICUs (see for examplethe gray histograms of 5-Emilia Romagna, 8-Liguria,9-Lombardia, and 14-Piemonte in Figure 7 and 8).The criticality zones for hospitalized people were thusobtained from the ones of hospitalized in ICUs by usinga factor 10.In Figure 9, we find the (7-day average) daily deathsfor million of inhabitants with colors bands fixed at2, 4, 6, and 8. To control the pandemic curves thedaily deaths should not exceed 5 deaths per million ofinhabitants. For one death, we approximatively find50 hospitalized in ICUs and this mean an occupancyof 30% for a country with 150 IUCs per million ofinhabitants (the number suggested by the WHO). VI. The pandemic criticality indexVI. The pandemic criticality index
The use of colors to graphically show the territorialpandemic criticality is understandable: Colored mapsallow to immediately recognize which areas are in a crit-ical situation. Nevertheless, the colored zones should always be accompanied by their corresponding numer-ical pandemic criticality index. Going from one colorto another is like making a quantum leap and it couldeven create confusion in the population. A numbercould better explain the evolution of the pandemiccriticality in a given area. In this Section, we will seehow, by using the four parameters given in the pre-vious Section, it is possible to introduce a numericalindex of pandemic criticality.Let us consider the following five criticality zoneswith the corresponding numerical index interval: • low risk - [ 0 , 1 ) , • medium risk - [ 1 , 2 ) , • medium/high risk - [ 2 , 3 ) , • high risk - [ 3 , 4 ) , • very high risk - [ 4 , ∞ ) .The 7-day average infection rate bands are at 10%, 20%,30%, and 40% (see Figure 6). So, the first normalisedparameter to be used in calculating the numericalpandemic criticality is ρ = 110% new confirmed casesnew tested people . (5)The ratio of 7-day average hospitalized and hospitalizedin ICUs over the available ICUs in each region arecharacterized by the following critical values: 150%,300%, 400%, 600% (Figure 7), and 15%, 30%, 40%,60% (Figure 8). In this case, we introduce the followingtwo normalised parameters ρ = 1150% hospitalizedICUs , (6) ρ = 115% hospitalized in ICUsICUs . Finally, the bands for the 7-day average daily deathsper million of inhabitants are found at 2, 4, 6, and 8.Consequently, the last normalised parameter is givenby ρ = 12 daily deaths per million . (7)These 4 numerical parameters can be then weighed,leading to the numerical pandemic criticality indexpci a,b,c,d = a ρ + b ρ + c ρ + d ρ a + b + c + d . (8)In Figure 10, we plot the numerical index for(a,b,c,d)=(1,1,1,1) and (1,2,3,4), see white lines. In the Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] ame Figure, we also find the mean criticality indexpci = ( pci , , , + pci , , , ) / , (9)see the blue dots in Figure 10. In Table 3, we give, foreach region, the pandemic criticality index correspond-ing to the last 15 pandemic weeks of 2020: From week31 (centred at September 24) to week 45 (centred atDecember 31). In Figure 10 and Table 3, we also asso-ciate a gradation of colors to facilitate the graphicalpresentation of the pandemic criticality index.By using the numerical pandemic criticality index,we can also check the containment measures adopted bythe Italian government. At the beginning of November,the Italian authorities divided the national territoryinto 3 pandemic risk areas: Yellow, orange and redareas with corresponding containment measures. Yel-low area: Curfew from 10pm to 5am of the followingday, public transport with 50% of occupancy, distancelearning for high schools and face-to-face for middleand elementary schools, shopping centres closed onweekends (with the exception of pharmacies, tobaccoshops, newspapers stands), bars and restaurants clos-ing at 6pm. Orange area: to the containment measuresof the yellow area we have to add the closing of barsand restaurants and prohibition of travel between dif-ferent municipalities. Red area: prohibition of anytype of movement if not justified.The first classification done by the Italian authorities(November 4) determines the red zone for Piemonte,Lombardia, Val d’Aosta and Calabria, the orange onefor Puglia and Sicilia, and the yellow area for all theother regions and the two autonomous provinces ofBolzano and Trento. Looking at Table 3, we observethat, at week 36 (centred at October 29) 3-Calabriahad a numerical pandemic index of 0.53 (the bestone in Italy) and 2 regions had an index greater than3 (8-Liguria, 3.15, and 20-Val d’Aosta, 6.24). TheItalian authorities determine the zone of Calabria tobe red and the one of Liguria to be yellow. In thesame Table, we also find that 21-Veneto, 1.34, and15-Puglia had practically the same pandemic index.One week later, Liguria turns into an orange zone. Thenew containment measures allowed to stop and thereduce its numerical pandemic index, see the pandemicweek 39 (centred at November 19). For Veneto, alwaysyellow zone, the pandemic index will increase duringthe following week reaching 6.14 at the last week ofthe year. Calabria never exceeds 2 (one of the bestresult in Italy) but it is one of the first regions tobe classified as a red area and only at December 5is turned into an orange zone. By comparing thepandemic criticality index given in Table 3 with therisk classification assigned by the Italian authoritiesdiscussed in Section 3, the reader will find many otherinconsistencies. VII. ConclusionsVII. Conclusions
The infection reproduction number (IRN) is only oneof the parameter to be checked and probably the onemost problematic. In the first wave of the pandemicthe number of tested people worldwide was often nota reliable number, this implied a wide and sometimesembarrassing IRN range. During the second pandemicwave, the number of tests made has certainly becomemore reliable but as we have seen in this article, inItaly the tests made were used instead of the newtested people . It is clear that monitoring the territorialincrease of the infection is essential to prevent the dif-fusion, but once the pandemic spreads on the territoryother parameters are important to determine the ap-propriate containment measures. If a region, due toa precarious health system or to lack of heath profes-sionals, is, for example, unable to treat patients, it isclear that, independently of its infection reproductionnumber, containment measures must be taken. Hos-pitalized, hospitalized in ICUs, and, obviously, dailydeaths must not only be monitored systematically butalso weighed appropriately. The use of a numerical pandemic criticality index based on few and effectiveparameters can also be easily understood by popula-tion and media. Another important point is that, byusing a numerical range instead of color bands, we canbetter differentiate the criteria of social distancing.CoViD19 web-page at Imecc/Unicamp (Prof. StefanoDe Leo) [30]. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] cknowledgementsAcknowledgements The authors are deeply grateful to Prof. EdmundoCapelas de Oliveira and Dr. Rita Katharina Krausfor their scientific comments and suggestions duringthe preparation of this article. The authors also thankFapesp (SDL) and Capes (MPA) for the financial sup-port.
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Nuovo Coronavirus , [19] S. De Leo, G. G. Maia, and L. Solidoro, Analysing andcomparing the COVID-19 data: The closed cases of Hubeiand South Korea, the dark March in Europe, the beginningof the outbreak in South America ,MedR χ iv, doi.org/10.1101/2020.04.06.20055327 [20] S. De Leo, Covid-19 testing strategies and lockdowns: theEuropean closed curves, analysed by “skew-normal” distri-butions, the forecasts for the UK, Sweden, and the USA,and the ongoing outbreak in Brazil ,MedR χ iv, doi.org/10.1101//2020.06.01.20119461 (to appear in JMIR Public Health and Surveillance).[21] J. K. Patel and C. B. Read, Handbook of the Normal Dis-tribution , (Volume 150 of Statistics: A Series of Textbooksand Monographs, CRC Press, 1996).[22] A. O’Hagan, and T. Leonard,
Bayes estimation subject touncertainty about parameter constraints , Biometrika ,201–202 (1976).[23] A. Azzalini, A Class of Distributions Which Includes theNormal Ones , Scand. J. Stat. , 171-178 (1985).[24] A. Azzalini and A. Dalla Valle, The multivariate skew-normal distribution , Biometrika , 715-726 (1996).[25] Hyoung-Moon Kima Bani K. Mallick A Bayesian predictionusing the skew Gaussian distribution , J. Stat. Planning andInference, 120, 85-101 (2004).[26] A. Azzalini,
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Infection fatality rate of SARS-CoV2in a super-spreading event in Germany , Nature Comm. I diversi tipi di test per il Covid-19 , [30] CoViD19 web-page at Imecc/Unicamp (Prof. Stefano DeLeo), ∼ deleo/CoVid19.html . Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] ppendixAppendix The list of 21 indicators for the pandemic risk controlestablished by the ministerial decree of April 30 [18]. (IA)
1) Number of symptomatic cases notified per monthfor which the starting date of symptoms is indicatedover the total symptomatic cases notified to the sur-veillance system in the same period;2) Number of cases notified per month with a historyof hospital admission, in wards other than intensivecare, for which the date of admission is indicated overthe total of cases with a history of hospital admission,in wards other than intensive care, notified to the tothe surveillance system in the same period;3) Number of cases notified per month with a historyof transfer/admission to the ICU for which the dateof transfer/admission is indicated over the total ofcases with a history of transfer/admission to the ICUnotified to the surveillance system;4) Number of cases notified per month for which themunicipality of domicile or residence is reported overthe total number of cases notified to the surveillancesystem in the same period;5) Number of checklists administered weekly to res-idential and health care facilities (optional);6) Number of residential and health care facilitiesthat respond to the checklist on a weekly basis withat least one criticality found (optional); (IB)
7) Percentage of positive swabs, excluding as far aspossible all screening activities and re-testing of thesame subjects, overall and by macro-setting (territorial,emergency room/hospital, other) per month.8) Time between symptom onset date and diagnosisdate.9) Time between symptom onset date and isolationdate (optional).10) Number, type of professional figures and timeover the total number of people dedicated to contact-tracing in each territorial service.11) Number, type of professional figures and timeover the total of people dedicated in each territorialservice to the activities of sampling/sending to thereference laboratories and monitoring of close contactsand cases placed respectively in quarantine and isola-tion.12) Number of confirmed cases of infection in theRegion for which a regular epidemiological investiga-tion was carried out with the search for close contacts,out of the total of new confirmed cases of infection. (IC)
13) Number of cases reported to the Civil Protectionin the last 14 days. 14) R t calculated on the basis of integrated ISSsurveillance (two indicators, based on the symptomstart and hospitalization dates, are used).15) Number of cases reported to Covid-net sentinelsurveillance per week (optional).16) Number of cases by diagnosis date and symptomonset date reported to integrated Covid surveillanceper day.17) Number of new transmission outbreaks (2 ormore epidemiologically linked cases or an unexpectedincrease in the number of cases in a defined time andplace).18) Number of new cases of confirmed SARS-CoV-2infection per region not associated with known trans-mission chains.19) Number of accesses to the emergency room withICD-9 classification compatible with syndromic pic-tures attributable to Covid-19 (optional)20) Occupancy rate of total intensive care beds (code49) for Covid patients.21) Occupancy rate of total medical area beds forCovid patients. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 1.: Worldwide deaths per million of inhabintants.
The infograhic shows the deaths per million (DpM) ofinhabitants of the countires with a population greater than 10 million of people and DpM greater than 100at December 31 (2020). In the attached Table, for the countries with DpM greater than 240, we also showthe absolute number of deaths.
Figure 2.:
Regional deaths per million of inhabintants.
The infograhic shows the deaths per million (DpM) ofinhabitants of the regions and autonomous provinces of Italy at December 31 (2020). The absolute numberof deaths appears in the attached Table. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] able 1.: Pandemic data.
The7-day averages of positives (A),hospitalized (B), hospitalized inICUs (C), and daily deaths (D)are given for the pandemic week2, 5, 36, 39, 42, and 45. Inthe Table, we also find the corres-ponding values per million of in-habitants (A ∗ , B ∗ , C ∗ , and C ∗ ).The regional populations appearin the central column, P[M]. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 3.: Pandemic plots.
The 7-day averages of hospitalized over positives, hospitalized in ICUs over ICUs, (B),and daily deaths are given for the pandemic week 2, 5, 36, 39, 42, and 45. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] able 2.: Skew-normal parameters.
The values of T , µ , σ , and s which allow to model the Italian pandemic curvesare given for the total confirmed cases, positives, hospitalized, hospitalized in ICUs, and deaths. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 4.: Skew-normal distributions.
The pandemic curves of total confirmed cases (colored histograms), positives(gray), and hospitalized (white) are modelled by skew-normal distribution. The analytical plots show anexcellent agreement with the pandemic data. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 5.: Skew-normal distributions.
The pandemic curves of total deaths (colored histograms) and hospitalized inICUs (white) are modelled by skew-normal distribution. The analytical plots show an excellent agreementwith the pandemic data. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 6.: The first pandemic parameter.
The 7-day averages of new confirmed cases over new tests done (white his-tograms) and new people tested (blue histograms). The use of the incorrect ratio implies an underestimationof the infection reproduction number. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 7.: The second pandemic parameter.
The 7-day averages of hospitalized per million of inhabitants are plottedfor the first 15 pandemic week (gray histograms) and for the last 15 ones (blue histograms). Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 8.: The third pandemic parameter.
The 7-day averages of hospitalized in ICUs per million of inhabitants areplotted for the first 15 pandemic week (gray histograms) and for the last 15 ones (blue histograms). Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 9.: The fourth pandemic parameter.
The 7-day averages of daily deaths per million of inhabitants are plottedfor the first 15 pandemic week (gray histograms) and for the last 15 ones (blue histograms). Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] able 3.: Numerical values of the pandemic criticality index (pci).
The numerical values of the regional pci aregiven for the last 15 pandemic weeks of the year. In the Table, we also find the color indicating the risk zone. Σ δ Λ S. De Leo and M. P. Araújo [arxiv.org/abs/2102.03373 (q-bio.PE)] igure 10.: The pandemic criticality index (pci).