Spread and Dynamics of the COVID-19 Epidemic in Italy: Effects of Emergency Containment Measures

Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures

Marino Gattoa,1 , Enrico Bertuzzob,c , Lorenzo Maria , Stefano Miccolid , Luca Carraroe,f , Renato Casagrandia , and Andrea Rinaldog,h,1

aDipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy; bDipartimento di Scienze Ambientali, Informatica e Statistica, Universita` Ca’ Foscari Venezia, 30172 Venezia-Mestre, Italy; cScience of Complexity Research Unit, European Centre for Living Technology, 30123 Venice, Italy; dDipartimento di Meccanica, Politecnico di Milano, 20133 Milano, Italy; eDepartment of Aquatic Ecology, Swiss Federal Institute of Aquatic Science and Technology, 8600 Dubendorf,¨ Switzerland; fDepartment of Evolutionary Biology and Environmental Studies, University of Zurich, 8057 Zurich, Switzerland; gLaboratory of Ecohydrology, Ecole´ Polytechnique Fed´ erale´ de Lausanne, 1015 Lausanne, Switzerland; and hDipartimento di Ingegneria Civile, Edile e Ambientale, Universita` di Padova, 35131 Padova, Italy

Contributed by Andrea Rinaldo, April 6, 2020 (sent for review March 26, 2020; reviewed by Andy P. Dobson and Giorgio Parisi)

The spread of coronavirus disease 2019 (COVID-19) in Italy eling predictions therein disregard the observed spatial nature of prompted drastic measures for transmission containment. We the progress of the wave of infections, and can treat only indi- examine the effects of these interventions, based on modeling of rectly the effects of containment measures. Critically, therefore, the unfolding epidemic. We test modeling options of the spatially to deal with what could happen next in terms of forthcom- explicit type, suggested by the wave of infections spreading from ing policy decisions, one needs to deal with spatially explicit the initial foci to the rest of Italy. We estimate parameters of a models (12, 28, 29). metacommunity Susceptible–Exposed–Infected–Recovered (SEIR)- We model in space and time the countrywide spread of the like transmission model that includes a network of 107 provinces COVID-19 epidemic in Italy (Materials and Methods), for which connected by mobility at high resolution, and the critical contri- detailed epidemiological data are continuously updated and bution of presymptomatic and asymptomatic transmission. We made public (16, 18, 30). Data are only a proxy of the actual estimate a generalized reproduction number (R0 = 3.60 [3.49 to epidemiological conditions because 1) the number of infected 3.84]), the spectral radius of a suitable next-generation matrix people on record depends on the sampling effort, namely, the that measures the potential spread in the absence of containment number of specimen collections (swabs) from persons under interventions. The model includes the implementation of progres- investigation (PUIs) (implications discussed in Materials and sive restrictions after the first case confirmed in Italy (February 21, Methods, and SI Appendix); and 2) the effects of systematic errors 2020) and runs until March 25, 2020. We account for uncertainty in or bias in the official data result mainly in underreporting and epidemiological reporting, and time dependence of human mobil- need to be considered. In fact, underreporting may apply even ity matrices and awareness-dependent exposure probabilities. to fatality counts, yet to a lesser extent with respect to reported We draw scenarios of different containment measures and their infections. Hospitalizations are known, but may underestimate impact. Results suggest that the sequence of restrictions posed to the actual situation because cases with mild symptoms (termed mobility and human-to-human interactions have reduced transmission by 45% (42 to 49%). Averted hospitalizations are mea- sured by running scenarios obtained by selectively relaxing the Significance imposed restrictions and total about 200,000 individuals (as of March 25, 2020). Although a number of assumptions need to be The ongoing pandemic of COVID-19 challenges globalized reexamined, like age structure in social mixing patterns and in societies. Scientific and technological cross-fertilization yields the distribution of mobility, hospitalization, and fatality, we con- broad availability of georeferenced epidemiological data and clude that verifiable evidence exists to support the planning of of modeling tools that aid decisions on emergency manage- emergency measures. ment. To this end, spatially explicit models of the COVID-19 epidemic that include e.g. regional individual mobilities, the SARS-CoV-2 | spatially explicit epidemiology | disease outbreak progression of social distancing, and local capacity of medical scenarios | SEIR models | social contact restrictions infrastructure provide significant information. Data-tailored spatial resolutions that model the disease spread geography ince December 2019, a cluster of pneumonia cases in the can include details of interventions at the proper geograph- Scity of Wuhan, China (1–7), has developed into a pandemic ical scale. Based on them, it is possible to quantify the wave currently ravaging several countries (8–12). The pathogen effect of local containment measures (like diachronic spatial causing the acute pneumonia among affected individuals is the maps of averted hospitalizations) and the assessment of the new coronavirus severe acute respiratory syndrome coronavirus spatial and temporal planning of the needs of emergency 2 (SARS-CoV-2) (8, 9, 13, 14). As of March 25, 2020, a total measures and medical infrastructure as a major contingency of 467, 593 cases of coronavirus disease 2019 (COVID-19) have planning aid. been confirmed worldwide in 181 countries (15). In Italy, a hotspot of the pandemic, the count, as of March 25, 2020, Author contributions: M.G., E.B., L.M., S.M., L.C., R.C., and A.R. designed research; M.G., E.B., L.M., S.M., L.C., R.C., and A.R. performed research; E.B., L.M., S.M., and L.C. analyzed refers to 74, 386 total confirmed cases and 7, 503 deaths (15– data; and M.G., E.B., L.M., S.M., L.C., R.C., and A.R. wrote the paper.y 18) (Figs. 1 and 2). The well-monitored progress of the wave of Reviewers: A.P.D., Princeton University; and G.P., Sapienza University of Rome.y infections highlighted in Fig. 1 (for complete documentation, see The authors declare no competing interest.y SI Appendix and Movies S1 and S2) clearly speaks of decisive This open access article is distributed under Creative Commons Attribution License 4.0 spatial effects. Models are often used to infer key processes or (CC BY).y evaluate strategies for mitigating influenza/SARS pandemics (5, 1 To whom correspondence may be addressed. Email: andrea.rinaldo@epfl.ch or 6, 12, 19–24). Early attempts to model the spread of COVID- [email protected] 19 in Italy (25, 26) aired concern regarding the Italian national This article contains supporting information online at https://www.pnas.org/lookup/suppl/ health system’s capacity to respond to the needs of patients (27), doi:10.1073/pnas.2004978117/-/DCSupplemental.y even considering aggregate isolation measures. However, mod- First published April 23, 2020.

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MEDICAL SCIENCES We propose an estimate of total infections computed from our Materials and Methods model (SI Appendix, Fig. S14). We find a significantly larger fig- Epidemiological Model. Many models have been developed to describe the ure than in the official counts: as of March 25, 2020, we estimate a course of the COVID-19 pandemic in individual countries or at the global median of about 600, 000 contagions, whereas the official count scale. Actually, no clear consensus has been reached on the different com- of confirmed infections is 74, 386. This result does not confirm partments that should be included in a proper model. Our model choice earlier, much larger estimates (63). However, the estimation of was motivated by a review of the existing approaches. Most models assume certain key epidemiological parameters proves remarkably simi- a standard SEIR structure but make different hypotheses on the nature of the different compartments and their respective residence times. Some of lar in ref. 63 and in this paper, possibly providing an avenue for the key epidemiological features characteristic of COVID-19 are summarized future convergence. in Table 1, together with the appropriate references, while the different We conclude that a detailed spatially explicit model of the approaches are described in more detail in SI Appendix. unfolding COVID-19 spread in Italy, inclusive of the imposed Here, we propose and use a model that is elaborated moving from restriction measures, closely reproduces the empirical evidence. the basic local scheme of ref. 5. By introducing the new compartment of This allows us to draw significant indications of the key processes presymptomatic infectious individuals, we account for a peculiar epidemi- involved in the contagion, together with their time-dependent ological state of the disease under study. Empirical evidence (see again nature and parameters. When applied by restarting the Table 1) shows, in fact, that the serial interval of COVID-19 tends to be simulation while removing the restrictive measures, the model shorter than the incubation period, thus suggesting that a substantial pro- portion of secondary transmission can occur prior to illness onset (68). shows, unequivocally, that their effects have been decisive. Presymptom transmission appears to play an important role in speeding Indeed, the total expected number of averted hospitalizations up the spread of the disease within a community, accounting for around in Italy, a significant measure of the needs of emergency man- 12.6% of case reports in China (49), 48% in Singapore, and 62% in Tianjin, agement (and the less error-prone epidemiological measure), China (74). The core of our model is thus termed SEPIA and includes the ran on the order of 200, 000 cases up to March 25, 2020, for following compartments: Susceptible (S), Exposed (E), Presymptomatic (P), the whole country, and is known with sufficient spatial granu- Infected with heavy symptoms (I), Asymptomatic/mildly symptomatic (A), larity. Implications on fatality rates and emergency management Hospitalized (H), Quarantined at home (Q), Recovered (R), and Dead (D) are direct, as the capacity of the Italian medical facilities— individuals. although continuously expanding—is known at each relevant The local dynamics of transmission is given by time. Thus our results bear social and economic significance, S˙ = −λS because they unquestionably support drastic governmental ˙ decisions. E = λS − δEE ˙ P = δEE − δP P ˙ I = σδP P − (η + γI + αI)I Table 1. Key epidemiological periods to model the dynamics of ˙ A = (1 − σ)δP P − γAA [1] COVID-19 together with values of R0 ˙ H = (1 − ζ)ηI − (γH + αH)H Period Values (days) Reference ˙ Q = ζηI − γQQ Latency 7 (5, 10) ˙ R = γII + γAA + γHH 5.2 (CI = [4.1–7.0]) (4, 9, 14) 95% ˙ 3.44–3.69 (28) D = αII + αHH. Serial interval 7.5 (mean, CI95% = [5.5–19], n = 6 (64) In the model, susceptible individuals (S) become exposed to the viral 5.1 (mean, CI95% = [1.3–11.6], n = 8579) (65) agent upon contact with infectious individuals, assumed to be those in the 4.56 (mean, CI95% = [2.69–6.42], n = 93) (66) presymptomatic, heavily symptomatic, or asymptomatic/mildly symptomatic 4.22 (mean, CI95% = [3.43–5.01], n = 135) classes. Although the hypothesis might not hold for some very sparse com- 4.4 (mean, CI95% = [2.9–6.7], n = 21) (67) munities, we assume frequency-dependent contact rates (as most authors do), so that exposure occurs at a rate described by the force of infection, 4.0 (mean, CI95% = [3.1–4.9], n = 28) (68) 3.96 (mean, CI95% = [3.53–4.39], n = 468) (49) βP P + βII + βAA Incubation 9 (mean, CI = [7.92–10.2], n = 135) (66) λ = , 95% S + E + P + I + A + R 7.1 (mean, CI95% = [6.13–8.25], n = 93) 6.6 (mean, CI95% = [0.7–19.0], n = 90) (55) where βP , βI, and βA are the specific transmission rates of the three infectious classes. Exposed individuals (E) are latently infected, that is, still not 5.1 (median, CI95% = [4.5–5.8] (69) contagious, until they enter the presymptom stage (at rate δE) and only 5.2 (mean, CI95% = [4.1–7.0], n = 10) (9) then become infectious. Presymptomatic individuals (P) progress (at rate δ ) 6.4 (mean, CI = [5.6–7.7], n = 88) (70) P 95% to become symptomatic infectious individuals who develop severe symp- 5 (mean, CI = [4.2–6.0], n = 52) (71) 95% toms (with probability σ). Alternatively, they become asymptomatic/mildly 5.6 (mean, CI95% = [5.0–6.3], n = 158) symptomatic individuals (with probability 1 − σ). Symptomatic infectious 5.2 (mean, CI95% = [1.8–12.4], N = 8579) (65) individuals (I) exit their compartment if/when 1) they are isolated from 4.8 (mean, SD = 2.6, n = 830) (64) the community (at rate η) because a fraction 1 − ζ of them is hospital- ∼= latency (12–14) ized, while a fraction ζ is quarantined at home, 2) they recover from lag of 5 (4) infection (at rate γI), or 3) they die (at rate αI). Asymptomatic/mildly Infectious 2.16 (range 1.64–3.10) (5) symptomatic individuals (A), on the other hand, leave their compartment 2.4 (13) after having recovered from infection (at rate γA). Hospitalized individuals (H) may either recover from infection (at rate γ ) or die because 2.9 (14) H of it (at rate α ), while home-isolated individuals (Q) leave their com- 3.5 (28) H partment upon recovery (at rate γQ). People who recover from infection 2–8 (12) or die because of COVID-19 populate the class of recovered (R) and R0 2.2 (CI95% = [1.4–3.9]) (9) dead (D) individuals, respectively, independently of their epidemiological 2.6 (CI 2.1 − 5.1) (72) compartment of origin. 3.1 (CI95% = [2.9–3.2]) (55) The model is made spatial by coupling n human communities at the suit- 4.5 (CI95% = [4.4–4.6]) (73) able resolution via a community-dependent force of infection. It results from local and imported infections due to contacts within the local com- 4.4 (CI95% = [4.4–4.6]) (73) munity or associated with citizens’ mobility. More precisely, the force of 6.47 (CI95% = [5.71–7.23]) (5) infection for community i is given by

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Matrix n. C A T ij X {S ∈ k IAppendix SI = nt that (note j o all for 1 seither as , P , I K , A}) L is i i 1/γ 1/η 1/δ 1/δ R with parameter and each estimates of MCMC priors parameters, relevant social estimated of in List 2. increase Table the and sim- behavior To social 37. in ref. in change collected presented the data and ulate to trav- applications people according of mobile province fraction through resident the the reducing from outside starting 2) eling S5–S7), and Figs. 2020, Appendix , 23, (SI February areas and red access the restricting from 1) exit by above described measures restriction data. mobility the from provincial derived Matrices the are to Appendix). upscaled (SI were level com- entities) administrative (7,904 which the at level available second areas), fluxes municipal mobility the metropolitan census Therefore, units. and of 107 prises provinces scale (mainly the level at implemented Estimation. been Parameter and Implementation Model extended; is area lockdown the 20), (day 2020 11, March On E) 15 and Lombardy of whole the 17), (day 2020 8, March On D) travel- to link clear no as 3), (day 2020 23, February On C) by one” “patient (dubbed patient a 2020, 18, February On A) summa- be human may follows: to Italy as in Reduction. posed rized contacts restrictions Contact human-to-human and progressive and mobility of Restrictions sequence Mobility detailed for Measures Parameter [a,b] interval the in distribution average of distribution ∆t β β β β 1/α ω )O eray2,22 dy1,“ain n”i fcal con- officially is one” “patient 1), (day 2020 21, February On B) P P I A 0 /β (-) 2 1 /β otro itiuin r hw in shown are distributions Posterior the of effects the simulations our in reproduce explicitly We 0 - .0[.9 3.84] [3.49, 3.60 (-) /β /β P E I A I eeelmttost oiiyfrtewoento are nation whole the for mobility to instituted. limitations severe toward moving and Italy northern regions. reac- other leaving panic of people a draft prompts with a measures tion, these of implementing leak law A the measures. distancing Italy of social rest The implements lockdown. under are provinces Italy northern Veneto, Province Trento. of Autonomous Emilia-Romagna, and Lombardy, Piedmont, Giulia, restric- in Friuli-Venezia some enacted areas); (red infection are lockdown as tions strict identified under Veneto, put in are one foci, municipal- and Ten Lombardy Padua). in of dis- ities province is (Veneto, infections Vo’ of in for cluster covered second transmission A local increases. for one” evidence “patient emerges, China from ers A confirmed. Veneto. are in Lombardy confirmed in are cases cases 16 the two by further other starts; day area the Codogno of the and end in path, population transmission of the Milano; testing trace in mass Sacco to Ospedale struggle by authorities COVID-19 local of case a as firmed in pneumonia. room for Lodi) emergency of the province to (Lombardy, admitted Codogno is outlets) media Italian (d) (d) P (d) (d) (d) (d) P P (-) (-) 1 (-) (-) PNAS 49 3.2 39.30] [31.62, 34.94 43 1.4 15.81] [13.64, 14.32 42 2.5 26.87] [22.35, 24.23 ein(5 CIs) (95% Median a .5[.5 4.29] [3.85, 4.05 .2[.7 0.86] [0.77, 0.82 .3[.9 1.38] [0.79, 1.03 .4[.0 8.34] [7.10, 7.84 .5[.1 1.02] [0.61, 0.75 .2[.3 3.66] [3.03, 3.32 .6[.4 0.70] [0.64, 0.66 .3 007 0.0036] [0.027, 0.033 n SD and | a 2 2020 12, May C and b, X i.S15. Fig. Appendix, SI [C = N ij | U X ] (a, (a, o.117 vol. (X en normal a being b) en uniform a being b) {S ∈ h oe has model The | , o 19 no. E N N N N N U U U U U U U , 0 100) (0, 0 100) (0, 4 0.4) (4, 0 0.5) (0, 0 1) (0, 0 1) (0, 0 100) (0, 0 100) (0, P 4 0.4) (4, 1 0.1) (1, ,0.25) (2.5, 1 0.2) (1, Prior , | I , 10489 The A})

MEDICAL SCIENCES distancing, we assume that the transmission parameters βP , βI , tion number R0 (SI Appendix). βP1 and βP2 represent the values and βA had a sharp decrease (within 2 d) after the measures of the parameter βP after the measures introduced on February announced on February 24 and March 8, 2020, and we esti- 22 and on March 8, 2020, respectively. The fraction of symp- mate those step reductions (Table 2). It should be noted that the tomatic infected being quarantined, ζ, is assumed to be equal to reduction in the transmission parameters is due not only to the 0.4, that is, the average value for Italy during the observed period implementation of restriction measures (e.g., school and office (17). During preliminary tests, we found a correlation between closures) but also to the increased awareness of the population, the asymptomatic fraction (1 − σ) and the asymptomatic trans- especially after the first cases were reported. mission rate βA. Indeed, in the early phase of an epidemic, Model parameters are estimated in a Bayesian framework by when the depletion of susceptible is not significant, it is diffi- sampling the posterior parameter distribution via the DREAMzs cult to estimate the role or asymptomatics. We therefore fixed (77) implementation of the MCMC algorithm. As testing effort σ to a reasonable value (σ = 0.25; see, e.g., ref. 80) and esti- and quarantine policy vary across different Italian regions, we mated βA. The parameter rX represents the fraction of total prefer to focus on more reliable variables like the number of personal contacts that individuals belonging to the X compart- hospitalized people, deaths, and patients discharged from the ment have in the destination community (SI Appendix). We hospital. Specifically, we define the likelihood based on daily assume rS = 0.5 (i.e., each individual has, on average, half of numbers of hospitalized cases (flux ηI ), discharged from hospital the contacts in the place of work or study) and that rE = rP = (γH H ), and recorded deaths (αH H ) at the province level. To rA = rR = rS , while rI = rQ = rH = 0 (no extra province mobility account for possible overdispersion of the data, we assume that of symptomatic infected, quarantined, and hospitalized individ- each data point follows a negative binomial distribution (78, 79) uals). Further assumptions aimed at reducing the number of with mean µ, equal to the value predicted by the model, and parameters to be estimated are γQ = γI = γH , γA = 2γI , and variance equal to ωµ (NB1 parametrization). We estimated the αH = αI . We use information summarized in Table 1 to define parameter ω. prior distributions of key timescale parameters (Table 2). More- To account for the temporal evolution of the epidemics prior over, the viral load of symptomatic cases is reportedly similar to to the first detected patient, we impose an initial condition of that of the asymptomatic (81). We use such information to define one exposed individual in the province of Lodi (where the first the prior of the ratio βI /βA. cases emerged) ∆t0 days before February 24, 2020, and we estimate this parameter. During this period, the disease was Data Availability. All data used in this manuscript are publicly likely seeded into other provinces via either human mobility available. COVID-19 epidemiological data for Italy are avail- or importation of cases from abroad. The process during this able at https://github.com/pcm-dpc/COVID-19. Mobility data at period was likely characterized by high demographic stochastic- municipality scale are available at https://www.istat.it/it/archivio/ ity due to the low number of involved individuals, and thus it 139381. Population census data are available at http://dati.istat. can hardly be captured by our deterministic modeling of average it/Index.aspx?QueryId=18460. mobility and disease transmission. Moreover, long-distance trav- els and importation of cases are not accounted for in the data ACKNOWLEDGMENTS. The work of M.G., R.C., L.M., and S.M. was per- used to represent human mobility, which mostly reflect commut- formed with the support of the resources provided by Politecnico di Milano. E.B. gratefully acknowledges the support of the Universita` Ca’ Foscari ing fluxes for work and study purposes. Therefore, to include Venezia. L.C. acknowledges the Swiss National Science Foundation Grant this possible seeding effect, we estimated also the initial con- PP00P3 179089. A.R. acknowledges the spinoffs of his European Research dition in each province. Specifically, this is done by seeding a Council Advanced Grant RINEC-227612 “River networks as ecological corri- small fraction of exposed individuals at the beginning of the dors: species, populations, pathogens,” and the funds provided by the Swiss National Science Foundation Grant 200021172578/1 “Optimal control of simulation. intervention strategies for waterborne disease epidemics.” We also thank The list of estimated parameters is reported in Table 2. The Arianna Azzellino, Fabrizio Pregliasco, Maria Caterina Putti, and Giovanni parameter βP is expressed as a function of the local reproduc- Seminara for useful suggestions.

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