The early phase of the COVID-19 outbreak in Lombardy, Italy
D Cereda, M Tirani, F Rovida, V Demicheli, M Ajelli, P Poletti, F Trentini, G Guzzetta, V Marziano, A Barone, M Magoni, S Deandrea, G Diurno, M Lombardo, M Facc… 展开作者
D Cereda, M Tirani, F Rovida, V Demicheli, M Ajelli, P Poletti, F Trentini, G Guzzetta, V Marziano, A Barone, M Magoni, S Deandrea, G Diurno, M Lombardo, M Faccini, A Pan, R Bruno, E Pariani, G Grasselli, A Piatti, M Gramegna, F Baldanti, A Melegaro, S Merler
In the night of February 20, 2020, the first case of novel coronavirus disease (COVID-19) was confirmed in the Lombardy Region, Italy. In the week that followed, Lombardy experienced a very rapid increase in the number of cases. We analyzed the first 5,830 laboratory-confirmed cases to provide the first epidemiological characterization of a COVID-19 outbreak in a Western Country. Epidemiological data were collected through standardized interviews of confirmed cases and their close contacts. We collected demographic backgrounds, dates of symptom onset, clinical features, respiratory tract specimen results, hospitalization, contact tracing. We provide estimates of the reproduction number and serial interval. The epidemic in Italy started much earlier than February 20, 2020. At the time of detection of the first COVID-19 case, the epidemic had already spread in most municipalities of Southern-Lombardy. The median age for of cases is 69 years (range, 1 month to 101 years). 47% of positive subjects were hospitalized. Among these, 18% required intensive care. The mean serial interval is estimated to be 6.6 days (95% CI, 0.7 to 19). We estimate the basic reproduction number at 3.1 (95% CI, 2.9 to 3.2). We estimated a decreasing trend in the net reproduction number starting around February 20, 2020. We did not observe significantly different viral loads in nasal swabs between symptomatic and asymptomatic. The transmission potential of COVID-19 is very high and the number of critical cases may become largely unsustainable for the healthcare system in a very short-time horizon. We observed a slight decrease of the reproduction number, possibly connected with an increased population awareness and early effect of interventions. Aggressive containment strategies are required to control COVID-19 spread and catastrophic outcomes for the healthcare system.
I use a very simple deterministic model for the spread of Covid-19 in a large population. Using this to compare the relative decay of the number of deaths per day between different regions in Italy, Spain and England, each applying in principle the same social distancing procedures across the whole country, I obtain an estimate of the total fraction of the population which had already become infected by April 10th. In the most heavily affected regions, Lombardy, Madrid and London, this fraction is higher than expected, i.e. $\approx 0.3$. This result can then be converted to a determination of…
The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed) model with a compartment for infected individuals with no symptoms or few symptoms was proposed by Giuseppe Gaeta, arXiv:2003.08720 [q-bio.PE] (2020). In this paper we investigate a slightly generalized version of the same model and propose a scheme for fitting the parameters of the model to real data using the time series only of the deceased individuals. The scheme is…
We present a compartmental mathematical model with demography for the spread of the COVID-19 disease, considering also asymptomatic infectious individuals. We compute the basic reproductive ratio of the model and study the local and global stability for it. We solve the model numerically based on the case of Italy. We propose a vaccination model and we derive threshold conditions for preventing infection spread in the case of imperfect vaccines.
During the COVID-19 outbreak, it is essential to monitor the effectiveness of measures taken by governments on the course of the epidemic. Here we show that there is already a sufficient amount of data collected in Italy to predict the outcome of the process. We show that using the proper metric, the data from Hubei Province and Italy has striking similarity, which enables us to calculate the expected number of confirmed cases and the number of deaths by the end of the process. Our predictions will improve as new data points are generated day by day, which can help to make further public decis…
The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is proposed with the aim of re…
The aim of this paper consists in the application of a recent epidemiological model, namely SEIR with Social Distancing (SEIR--SD), extended here through the definition of a social distancing function varying over time, to assess the situation related to the spreading of the coronavirus Covid--19 in Italy and in two of its most important regions, i.e., Lombardy and Campania. To profitably use this model, the most suitable values of its parameters must be found. The estimation of the SEIR--SD model parameters takes place here through the use of Differential Evolution, a heuristic optimization t…
In this paper we propose a Susceptible-Infected-Exposed-Recovered-Dead (SEIRD) differential model for the analysis and forecast of the COVID-19 spread in some regions of Italy, using the data from the Italian Protezione Civile from February 24th 2020. In this study investigate an adaptation of the model. Since several restricting measures have been imposed by the Italian government at different times, starting from March 8th 2020, we propose a modification of SEIRD by introducing a time dependent transmitting rate. In the numerical results we report the maximum infection spread for the three I…
We use daily data from Lombardy, the Italian region most affected by the COVID-19 outbreak, to calibrate a SIR model individually on each municipality. These are all covered by the same health system and, in the post-lockdown phase we focus on, all subject to the same social distancing regulations. We find that municipalities with a higher number of cases at the beginning of the period analyzed have a lower rate of diffusion, which cannot be imputed to herd immunity. In particular, there is a robust and strongly significant negative correlation between the estimated basic reproduction number (…
A great issue of discussion of an infectious disease is its basic reproduction number R0, which provides an estimation of the contagiousness of the disease. When R0 > 1, the disease spread will potentially lead to an outbreak, such that of the ongoing COVID-19 pandemics. During the evolution of an outbreak, various non-pharmaceutical interventions are employed, the impact of which is frequently assessed by the reduction that they introduce to the effective reproduction number Rt; reduction below 1 is an indication of eventual dying out of the disease spread. Motivated by the fact that R0 essen…
West Nile virus outbreak in Italy modelled with the quantum Game of Life
Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）；INFN Napoli（意大利国家核物理研究所那不勒斯分部）；Università degli Studi di Palermo（巴勒莫大学）；Lobachevsky University of Nizhny Novgorod（下诺夫哥罗德罗巴切夫斯基大学）
This paper presents an dashboard developed to analyse the outbreak of the Covid-19 infection in Italy considering daily NUTS-3 data on positive cases provided by the Italian Ministry of Health and on deaths derived from Italian regional authorities' official press conferences. Descriptive time series plots are provided together with a map describing the spatial distribution of province cumulative cases and rates. A section on a proposed time-dependent adjusted SIRD model for NUTS-3 regions is also provided in the dashboard.
We propose a novel data-driven framework for assessing the a-priori epidemic risk of a geographical area and for identifying high-risk areas within a country. Our risk index is evaluated as a function of three different components: the hazard of the disease, the exposure of the area and the vulnerability of its inhabitants. As an application, we discuss the case of COVID-19 outbreak in Italy. We characterize each of the twenty Italian regions by using available historical data on air pollution, human mobility, winter temperature, housing concentration, health care density, population size and …
In this paper we introduce a space-dependent multiscale model to describe the spatial spread of an infectious disease under uncertain data with particular interest in simulating the onset of the COVID-19 epidemic in Italy. While virus transmission is ruled by a SEIAR type compartmental model, within our approach the population is given by a sum of commuters moving on a extra-urban scale and non commuters interacting only on the smaller urban scale. A transport dynamic of the commuter population at large spatial scales, based on kinetic equations, is coupled with a diffusion model for non commu…
The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation (ODE) models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of a…
In the absence of other tools, monitoring the effects of protective measures, including social distancing and forecasting the outcome of outbreaks is of immense interest. Real-time data is noisy and very often hampered by systematic errors in reporting. Detailed epidemic models may contain a large number of empirical parameters, which cannot be determined with sufficient accuracy. In this paper, we show that the cumulative number of deaths can be regarded as a master variable, and the parameters of the epidemic such as the basic reproduction number, the size of the susceptible population, and …
We discuss the generation of various reproduction ratios or numbers that are very useful to monitor an ongoing epidemic like Covid-19 and examine the effects of intervention measures. A detailed SEIR algorithm is described for their computation, with applications given to the current Covid-19 outbreaks in a number of countries (Argentina, Brazil, France, Italy, Mexico, Spain, UK and USA). The corresponding matlab script, complete and ready to use, is provided for free downloading.
Using the classical Susceptible-Infected-Recovered epidemiological model, an analytical formula is derived for the number of beds occupied by Covid-19 patients. The analytical curve is fitted to data in Belgium, France, New York City and Switzerland, with a correlation coefficient exceeding 98.8%, suggesting that finer models are unnecessary with such macroscopic data. The fitting is used to extract estimates of the doubling time in the ascending phase of the epidemic, the mean recovery time and, for those who require medical intervention, the mean hospitalization time. Large variations can be…
The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources, such as the amount of infectious individuals. In this paper we address the above aspects through a hyperbolic compartmental model on networks, in which nodes identify locations of interest, such as cities or regions, and arcs represent the ensemble of main mobility paths. The model describes the spatial movement and interacti…
Background: Northern Italy was one of the most impacted areas by COVID. It is now widely assumed that the virus was silently spreading for at least 2 weeks before the first patient was identified. During this silent phase, and in the following weeks when the hospital system was overburdened, data collection was not performed in an accurate enough way to estimate an epidemic curve. With the aim of assessing both the dynamics of the introduction of the virus and the effectiveness of containment measures introduced, we try to reconstruct the epidemic curve using all cause mortality data. Methods:…
The current COVID-19 pandemic is having detrimental consequences worldwide. The pandemic started to develop strongly by the end of January and beginning of February 2020, first in China with subsequent rapid spread to other countries with new epicenters of the outbreaks concentrated mainly within the 30-50 degrees North latitudinal band (e.g., South Korea, Japan, Iran, Italy, Spain). Simultaneously, an unusual persistent anticyclonic situation prevailing at latitudes around 40 degrees North was observed on global scale, in line with an anomalously strong positive phase of the Arctic Oscillatio…
In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window $22/01-09/03/2020$. A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-(confirmed) infected-recovered-deaths model indicates that the kinetic parameter that des…
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in…
The impact of the outbreak of COVID-19 on health has been widely concerned. Disease risk assessment, prediction, and early warning have become a significant research field. Previous research suggests that there is a relationship between air quality and the disease. This paper investigated the impact of the atmospheric environment on the basic reproduction number (R$_0$) in Australia, South Korea, and Italy by using atmospheric environment data, confirmed case data, and the distributed lag non-linear model (DLNM) model based on Quasi-Poisson regression. The results show that the air temperature…
Background. The paper concerns the SARS-CoV2 (COVID-19) pandemic that, starting from the end of February 2020, began spreading along the Italian peninsula, by first attacking small communities in north regions, and then extending to the center and south of Italy, including the two main islands. Objective. The creation of a forecast model that manages to alert the decision-making bodies and, in particular, the healthcare system, to hinder the emergence of any other pandemic outbreaks, or the arrival of subsequent pandemic waves. Methods. A new mathematical model to describe the pandemic is give…
Accurate modeling of lockdown effects on SARS-CoV-2 epidemic evolution is a key issue in order e.g. to inform health-care decisions on emergency management. The compartmental and spatial models so far proposed use parametric descriptions of the contact rate, often assuming a time-invariant effect of the lockdown. In this paper we show that these assumptions may lead to erroneous evaluations on the ongoing pandemic. Thus, we develop a new class of nonparametric compartmental models able to describe how the impact of the lockdown varies in time. Exploiting regularization theory, hospitalized dat…
The spread of the coronavirus (COVID-19), starting in late 2019, has determined in Italy several interventions aimed to prevent saturation of the health system. We have examined the effects of such measures by proposing a mean-field model describing the spread of the infection based on a simple diffusion process where all the observable variables (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depend on average parameters, namely diffusion coefficient, infection cross-section, and…
In late December 2019, a novel strand of Coronavirus (SARS-CoV-2) causing a severe, potentially fatal respiratory syndrome (COVID-19) was identified in Wuhan, Hubei Province, China and is causing outbreaks in multiple world countries, soon becoming a pandemic. Italy has now become the most hit country outside of Asia: on March 16, 2020, the Italian Civil Protection documented a total of 27980 confirmed cases and 2158 deaths of people tested positive for SARS-CoV-2. In the context of an emerging infectious disease outbreak, it is of paramount importance to predict the trend of the epidemic in o…
One major bottleneck in the ongoing COVID-19 pandemic is the limited number of critical care beds. Due to the dynamic development of infections and the time lag between when patients are infected and when a proportion of them enters an intensive care unit (ICU), the need for future intensive care can easily be underestimated. To infer future ICU load from reported infections, we suggest a simple statistical model that (1) accounts for time lags and (2) allows for making predictions depending on different future growth of infections. We have evaluated our model for three regions, namely Berlin …
We have further extended our compartmental model describing the spread of the infection in Italy. The model is based on the assumption that the time evolution of all of the observable quantities (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depend on average parameters, namely people diffusion coefficient, infection cross-section, and population density. The model provides precious information on the tight relationship between the variation of the reported infection cases and a …
IMT School for Advanced Studies Lucca（卢cca高等研究院）；TREE-TOWER S.R.L.（TREE-TOWER有限责任公司）
Computational models for the simulation of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic evolution would be extremely useful to support authorities in designing healthcare policies and lockdown measures to contain its impact on public health and economy. In Italy, the devised forecasts have been mostly based on a pure data-driven approach, by fitting and extrapolating open data on the epidemic evolution collected by the Italian Civil Protection Center. In this respect, SIR epidemiological models, which start from the description of the nonlinear interactions between…
Understanding Covid-19 lethality and its variation from country to country is essential for supporting governments in the choice of appropriate strategies. Adopting correct indicators to monitor the lethality of the infection in the course of the outbreak is a crucial issue. This works highlights how far the time-dependent case fatality rate is a misleading indicator for estimating the fatality in the course of the outbreak, even if our attention is only restricted to the subset of confirmed cases. Our analysis proves that the final case fatality ratio for several major European countries is b…
OBJECTIVES: to describe the first wave of the COVID-19 pandemic with a focus on undetected cases and to evaluate different post-lockdown scenarios. DESIGN: the study introduces a SEIR compartmental model, taking into account the region-specific fraction of undetected cases, the effects of mobility restrictions, and the personal protective measures adopted, such as wearing a mask and washing hands frequently. SETTING AND PARTICIPANTS: the model is experimentally validated with data of all the Italian regions, some European countries, and the US. MAIN OUTCOME MEASURES: the accuracy of the model …
As the COVID-19 outbreak is developing the two most frequently reported statistics seem to be the raw confirmed case and case fatalities counts. Focusing on Italy, one of the hardest hit countries, we look at how these two values could be put in perspective to reflect the dynamics of the virus spread. In particular, we find that merely considering the confirmed case counts would be very misleading. The number of daily tests grows, while the daily fraction of confirmed cases to total tests has a change point. It (depending on region) generally increases with strong fluctuations till (around, de…
This paper provides a mathematical model to show that the incorrect estimation of r, the fraction of asymptomatic COVID-19 carriers in the general population, can account for much of the world's failure to contain the pandemic in its early phases. The SE(A+O)R model with infectives separated into asymptomatic and ordinary carriers, supplemented by a model of the data generation process, is calibrated to standard datasets for several countries. It is shown that certain fundamental parameters, notably r, are unidentifiable with this data. A number of potential types of policy intervention are an…
The COVID-19 epidemic that emerged in Wuhan China at the end of 2019 hit Italy particularly hard, yielding the implementation of strict national lockdown rules (Phase 1). There is now a hot ongoing debate in Italy and abroad on what the best strategy is to restart a country to exit a national lockdown (Phase 2). Previous studies have focused on modelling possible restarting scenarios at the national level, overlooking the fact that Italy, as other nations around the world, is divided in administrative regions who can independently oversee their own share of the Italian National Health Service.…
The sudden outbreak of the Coronavirus disease (COVID-19) swept across the world in early 2020, triggering the lockdowns of several billion people across many countries, including China, Spain, India, the U.K., Italy, France, Germany, and most states of the U.S. The transmission of the virus accelerated rapidly with the most confirmed cases in the U.S., and New York City became an epicenter of the pandemic by the end of March. In response to this national and global emergency, the NSF Spatiotemporal Innovation Center brought together a taskforce of international researchers and assembled imple…
In this work, using a detailed dataset furnished by National Health Authorities concerning the Province of Pavia (Lombardy, Italy), we propose to determine the essential features of the ongoing COVID-19 pandemic in term of contact dynamics. Our contribution is devoted to provide a possible planning of the needs of medical infrastructures in the Pavia Province and to suggest different scenarios about the vaccination campaign which possibly help in reducing the fatalities and/or reducing the number of infected in the population. The proposed research combines a new mathematical description of th…
We study the datafor the cumulative as well as daily number of cases in the Covid-19 outbreak in China. The cumulative data can be fit to an empirical form obtained from a Susceptible-Infected-Removed (SIR) model studied on an Euclidean network previously. Plotting the number of cases against the distance from the epicenter for both China and Italy, we find an approximate power law variation with an exponent $\sim 1.85$ showing strongly that the spatial dependence plays a key role, a factor included in the model. We report here that the SIR model on the Eucledean network can reproduce with a h…
A dynamical epidemic model optimized using genetic algorithm and cross validation method to overcome the overfitting problem is proposed. The cross validation procedure is applied so that available data are split into a training subset used to fit the algorithm's parameters, and a smaller subset used for validation. This process is tested on the countries of Italy, Spain, Germany and South Korea before being applied to Algeria. Interestingly, our study reveals an inverse relationship between the size of the training sample and the number of generations required in the genetic algorithm. Moreov…
An epidemic disease caused by a new coronavirus has spread in Northern Italy with a strong contagion rate. We implement an SEIR model to compute the infected population and number of casualties of this epidemic. The example may ideally regard the situation in the Italian Region of Lombardy, where the epidemic started on February 25. We calibrate the model with the number of dead individuals to date (May 5, 2020) and constraint the parameters on the basis of values reported in the literature. The peak occurs at day 37 (March 31) approximately, when there is a rapid decrease, with a reproduction…
The Italian government has been one of the most responsive to COVID-19 emergency, through the adoption of quick and increasingly stringent measures to contain the outbreak. Despite this, Italy has suffered a huge human and social cost, especially in Lombardy. The aim of this paper is dual: i) first, to investigate the reasons of the case fatality rate (CFR) differences across Italian 20 regions and 107 provinces, using a multivariate OLS regression approach; and ii) second, to build a taxonomy of provinces with similar mortality risk of COVID-19, by using the Ward hierarchical agglomerative cl…
Since the onset of the COVID-19 outbreak in Wuhan, China, numerous forecasting models have been proposed to project the trajectory of coronavirus infection cases. We propose a new discrete-time Markov chain transition matrix model that directly incorporates stochastic behavior and for which parameter estimation is straightforward from available data. Using such data from China's Hubei province (for which Wuhan is the provincial capital city), the model is shown to be flexible, robust, and accurate. As a result, it has been adopted by the first Shanghai assistance medical team in Wuhan's Jinyin…
SARS-CoV-2 has disrupted the life of billions of people around the world since the first outbreak was officially declared in China at the beginning of 2020. Yet, important questions such as how deadly it is or its degree of spread within different countries remain unanswered. In this work, we exploit the `universal' growth of the mortality rate with age observed in different countries since the beginning of their respective outbreaks, combined with the results of the antibody prevalence tests in the population of Spain, to unveil both unknowns. We validate these results with an analogous antib…
This is a pedagogical paper on estimating the number of people that can be infected by one infectious person during an epidemic outbreak, known as the reproduction number. Knowing the number is crucial for developing policy responses. There are generally two types of such a number, i.e., basic and effective (or instantaneous). While basic reproduction number is the average expected number of cases directly generated by one case in a population where all individuals are susceptible, effective reproduction number is the number of cases generated in the current state of a population. In this pape…
Background: Rapid testing for an infection is paramount during a pandemic to prevent continued viral spread and excess morbidity and mortality. This study aimed to determine whether alternative testing strategies based on sample pooling can increase the speed and throughput of screening for SARS-CoV-2. Methods: A mathematical modelling approach was chosen to simulate six different testing strategies based on key input parameters (infection rate, test characteristics, population size, testing capacity etc.). The situations in five countries (US, DE, UK, IT and SG) currently experiencing COVID-1…
