This contribution analyzes the COVID-19 outbreak by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. This is done by an algorithm motivated by standard SIR models and aligned with the standard data provided by the Johns Hopkins University. To reconstruct data for the unregistered Infected, the algorithm uses current values of the infection fatality rate and a data-driven estimation of a specific form of the recovery rate. All other ingredients are data-driven as well. Various examples of predictions are provided for illustration.
We analyse the data for the global corona virus (COVID-19) outbreak using the results of a previously studied Susceptible-Infected-Removed (SIR) model of epidemic spreading on Euclidean networks. We also directly study the correlation of the distance from the epicenter and the number of cases. An inverse square law is seen to exist approximately. The studies are made for China and the rest of the world separately.
From late December, 2019, the novel Corona-Virus began to spread in the mainland of China. For predicting the trend of the Corona Virus spread, several time delay dynamic systems (TDD) are proposed. In this paper, we establish a novel fractional time delay dynamic system (FTDD) to describe the local outbreak of COVID-19. The fractional derivative is introduced to account for the sub-diffusion process of the confirmed and cured peoples growth. Based on the public health data by the government, we propose a stable reconstruction algorithm of the coefficients. The reconstructed coefficients are u…
The prediction of spread patterns of COVID19 virus in India is very difficult due to its versatile demographic as well as meteorological data distribution. Various researchers across the globe have attempted to correlate the interdependency of these data with the spread pattern of COVID19 cases in India. But it is hard to predict the exact pattern, especially the peak in the number of active cases. In the present article we have tried to predict the number of active, recovered, death and total cases of COVID19 in India using generalized SEIR model. In our prediction, the occurrence of peak in …
A mathematical model is proposed for quantitative description of the outbreak of novel coronavirus COVID-19 in China. Although the model is relatively simple, the comparison with the public data shows that an exact solution solution of the model (with the correctly-specified parameters) leads to the results, which are in good agreement with the measured data. Prediction of the total number of the COVID-19 cases is discussed and an example is presented using the measured data in Austria.
Unlike the lockdown measures taken in some countries or cities, the Japanese government declared a "State of Emergency" (SOE) under which people were only requested to reduce their contact with other people by at least 70 %, while some local governments also implemented their own mobility-reduction measures that had no legal basis. The effects of these measures are still unclear. Thus, in this study, we investigate changes in travel patterns in response to the COVID-19 outbreak and related policy measures in Japan using longitudinal aggregated mobile phone data. Specifically, we consider daily…
COVID-19 outbreaks have proven to be very difficult to isolate and extinguish before they spread out. An important reason behind this might be that epidemiological barriers consisting in stopping symptomatic people are likely to fail because of the contagion time before onset, mild cases and/or asymptomatics carriers. Motivated by these special COVID-19 features, we study a scheme for containing an outbreak in a city that consists in adding an extra firewall block between the outbreak and the rest of the city. We implement a coupled compartment model with stochastic noise to simulate a localiz…
During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19, we provide a toolkit of statistical and mathematical models beyond the simple SIR-type differential equation models for analysing the early stages of an outbreak and assessing interventions. In particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulation…
The COVID-19 pandemic poses challenges for continuing economic activity while reducing health risks. While these challenges can be mitigated through testing, testing budget is often limited. Here we study how institutions, such as nursing homes, should utilize a fixed test budget for early detection of an outbreak. Using an extended network-SEIR model, we show that given a certain budget of tests, it is generally better to test smaller subgroups of the population frequently than to test larger groups but less frequently. The numerical results are consistent with an analytical expression we der…
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.
Intent of this research is to explore how mathematical models, specifically Susceptible-Infected-Removed (SIR) model, can be utilized to forecast peak outbreak timeline of COVID-19 epidemic amongst a population of interest starting from the date of first reported case. Till the time of this research, there was no effective and universally accepted vaccine to control transmission and spread of this infection. COVID-19 primarily spreads in population through respiratory droplets from an infected person cough and sneeze which infects people who are in proximity. COVID-19 is spreading contagiously…
The Covid-19 outbreak of 2020 has required many governments to develop mathematical-statistical models of the outbreak for policy and planning purposes. This work provides a tutorial on building a compartmental model using Susceptibles, Exposed, Infected, Recovered and Deaths status through time. A Bayesian Framework is utilized to perform both parameter estimation and predictions. This model uses interventions to quantify the impact of various government attempts to slow the spread of the virus. Predictions are also made to determine when the peak Active Infections will occur.
Recent literature has suggested that climate conditions have considerably significant influences on the transmission of coronavirus COVID-19. However, there is a lack of comprehensive study that investigates the relationships between multiple weather factors and the development of COVID-19 pandemic while excluding the impact of social factors. In this paper, we study the relationships between six main weather factors and the infection statistics of COVID-19 on 250 cities in Mainland China. Our correlation analysis using weather and infection statistics indicates that all the studied weather fa…
As of July, 2020, acute respiratory syndrome caused by coronavirus COVID-19 is spreading over the world and causing severe economic damages. While minimizing human contact is effective in managing the outbreak, it causes severe economic losses. Strategies solving this dilemma by considering interrelation between the spread of the virus and economic activities are in urgent needs for mitigating the health and economic damage. Here we propose an abstract agent-based model for the outbreak of COVID-19 in which economic activities are taken into account. The computational simulation of the model r…
The Covid-19 has presented an unprecedented challenge to public health worldwide. However, residents in different countries showed diverse levels of Covid-19 awareness during the outbreak and suffered from uneven health impacts. This study analyzed the global Twitter data from January 1st to June 30th, 2020, seeking to answer two research questions. What are the linguistic and geographical disparities of public awareness in the Covid-19 outbreak period reflected on social media? Can the changing pandemic awareness predict the Covid-19 outbreak? We established a Twitter data mining framework ca…
The COVID-19 disease has forced countries to make a considerable collaborative effort between scientists and governments to provide indicators to suitable follow-up the pandemic's consequences. Mathematical modeling plays a crucial role in quantifying indicators describing diverse aspects of the pandemic. Consequently, this work aims to develop a clear, efficient, and reproducible methodology for parameter optimization, whose implementation is illustrated using data from three representative regions from Chile and a suitable generalized SIR model together with a fitted positivity rate. Our res…
After steep drops and then rebounds in transportation-related CO$_2$ emissions over the first half of 2020, a second wave of COVID-19 this fall has caused further -- but less substantial -- emissions reductions. Here, we use near-real-time estimates of daily emissions to explore differences in human behavior and restriction policies over the course of 2020.
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.
The current outbreak of novel coronavirus disease 2019 (COVID-19) poses an unprecedented global health and economic threat to interconnected human societies. Until a vaccine is developed, strategies for controlling the outbreak rely on aggressive social distancing. These measures largely disconnect the social network fabric of human societies, especially in urban areas. Here, we estimate the growth rates and reproductive numbers of COVID-19 in US cities from March 14th through March 19th to reveal a power-law scaling relationship to city population size. This means that COVID-19 is spreading f…
Background: Wuhan, China was the epicenter of COVID-19 pandemic. The goal of current study is to understand the infection transmission dynamics before intervention measures were taken. Methods: Data and key events were searched through pubmed and internet. Epidemiological data were calculated using data extracted from a variety of data sources. Results: We established a timeline showing by January 1, 2020, Chinese authorities had been presented convincing evidence of human-to-human transmission; however, it was not until January 20, 2020 that this information was shared with the public. Our st…
I employ a simple mathematical model of an epidemic process to evaluate how four basic quantities: the reproduction number (R), the numbers of sensitive (S) and infectious individuals(I), and total community size (N) affect strategies to control COVID-19. Numerical simulations show that strict suppression measures at the beginning of an epidemic can create low infectious numbers, which thereafter can be managed by mitigation measures over longer periods to flatten the epidemic curve. The stronger the suppression measure, the faster it achieves the low numbers of infections that are conducive t…
The coronavirus disease 2019 (COVID-19) had caused more that 8 million infections as of middle June 2020. Recently, Brazil has become a new epicentre of COVID-19, while India and African region are potential epicentres. This study aims to predict the inflection point and outbreak size of these new/potential epicentres at the early phase of the epidemics by borrowing information from more `mature' curves from other countries. We modeled the cumulative cases to the well-known sigmoid growth curves to describe the epidemic trends under the mixed-effect models and using the four-parameter logistic…
As a highly infectious respiratory disease, COVID-19 has become a pandemic that threatens global health. Without an effective treatment, non-pharmaceutical interventions, such as travel restrictions, have been widely promoted to mitigate the outbreak. Current studies analyze mobility metrics such as travel distance; however, there is a lack of research on interzonal travel flow and its impact on the pandemic. Our study specifically focuses on the inter-county mobility pattern and its influence on the COVID-19 spread in the United States. To retrieve real-world mobility patterns, we utilize an …
We analyze data from Twitter to uncover early-warning signals of COVID-19 outbreaks in Europe in the winter season 2019-2020, before the first public announcements of local sources of infection were made. We show evidence that unexpected levels of concerns about cases of pneumonia were raised across a number of European countries. Whistleblowing came primarily from the geographical regions that eventually turned out to be the key breeding grounds for infections. These findings point to the urgency of setting up an integrated digital surveillance system in which social media can help geo-locali…
This short note provides estimates of the number of passengers that travel from China to all world airports in the period October 2019 - March 2020 on the basis of historical data. From this baseline we subtract the expected reduction in the number of passengers taking into account the temporary ban of some routes which was put in place since 23 January 2020 following the COVID-2019 Coronavirus outbreak. The results indicate a reduction of the number of passengers in the period January - March 2020 of -2.5%. This calculation considers only the complete closure of routes (not just direct flight…
The recent outbreak of COVID-19 in Mainland China is characterized by a distinctive algebraic, sub-exponential increase of confirmed cases during the early phase of the epidemic, contrasting an initial exponential growth expected for an unconstrained outbreak with sufficiently large reproduction rate. Although case counts vary significantly between affected provinces in Mainland China, the scaling law $t^μ$ is surprisingly universal, with a range of exponents $μ=2.1\pm0.3$. The universality of this behavior indicates that despite social, regional, demographical, geographical, and socio-economi…
The COVID-19, the disease caused by the novel coronavirus 2019 (SARS-CoV-2), has caused graving woes across the globe since first reported in the epicenter Wuhan, Hubei, China, December 2019. The spread of COVID-19 in China has been successfully curtailed by massive travel restrictions that put more than 900 million people housebound for more than two months since the lockdown of Wuhan on 23 January 2020 when other provinces in China followed suit. Here, we assess the impact of China's massive lockdowns and travel restrictions reflected by the changes in mobility patterns before and during the…
We illustrate and study the evolution of reported infections over the month from March 1st to April 1st in the New York State as a whole, as well as in each individual county. We search for exponential trends, and try to understand whether there is any correlation of the timing and dynamics of these trends with state mandated measures on social distancing and testing. We conclude that the reports on April 1st may be dramatically under-representing the actual number of state-wide infections, and we propose reassessment of the data over the coming weeks, to monitor for effects of the PAUSE direc…
In this study, we use US county-level COVID-19 case data from January 21-March 25, 2020 to study the exponential behavior of case growth at the metropolitan scale. In particular, we assume that all localized outbreaks are in an early stage (either undergoing exponential growth in the number of cases, or are effectively contained) and compare the explanatory performance of different simple exponential and linear growth models for different metropolitan areas. While we find no relationship between city size and exponential growth rate (directly related to $R0$, which denotes average the number o…
In this paper, we introduce a novel modeling framework for incorporating fear of infection and frustration with social distancing into disease dynamics. We show that the resulting SEIR behavior-perception model has three principal modes of qualitative behavior---no outbreak, controlled outbreak, and uncontrolled outbreak. We also demonstrate that the model can produce transient and sustained waves of infection consistent with secondary outbreaks. We fit the model to cumulative COVID-19 case and mortality data from several regions. Our analysis suggests that regions which experience a significa…
Reopening strategies are crucial to balance efforts of economic revitalization and bringing back a sense of normalcy while mitigating outbreaks and effectively flattening the infection curve. This paper proposes practical reopening, monitoring and testing strategies for institutions to reintroduce physical meetings based on SIR simulations run on a student friendship network collected pre-Covid-19. These serve as benchmarks to assess several testing strategies that can be applied in physical classes. Our simulations show that the best outbreak mitigation results are obtained with full knowledg…
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 (…
The COVID-19 pandemic has, worldwide and up to December 2020, caused over 1.7 million deaths, and put the world's most advanced healthcare systems under heavy stress. In many countries, drastic restrictive measures adopted by political authorities, such as national lockdowns, have not prevented the outbreak of new pandemic's waves. In this article, we propose an integrated detection-estimation-forecasting framework that, using publicly available data, is designed to: (i) learn relevant features of the pandemic (e.g., the infection rate); (ii) detect as quickly as possible the onset (or the ter…
There were 27 novel coronavirus pneumonia cases found in Wuhan, China in December 2019, named as 2019-nCoV temporarily and COVID-19 formally by WHO on 11 February, 2020. In December 2019 and January 2020, COVID-19 has spread in large scale among the population, which brought terrible disaster to the life and property of the Chinese people. In this paper, we will first analyze the feature and pattern of the virus transmission, and discuss the key impact factors and uncontrollable factors of epidemic transmission based on public data. Then the virus transmission can be modelled and used for the …
This manuscript proposes a model of $n$ distinct populations interaction structured SEIR to describe the spread of COVID-19 pandemic diseases. The proposed model has the flexibility to include geographically separated communities as well as taking into account aging population groups and their interactions. We show that distinct assumptions on the dynamics of the proposed model lead to a plateau-like curve of the infected population, reflecting collected data from large countries like Brazil. Such observations aim to the following conjecture: " Covid-19 diseased diffusion from the capitals to …
Understanding influencing factors is essential for the surveillance and prevention of infectious diseases, and the factors are likely to vary spatially and temporally as the disease progresses. Taking daily cases and deaths data during the coronavirus disease 2019 (COVID-19) outbreak in the U.S. as a case study, we develop a mobility-augmented geographically and temporally weighted regression (M-GTWR) model to quantify the spatiotemporal impacts of social-demographic factors and human activities on the COVID-19 dynamics. Different from the base GTWR model, we incorporate a mobility-adjusted di…
The COVID-19 pandemic has caused, in general, a sharp reduction in traffic and industrial activities. This in turn leaded to a reduction in air pollution around the world. It is important to quantity the amount of that reduction in order to estimate the influence weight of traffic and industrial activities over the total variation of air quality. The aim of this paper is to evaluate the impact of the COVID-19 outbreak on air pollution in Israel, which is considered one of the countries with a higher air pollution than other Western countries. The results reveal two main findings: 1. During the…
In individual SARS-CoV-2 outbreaks, the count of confirmed cases and deaths follow a Gompertz growth function for locations of very different sizes. This lack of dependence on region size leads us to hypothesize that virus spread depends on universal properties of the network of social interactions. We test this hypothesis by simulating the propagation of a virus on networks of different topologies. Our main finding is that Gompertz growth observed for early outbreaks occurs only for a scale-free network, in which nodes with many more neighbors than average are common. These nodes that have ve…
The goal of this study is to establish a general framework for predicting the so-called critical Turning Period in an infectious disease epidemic such as the COVID-19 outbreak in China early this year. This framework enabled a timely prediction of the turning period when applied to Wuhan COVID-19 epidemic and informed the relevant authority for taking appropriate and timely actions to control the epidemic. It is expected to provide insightful information on turning period for the world's current battle against the COVID-19 pandemic. The underlying mathematical model in our framework is the ind…
We analyze mobility changes following the implementation of containment measures aimed at mitigating the spread of COVID-19 in Bogotá, Colombia. We characterize the mobility network before and during the pandemic and analyze its evolution and changes between January and July 2020. We then link the observed mobility changes to socioeconomic conditions, estimating a gravity model to assess the effect of socioeconomic conditions on mobility flows. We observe an overall reduction in mobility trends, but the overall connectivity between different areas of the city remains after the lockdown, reflec…
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 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 …
Risk mapping for COVID-19 outbreaks in Australia using mobility data
The University of Melbourne（墨尔本大学）；The University of Adelaide（阿德莱德大学）；Victorian Department of Health and Human Services, Government of Victoria（维多利亚州卫生与人类服务部）；Department of Infectious Diseases, The Alfred and Central Clinical School, Monash University（蒙纳士大学阿尔弗雷德医院与中央临床学院传染病系）；University of New South Wales（新南威尔士大学）；Melbourne School of Engineering（墨尔本工程学院）；The Peter Doherty Institute for Infection and Immunity, The Royal Melbourne Hospital and The University of Melbourne（彼得·多赫蒂感染与免疫研究所、皇家墨尔本医院和墨尔本大学）
COVID-19 has disrupted the global economy and well-being of people at an unprecedented scale and magnitude. To contain the disease, an effective early warning system that predicts the locations of outbreaks is of crucial importance. Studies have shown the effectiveness of using large-scale mobility data to monitor the impacts of non-pharmaceutical interventions (e.g., lockdowns) through population density analysis. However, predicting the locations of potential outbreak occurrence is difficult using mobility data alone. Meanwhile, web search queries have been shown to be good predictors of the…
Since May 2020, several COVID-19 outbreaks have occurred in the German meat industry despite various protective measures, and temperature and ventilation conditions were considered as possible high-risk factors. This cross-sectional study examined meat and poultry plants to examine possible risk factors. Companies completed a self-administered questionnaire on the work environment and protective measures taken to prevent SARS-CoV-2 infection. Multivariable logistic regression analysis adjusted for the possibility to distance at least 1.5 meters, break rules, and employment status was performed…
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…
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 …
COVID-19 has spread from China across Europe and the United States and has become a global pandemic. In countries of the Global South, due to often weaker socioeconomic options and health care systems, effective local countermeasures remain debated. We combine large-scale socioeconomic and traffic survey data with detailed agent-based simulations of local transportation to analyze COVID-19 spreading in a regional model for the Nelson Mandela Bay Municipality in South Africa under a range of countermeasure scenarios. The simulations indicate that any realistic containment strategy, including th…
In the absence of neither an effective treatment or vaccine and with an incomplete understanding of the epidemiological cycle, Govt. has implemented a nationwide lockdown to reduce COVID-19 transmission in India. To study the effect of social distancing measure, we considered a new mathematical model on COVID-19 that incorporates lockdown effect. By validating our model to the data on notified cases from five different states and overall India, we estimated several epidemiologically important parameters as well as the basic reproduction number ($R_{0}$). Combining the mechanistic mathematical …
The 6th wave of COVID-19 in Tokyo continued for the longest period of infection (about 190 days from late Nov. 2021), and the 7th wave, which occurred in mid-May 2022, was the largest wave ever (cumulative 1.7 million people). In order to elucidate their factors, the infection wave was analyzed by using the Avrami equation. The main component of the 6th wave was formed by the coupling of increased human interaction due to the New Year holidays and the invasion of the new virus variant Omicron BA.1. After that, side waves were formed by the coupling of the invasion of the new virus variant Omic…
By the emergence of the novel coronavirus disease (COVID-19) in Wuhan, China, and its rapid outbreak worldwide, the infectious illness has changed our everyday travel patterns. In this research, our team investigated the changes in the daily mobility pattern of people during the pandemic by utilizing an integrated data panel. To incorporate various aspects of human mobility, the team focused on the Social Distancing Index (SDI) which was calculated based on five basic mobility measures. The SDI patterns showed a plateau stage in the beginning of April that lasted for about two weeks. This phen…
We consider the SIR epidemiological model applied to the evolution of COVID-19 with two approaches. In the first place we fit a global SIR model, with time delay, and constant parameters throughout the outbreak, including the contagion rate. The contention measures are reflected on an effective reduced susceptible population $N_{eff}$. In the second approach we consider a time-dependent contagion rate that reflects the contention measures either through a step by step fitting process or by following an exponential decay. In this last model the population is considered the one of the country $N…
With the unfolding of the COVID-19 pandemic, mathematical modeling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long term predictions were extremely challenging to address. Moreover, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modeling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitiga…
The effect of masking the general population on a COVID-19 epidemic is estimated by computer simulation using two separate state-of-the-art web-based softwares, one of them calibrated for the SARS-CoV-2 virus. The questions addressed are these: 1. Can mask use by the general population limit the spread of SARS-CoV-2 in a country? 2. What types of masks exist, and how elaborate must a mask be to be effective against COVID-19? 3. Does the mask have to be applied early in an epidemic? 4. A brief general discussion of masks and some possible future research questions regarding masks and SARS-CoV-2…
The outbreak of Covid-19 led the world to an unprecedent health and economical crisis. In an attempt to responde to this emergency researchers worldwide are intensively studying the Covid-19 pandemic dynamics. In this work, a SIRSi compartmental model is proposed, which is a modification of the known classical SIR model. The proposed SIRSi model considers differences in the immunization within a population, and the possibility of unreported or asymptomatic cases. The model is adjusted to three major cities of São Paulo State, in Brazil, namely, São Paulo, Santos and Campinas, providing estimat…
The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for a while, they can follow the restrictions again. But during this pause the second wave can come and become even stronger then the first on…
The sudden spread of Covid-19 outside China has pushed on March 11 the World Health Organization to acknowledge the ongoing outbreak as a pandemic. It is crucial in this phase to understand what should countries which presently lag behind in the spread of the infection learn from countries where the infection spread earlier. The choice of this work is to prefer timeliness to comprehensiveness. By adopting a purely empirical approach, we will limit ourselves to identifying different phases in the plots of different countries, based on their different functional behaviour, and to make a comparat…
