We model and forecast the early evolution of the COVID-19 pandemic in Brazil using Brazilian recent data from February 25, 2020 to March 30, 2020. This early period accounts for unawareness of the epidemiological characteristics of the disease in a new territory, sub-notification of the real numbers of infected people and the timely introduction of social distancing policies to flatten the spread of the disease. We use two variations of the SIR model and we include a parameter that comprises the effects of social distancing measures. Short and long term forecasts show that the social distancing policy imposed by the government is able to flatten the pattern of infection of the COVID-19. However, our results also show that if this policy does not last enough time, it is only able to shift the peak of infection into the future keeping the value of the peak in almost the same value. Furthermore, our long term simulations forecast the optimal date to end the policy. Finally, we show that the proportion of asymptomatic individuals affects the amplitude of the peak of symptomatic infected, suggesting that it is important to test the population.
In this work Data Envelopment Analysis (DEA) is employed in thirty-day windows to quantify temporal evolution of relative pandemic mitigation inefficiency of Brazilian municipalities. For each thirty-day window the results of inefficiency scores of over five thousand Brazilian municipalities are displayed on maps, to address the spatial distribution of the corresponding values. This phenomenological spatiotemporal approach reveals location of the hotspots, in terms of relative pandemic inefficiency of the municipalities, at different points in time along the pandemic. It is expected that the c…
This paper deals with the mathematical modeling and numerical simulations related to the coronavirus dynamics. A description is developed based on the framework of susceptible-exposed-infectious-recovered model. Initially, a model verification is carried out calibrating system parameters with data from China, Italy, Iran and Brazil. Afterward, numerical simulations are performed to analyzed different scenarios of COVID-19 in Brazil. Results show the importance of governmental and individual actions to control the number and the period of the critical situations related to the pandemic.
During the COVID-19 pandemic, many countries opted for strict public health measures, including closing schools. They have now started relaxing some of those restrictions. To avoid overwhelming health systems, predictions for the number of new COVID-19 cases need to be considered when choosing a school reopening strategy. Using computer simulation, we analyze different strategies to reopen schools in the Sao Paulo Metropolitan Area, including the official reopening plan. Our results indicate that reopening schools with all students at once has a big impact on the number of new COVID-19 cases, …
Visual analytics techniques are useful tools to support decision-making and cope with increasing data, which is particularly important when monitoring natural or artificial phenomena. When monitoring disease progression, visual analytics approaches help decision-makers choose to understand or even prevent dissemination paths. In this paper, we propose a new visual analytics tool for monitoring COVID-19 dissemination. We use k-nearest neighbors of cities to mimic neighboring cities and analyze COVID-19 dissemination based on the comparison of a city under consideration and its neighborhood. Mor…
The COVID-19 pandemic has had a great impact in most countries worldwide, in particular impacting Chile greatly to become one of the worst hit countries in the world, despite its low population compared to other affected countries around the world. In this study we report the evolution of the COVID-19 pandemic and the spread of the SARS-CoV-2 virus in Chile since the first positive case was announced on March 3, 2020, and until November 30, 2020. We provide a detailed description of the data provided by the Chilean Ministry of Science per administrative region on the number of new cases, tests…
We developed a mathematical model to describe the transmission of new coronavirus in the São Paulo State, Brazil. The model divided a community in subpopulations comprised by young and elder persons, in order to take into account higher risk of fatality among elder persons with severe CoViD-19. From data collected in the São Paulo State, we estimated the transmission and additional mortality rates, from which we calculated the basic reproduction number R0. From estimated parameters, estimation of the deaths due to CoViD-19 was three times lower than those found in literature. Considering isola…
The COVID-19 pandemic is the profoundest health crisis of the 21rst century. The SARS-CoV-2 virus arrived in Brazil around March, 2020 and its social and economical backlashes are catastrophic. In this paper, it is investigated how Model Predictive Control (MPC) could be used to plan appropriate social distancing policies to mitigate the pandemic effects in Bahia and Santa Catarina, two states of different regions, culture, and population demography in Brazil. In addition, the parameters of Susceptible-Infected-Recovered-Deceased (SIRD) models for these two states are identified using an optim…
Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic properties of simple Kermack-McKendrick type models. Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g. mixing functions and superspreading events, …
In this paper, we firstly propose SQIARD and SIARD models to investigate the transmission of COVID-19 with quarantine, infected and asymptomatic infected, and discuss the relation between the respective basic reproduction number $R_0, R_Q$ and the stability of the equilibrium points of model. Secondly, after training the related data parameters, in our numerical simulations, we respectively conduct the forecast of the data of US, South Korea, Brazil, India, Russia and Italy, and the effect of prediction of the epidemic situation in each country. Furthermore, we apply US data to compare SQIARD …
Modeling and analysis of the large scale Covid-19 pandemic data can yield inferences about it's dynamics and characteristics of disease propagation. These inferences can then be correlated with contextual factors like population density, effects of strategic interventions, heterogeneous disease propagation etc, and such set of validated inferences can serve as precedents for designing of subsequent mitigation strategies. In this work, we present the analysis of Covid-19 pandemic data in Indian context using growth functions fitting procedure and harmonic analysis method. Our results of growth …
The subset selection problem of linear algebra is applied to identify independent patterns of COVID-19 evolution within Brazil. The data consist of a set of mortality curves in states of Brazil. A subset of the most independent curves is selected by using a functional version of the QR matrix decomposition technique with column pivoting. The selected subset is used next as a basis to represent the remaining curves filtering out any data redundancy. For each independent curve, an associated epidemiological region of influence is defined. The results show two main independent curves with a simil…
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 …
We shall apply a generalized SEIR model to study the outbreak of COVID-19 in Brazil. In particular, we would like to explain the projections of the increase in the level of infection over a long period of time, overlapping large local outbreaks in the most populous states in the country. A time-dependent dynamic SEIR model inspired in a model previously used during the outbreak in China was used to analyses the time trajectories of infected, recovered, and deaths. The model has parameters that vary with time and are fitted considering a nonlinear least-squares method. The simulations starting …
This paper has a twofold contribution. The first is a data driven approach for predicting the Covid 19 pandemic dynamics, based on data from more advanced countries. The second is to report and discuss the results obtained with this approach for Brazilian states, as of May 4th, 2020. We start by presenting preliminary results obtained by training an LSTM SAE network, which are somewhat disappointing. Then, our main approach consists in an initial clustering of the world regions for which data is available and where the pandemic is at an advanced stage, based on a set of manually engineered fea…
In the absence of any available vaccines or drugs, prevention of the spread of Coronavirus Disease 2019 (COVID-19) pandemic is being achieved by putting many mitigation measures in place. It is indispensable to have robust and reliable ways of evaluating the effectiveness of these measures. In this work, we assume that, at a very coarse-grained level of description, the overall effect of all the mitigation measures is that we can still describe the spread of the pandemic using the most basic Susceptible-Exposed-Infectious-Removed ($SEIR$) model but with an "effective contact rate" ($β$) which …
We collected individualized (unidentifiable) and aggregated openly available data from various sources related to suspected/confirmed SARS-CoV-2 infections, vaccinations, non-pharmaceutical government interventions, human mobility, and levels of population inequality in Brazil. In addition, a data structure allowing real-time data collection, curation, integration, and extract-transform-load processes for different objectives was developed. The granularity of this dataset (state- and municipality-wide) enables its application to individualized and ecological epidemiological studies, statistica…
The world evolution of the Severe acute respiratory syndrome coronavirus 2 (SARS-Cov2 or simply COVID-19) led the World Health Organization to declare it a pandemic. The disease appeared in China in December 2019, and it has spread fast around the world, specially in european countries like Italy and Spain. The first reported case in Brazil was recorded in February 26, and after that the number of cases growed fast. In order to slow down the initial growth of the disease through the country, confirmed positive cases were isolated to not transmit the disease. To better understand the early evol…
An epidemiological compartmental model was used to simulate social distancing strategies to contain the COVID-19 pandemic and prevent a second wave in Sao Paulo, Brazil. Optimization using genetic algorithm was used to determine the optimal solutions. Our results suggest the best-case strategy for Sao Paulo is to maintain or increase the current magnitude of social distancing for at least 60 more days and increase the current levels of personal protection behaviors by a minimum of 10% (e.g., wearing facemasks, proper hand hygiene and avoid agglomeration). Followed by a long-term oscillatory le…
We analytically study the SEIR (Susceptible Exposed Infectious Removed) epidemic model. The aim is to provide simple analytical expressions for the peak and asymptotic values and their characteristic times of the populations affected by the COVID-19 pandemic.
We provide a probabilistic SIRD model for the COVID-19 pandemic in Italy, where we allow the infection, recovery and death rates to be random. In particular, the underlying random factor is driven by a fractional Brownian motion. Our model is simple and needs only some few parameters to be calibrated.
India is one of the worst affected countries by the Covid-19 pandemic at present. We studied publicly available data of the Covid-19 patients in India and analyzed possible impacts of quarantine and social distancing within the stochastic framework of the SEQIR model to illustrate the controlling strategy of the pandemic. Our simulation results clearly show that proper quarantine and social distancing should be maintained from an early time just at the start of the pandemic and should be continued till its end to effectively control the pandemic. This calls for a more socially disciplined life…
Pontifical Catholic University of Parana (PUCPR)（巴拉那天主教大学）；Federal Technological University of Parana (UTFPR)（巴拉那联邦理工大学）；Federal University of Parana (UFPR)（巴拉那联邦大学）
The novel coronavirus disease (COVID-19) is a public health problem once according to the World Health Organization up to June 10th, 2020, more than 7.1 million people were infected, and more than 400 thousand have died worldwide. In the current scenario, the Brazil and the United States of America present a high daily incidence of new cases and deaths. It is important to forecast the number of new cases in a time window of one week, once this can help the public health system developing strategic planning to deals with the COVID-19. In this paper, Bayesian regression neural network, cubist re…
Understanding the dynamics of the COVID-19 pandemic is crucial for improved control and social distancing strategies. To that effect, we have employed the susceptible-exposed-infectious-recovered model, refined by contact tracing and hospitalization data from Indian provinces Kerala, Delhi, Maharashtra, and West Bengal, as well as from overall India. We have performed a sensitivity analysis to identify the most crucial input parameters, and we have calibrated the model to describe the data as best as possible. Short-term predictions reveal an increasing and worrying trend of COVID-19 cases for…
The current outbreak of the coronavirus disease 2019 (COVID-19) is an unprecedented example of how fast an infectious disease can spread around the globe (especially in urban areas) and the enormous impact it causes on public health and socio-economic activities. Despite the recent surge of investigations about different aspects of the COVID-19 pandemic, we still know little about the effects of city size on the propagation of this disease in urban areas. Here we investigate how the number of cases and deaths by COVID-19 scale with the population of Brazilian cities. Our results indicate small…
In the present article we introduce an epidemiological model for the investigation of the spread of epidemics caused by viruses. The model is applied specifically to COVID-19, the disease caused by the SARS-Cov-2 virus (aka "novel coronavirus"). The SIR (Susceptible - Infectious - Recovered) model is used as a basis for studying the evolution of the epidemic. Nevertheless, we have modified some of the model hypotheses in order to obtain an estimate of the contamination free of overestimated predictions. This extended model is then applied to the case of the recent advance of the epidemic in Br…
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 this paper, we deal with the study of the impact of nationwide measures COVID-19 anti-pandemic. We drive two processes to analyze COVID-19 data considering measures. We associate level of nationwide measure with value of parameters related to the contact rate of the model. Then a parametric solve, with respect to those parameters of measures, shows different possibilities of the evolution of the pandemic. Two machine learning tools are used to forecast the evolution of the pandemic. Finally, we show comparison between deterministic and two machine learning tools.
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 consider a global (location independent) model of pandemic growth which generalizes the SIR model to accommodate important features of the COVID-19 pandemic, notably the implementation of pandemic reduction measures. This "SHIR" model is applied to COVID-19 data, and shows promise as a simple, tractable formalism with few parameters that can be used to model pandemic case numbers. As an example we show that the average time dependence of new COVID-19 cases per day from 15 Central and Western European countries is in good agreement with the analytic, parameter-free prediction of the model
A second wave pandemic constitutes an imminent threat to society, with a potentially immense toll in terms of human lives and a devastating economic impact. We employ the epidemic renormalisation group approach to pandemics, together with the first wave data for COVID-19, to efficiently simulate the dynamics of disease transmission and spreading across different European countries. The framework allows us to model, not only inter and extra European border control effects, but also the impact of social distancing for each country. We perform statistical analyses averaging on different level of …
Chalmers University（查尔姆斯大学）；Department of Computer Science, University of Virginia（弗吉尼亚大学计算机科学系）
COVID-19 pandemic represents an unprecedented global health crisis in the last 100 years. Its economic, social and health impact continues to grow and is likely to end up as one of the worst global disasters since the 1918 pandemic and the World Wars. Mathematical models have played an important role in the ongoing crisis; they have been used to inform public policies and have been instrumental in many of the social distancing measures that were instituted worldwide. In this article we review some of the important mathematical models used to support the ongoing planning and response efforts. T…
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…
Population-wide vaccination is critical for containing the SARS-CoV-2 (Covid-19) pandemic when combined with restrictive and prevention measures. In this study, we introduce SAIVR, a mathematical model able to forecast the Covid-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains several parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neur…
The present article studies the extension of two deterministic models for describing the novel coronavirus pandemic crisis, the SIR model and the SEIR model. The models were studied and compared to real data in order to support the validity of each description and extract important information regarding the pandemic, such as the basic reproductive number R0, which might provide useful information concerning the rate of increase of the pandemic predicted by each model. We next proceed to making predictions and comparing more complex models derived from the SEIR model with the SIRD model, in ord…
Official counts of COVID-19 deaths have been criticized for potentially including people who did not die of COVID-19 but merely died with COVID-19. I address that critique by fitting a generalized additive model to weekly counts of all deaths registered in England and Wales during the 2010s. The model produces baseline rates of death registrations expected without the COVID-19 pandemic, and comparing those baselines to recent counts of registered deaths exposes the emergence of excess deaths late in March 2020. By April's end, England and Wales registered 45,300 $\pm$ 3200 excess deaths of adu…
Currently, Brazil has one of the fastest increasing COVID-19 epidemics in the world, that has caused at least 94 thousand confirmed deaths until now. The city of Sao Paulo is particularly vulnerable because it is the most populous in the country. Analyzing the spatiotemporal dynamics of COVID-19 is important to help the urgent need to integrate better actions to face the pandemic. Thus, this study aimed to analyze the COVID-19 mortality, from March to July 2020, considering the spatio-time architectures, the socio-economic context of the population, and using a fine granular level, in the most…
Several analytical models have been used in this work to describe the evolution of death cases arising from coronavirus (COVID-19). The Death or `D' model is a simplified version of the SIR (susceptible-infected-recovered) model, which assumes no recovery over time, and allows for the transmission-dynamics equations to be solved analytically. The D-model can be extended to describe various focuses of infection, which may account for the original pandemic (D1), the lockdown (D2) and other effects (Dn). The evolution of the COVID-19 pandemic in several countries (China, Spain, Italy, France, UK,…
Monitoring the evolution of the Covid19 pandemic constitutes a critical step in sanitary policy design. Yet, the assessment of the pandemic intensity within the pandemic period remains a challenging task because of the limited quality of data made available by public health authorities (missing data, outliers and pseudoseasonalities, notably), that calls for cumbersome and ad-hoc preprocessing (denoising) prior to estimation. Recently, the estimation of the reproduction number, a measure of the pandemic intensity, was formulated as an inverse problem, combining data-model fidelity and space-ti…
With the emergence of a new pandemic worldwide, a novel strategy to approach it has emerged. Several initiatives under the umbrella of "open science" are contributing to tackle this unprecedented situation. In particular, the "R Language and Environment for Statistical Computing" offers an excellent tool and ecosystem for approaches focusing on open science and reproducible results. Hence it is not surprising that with the onset of the pandemic, a large number of R packages and resources were made available for researches working in the pandemic. In this paper, we present an R package that all…
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…
In this paper, we propose a machine learning technics and SIR models (deterministic and stochastic cases) with numerical approximations to predict the number of cases infected with the COVID-19, for both in few days and the following three weeks. Like in [1] and based on the public data from [2], we estimate parameters and make predictions to help on how to find concrete actions to control the situation. Under optimistic estimation, the pandemic in some countries will end soon, while for most of the countries in the world, the hit of anti-pandemic will be no later than the beginning of May.
This work is a trial in which we propose SIR model and machine learning tools to analyze the coronavirus pandemic in the real world. Based on the public data from \cite{datahub}, we estimate main key pandemic parameters and make predictions on the inflection point and possible ending time for the real world and specifically for Senegal. The coronavirus disease 2019, by World Health Organization, rapidly spread out in the whole China and then in the whole world. Under optimistic estimation, the pandemic in some countries will end soon, while for most part of countries in the world (US, Italy, e…
Data assimilation is used to optimally fit a classical epidemiology model to the Johns Hopkins data of the Covid-19 pandemic. The optimisation is based on the confirmed cases and confirmed deaths. This is the only data available with reasonable accuracy. Infection and recovery rates can be infered from the model as well as the model parameters. The parameters can be linked with government actions or events like the end of the holiday season. Based on this numbers predictions for the future can be made and control targets specified. With other words: We look for a solution to a given model whic…
