Since the beginning of March 2020, the cumulative numbers of cases of infection with the novel coronavirus SARS-CoV-2 in Germany have been reported on a daily basis. The reports originate from national laws, according to which positive test findings must be submitted to the Federal Health Authorities, the Robert Koch Institute, via the local health authorities. Since an enormous number of unreported cases can be expected, the question of how widespread the disease has been in the population cannot be answered based on these administrative reports. Using mathematical modeling, however, estimates can be made. These estimates indicate that the small numbers of diagnostic tests carried out at the beginning of the outbreak overlooked considerable parts of the infection. In order to cover the initial phase of future waves of the disease, wide-spread and comprehensive tests are recommended.
Heidelberg University（海德堡大学）；Chinese Academy of Medical Sciences and Peking Union Medical College（中国医学科学院与北京协和医学院）；University Hospital Bonn（波恩大学医院）；University Hospital Heidelberg（海德堡大学医院）；Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；Africa Health Research Institute（非洲健康研究所）
Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and intervention measures during an ongoing outbreak. However, reliably inferring the dynamics of ongoing outbreaks by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address …
Age-dependent distribution of officially reported cases of vector-borne infections
Faculdade de Medicina, Universidade de São Paulo（圣保罗大学医学院）；Instituto de Física, Universidade de São Paulo（圣保罗大学物理研究所）；Instituto Butantan（布坦坦研究所）；Faculdade de Saúde Pública, Universidade de São Paulo（圣保罗大学公共卫生学院）
In the wake of the COVID-19 virus outbreak, a brief phenomenological (descriptive, comparative) analysis of the dynamics of the disease spread among different countries is presented. Results indicate that the infection spread dynamics is currently the most pronounced in the USA (confirmed cases are currently doubling every 2.16 days, with a decreasing doubling time tendency), while other countries with the most confirmed cases show different values, and tendencies. The reported number of deaths is currently doubled every 2.28 days in Germany, 2.56 days in France, 2.57 days in Switzerland, 2.59…
We are currently facing a highly critical case of a world-wide pandemic. The novel coronavirus (SARS-CoV-2, a.k.a. COVID-19) has proved to be extremely contagious and the original outbreak from Asia has now spread to all continents. This situation will fruitfully profit from the study in regards of the spread of the virus, assessing effective countermeasures to weight the impact of the adopted strategies. The standard Susceptible-Infectious-Recovered (SIR) model is a very successful and widely used mathematical model for predicting the spread of an epidemic. We adopt the SIR model on a random …
Knowledge about the daily number of new infections of Covid-19 is important because it is the basis for political decisions resulting in lockdowns and urgent health care measures. We use Germany as an example to illustrate shortcomings of official numbers, which are, at least in Germany, disclosed only with several days of delay and severely underreported on weekends (more than 40%). These shortcomings outline an urgent need for alternative data sources. The other widely cited source provided by the Center for Systems Science and Engineering at Johns Hopkins University (JHU) also deviates for …
Background: There is limited information about the role of different age groups, particularly subgroups of school-age children and younger adults in propagating influenza epidemics. Methods: For a communicable disease outbreak, some subpopulations may play a disproportionate role during the ascent of the outbreak due to increased susceptibility and/or contact rates. Such subpopulations can be identified by considering the proportion that cases in a subpopulation represent among all cases in the population occurring before the epidemic peak (Bp), the corresponding proportion after the epidemic …
The paper deals with a modeling of the ongoing epidemic caused by Coronavirus disease 2019 (COVID-19) on the closed territory of the Republic of Croatia. Using the official public information on the number of confirmed infected, recovered and deceased individuals, the modified SEIR compartmental model is developed to describe the underlying dynamics of the epidemic. Fitted modified SEIR model provides the prediction of the disease progression in the near future, considering strict control interventions by means of social distancing and quarantine for infected and at-risk individuals introduced…
To control African swine fever (ASF) efficiently, easily interpretable metrics of the outbreak dynamics are needed to plan and adapt the required measures. We found that the spread pattern of African Swine Fever cases in wild boar follows the mechanics of a diffusion process, at least in the early phase, for the cases that occurred in Germany. Following incursion into a previously unaffected area, infection disseminates locally within a naive and abundant wild boar population. Using real case data for Germany, we derive statistics about the time differences and distances between consecutive ca…
Background: The analysis of the Sars-CoV-2 epidemic is of paramount importance to understand the dynamics of the coronavirus spread. This can help health and government authorities take the appropriate measures and implement suitable politics aimed at fighting and preventing it. Methods: A time-dependent dynamic SEIR model inspired in a model previously used during the MERS outbreak in South Korea was used to analyse the time trajectories of active and hospitalized cases in Portugal. Results: The time evolution of the virus spread in the country was adequately modelled. The model has changeabl…
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 …
We assess the impact of COVID-19 response measures implemented in Germany and Switzerland on cumulative COVID-19-related hospitalization and death rates. Our analysis exploits the fact that the epidemic was more advanced in some regions than in others when certain lockdown measures came into force, based on measuring health outcomes relative to the region-specific start of the epidemic and comparing outcomes across regions with earlier and later start dates. When estimating the effect of the relative timing of measures, we control for regional characteristics and initial epidemic trends by lin…
After the introduction of drastic containment measures aimed at stopping the epidemic contagion from SARS-CoV2, many governments have adopted a strategy based on a periodic relaxation of such measures in the face of a severe economic crisis caused by lockdowns. Assessing the impact of such openings in relation to the risk of a resumption of the spread of the disease is an extremely difficult problem due to the many unknowns concerning the actual number of people infected, the actual reproduction number and infection fatality rate of the disease. In this work, starting from a compartmental mode…
The coronavirus disease 2019 (COVID-19) has changed the world since the World Health Organization declared its outbreak on 30th January 2020, recognizing the outbreak as a pandemic on 11th March 2020. As often said by politicians and scientific advisors, the objective is "to flatten the curve", or "push the peak down", or similar wording, of the virus spreading. Central to the official advice are mathematical models and data, which provide estimates on the evolution of the number of infected, recovered and deaths. The accuracy of the models is improved day by day by inferring the contact, reco…
When the novel coronavirus disease SARS-CoV2 (COVID-19) was officially declared a pandemic by the WHO in March 2020, the scientific community had already braced up in the effort of making sense of the fast-growing wealth of data gathered by national authorities all over the world. However, despite the diversity of novel theoretical approaches and the comprehensiveness of many widely established models, the official figures that recount the course of the outbreak still sketch a largely elusive and intimidating picture. Here we show unambiguously that the dynamics of the COVID-19 outbreak belong…
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…
In this work, we adapt the epidemiological SIR model to study the evolution of the dissemination of COVID-19 in Germany and Brazil (nationally, in the State of Paraiba, and in the City of Campina Grande). We prove the well posedness and the continuous dependence of the model dynamics on its parameters. We also propose a simple probabilistic method for the evolution of the active cases that is instrumental for the automatic estimation of parameters of the epidemiological model. We obtained statistical estimates of the active cases based the probabilistic method and on the confirmed cases data. …
Aims: Nonpharmaceutical interventions against the spread of SARS-CoV-2 in Germany included the cancellation of mass events (from March 8), closures of schools and child day care facilities (from March 16) as well as a "lockdown" (from March 23). This study attempts to assess the effectiveness of these interventions in terms of revealing their impact on infections over time. Methods: Dates of infections were estimated from official German case data by incorporating the incubation period and an empirical reporting delay. Exponential growth models for infections and reproduction numbers were esti…
Human mobility contributes to the fast spatio-temporal propagation of infectious diseases. During an outbreak, monitoring the infection situation on either side of an international border is very crucial as there is always a higher risk of disease importation associated with cross-border migration. Mechanistic models are effective tools to investigate the consequences of cross-border mobility on disease dynamics and help in designing effective control strategies. However, in practice, due to the unavailability of cross-border mobility data, it becomes difficult to propose reliable, model-based…
Background: Animal trade plays an important role for the spread of infectious diseases in livestock populations. As a case study, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. The central question is how infectious diseases can potentially spread within the system of trade contacts. We address this question by analyzing the underlying network of animal movements. Methodology/Findings: The considered pig trade dataset spans several years and is analyzed with respect to its potential to spread infectious diseases. Focusing on measurements of…
Boston Children’s Hospital（波士顿儿童医院）；Harvard Medical School（哈佛医学院）；Tecnológico de Monterrey（蒙特雷理工学院）；Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；Northeastern University（东北大学）；ISI Foundation（ISI基金会）
We present a timely and novel methodology that combines disease estimates from mechanistic models with digital traces, via interpretable machine-learning methodologies, to reliably forecast COVID-19 activity in Chinese provinces in real-time. Specifically, our method is able to produce stable and accurate forecasts 2 days ahead of current time, and uses as inputs (a) official health reports from Chinese Center Disease for Control and Prevention (China CDC), (b) COVID-19-related internet search activity from Baidu, (c) news media activity reported by Media Cloud, and (d) daily forecasts of COVI…
We investigate adaptive strategies to robustly and optimally control the COVID-19 pandemic via social distancing measures based on the example of Germany. Our goal is to minimize the number of fatalities over the course of two years without inducing excessive social costs. We consider a tailored model of the German COVID-19 outbreak with different parameter sets to design and validate our approach. Our analysis reveals that an open-loop optimal control policy can significantly decrease the number of fatalities when compared to simpler policies under the assumption of exact model knowledge. In …
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.
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…
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…
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…
Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet, contributes to the development and implementation of policies aimed at stopping or ameliorating the spread of diseases. In this manuscript, the role of official social network perturbations generated by public health officials to slow down or stop a disease outbreak are studied over distinct classes of static social networks. The dynamics are stochastic in nature with individuals (nodes) being assigned fixed levels of education or wealth. Nodes may change their ep…
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…
Viral outbreaks, such as the current COVID-19 pandemic, are commonly described by compartmental models by means of ordinary differential equation (ODE) systems. The parameter values of these ODE models are typically unknown and need to be estimated based on accessible data. In order to describe realistic pandemic scenarios with strongly varying situations, these model parameters need to be assumed as time-dependent. While parameter estimation for the typical case of time-constant parameters does not pose larger issues, the determination of time-dependent parameters, e.g.~the transition rates o…
We consider the pandemic spreading of COVID-19 for some selected countries after the outbreak of the coronavirus in Wuhan City, China. We estimated the infection rate and the initial infected individuals of COVID-19 by using the officially reported data at the early stage of the epidemic for the susceptible (S), infectable (I), quarantined (Q), and the cofirmed recovered (Rk) population model, so called SIQRk model. In the reported data we know the quarantined cases and the recovered cases. We can not know the recovered cases from the asymptomatic cases. In the SIQRk model we can estimated the…
Can public social media data be harnessed to predict COVID-19 case counts? We analyzed approximately 15 million COVID-19 related posts on Weibo, a popular Twitter-like social media platform in China, from November 1, 2019 to March 31, 2020. We developed a machine learning classifier to identify "sick posts," which are reports of one's own and other people's symptoms and diagnosis related to COVID-19. We then modeled the predictive power of sick posts and other COVID-19 posts on daily case counts. We found that reports of symptoms and diagnosis of COVID-19 significantly predicted daily case cou…
Faced with the 2020 SARS-CoV2 epidemic, public health officials have been seeking models that could be used to predict not only the number of new cases but also the levels of hospitalisation, critical care and deaths. In this paper we present a stochastic compartmental model capable of real-time monitoring and forecasting of the pandemic incorporating multiple streams of real-world data, reported cases, testing intensity, deaths, hospitalisations and critical care occupancy. Model parameters are estimated via a Bayesian particle filtering technique. The model successfully tracks the key variab…
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…
In this paper, we propose a dynamical model to describe the transmission of COVID-19, which is spreading in China and many other countries. To avoid a larger outbreak in the worldwide, Chinese government carried out a series of strong strategies to prevent the situation from deteriorating. Home quarantine is the most important one to prevent the spread of COVID-19. In order to estimate the effect of population quarantine, we divide the population into seven categories for simulation. Based on a Least-Squares procedure and officially published data, the estimation of parameters for the proposed…
We introduce a new probabilistic model to estimate the real spread of the novel SARS-CoV-2 virus along regions or countries. Our model simulates the behavior of each individual in a population according to a probabilistic model through an inverse problem; we estimate the real number of recovered and infected people using mortality records. In addition, the model is dynamic in the sense that it takes into account the policy measures introduced when we solve the inverse problem. The results obtained in Spain have particular practical relevance: the number of infected individuals can be $17$ time…
The novel coronavirus and its deadly outbreak have posed grand challenges to human society: as of March 26, 2020, there have been 85,377 confirmed cases and 1,293 reported deaths in the United States; and the World Health Organization (WHO) characterized coronavirus disease (COVID-19) - which has infected more than 531,000 people with more than 24,000 deaths in at least 171 countries - a global pandemic. A growing number of areas reporting local sub-national community transmission would represent a significant turn for the worse in the battle against the novel coronavirus, which points to an u…
