In this investigation I used the Logistic Model to fit the COVID-19 pandemic data for some countries. The data modeled is the death numbers per day in China, Iran, Italy, South Korea, Spain and United States. Considering the current growth rate of the pandemic, it was possible to show that the death toll should be between 3,277-3,327 deaths in China, 2,035-2,107 in Iran, 120-134 in South Korea, 11,227-12,793 in Italy and 6,217-7,405 in Spain. Also, with this toy model it was possible to show a clear emergence of a new outbreak within the same country (Iran, China and the United States). The growth rate of deaths found for South Korea was the lowest among the countries studied ($0.14701\pm0.00923$) and for China ($0.16667\pm0.00284$). Italy ($0.22594\pm0.00599$) and Spain ($0.31213\pm0.02337$) had the highest rates and in the second wave in Iran ($0.37893\pm0.02712$).
Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized Richards model and the generalized growth model to the reported number of infected cases for the whole of China, 29 provinces in China, and 33 countries and regions that have been or are undergoing major outbreaks. We dissect the development of the epidemics in China and the impact of the drastic control measures both at the aggregate level and within each province. We quantitatively document four phases of the outbreak in C…
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…
We present a compartmental SEIRD model aimed at forecasting hospital occupancy in metropolitan areas during the current COVID-19 outbreak. The model features asymptomatic and symptomatic infections with detailed hospital dynamics. We model explicitly branching probabilities and non exponential residence times in each latent and infected compartments. Using both hospital admittance confirmed cases and deaths we infer the contact rate and the initial conditions of the dynamical system, considering break points to model lockdown interventions. Our Bayesian approach allows us to produce timely pro…
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…
Some ideas are presented about the physical motivation of the apparent capacity of generalized logistic equations to describe the outbreak of the COVID-19 infection, and in general of quite many other epidemics. The main focuses here are: the complex, possibly fractal, structure of the locus describing the "contagion event set"; what can be learnt from the models of trophic webs with "herd behaviour".
The current outbreak is known as Coronavirus Disease or COVID-19 caused by the virus SAR-COV-2 which continues to wreak havoc across the globe. The World Health Organization (WHO) has declared the outbreak a Public Health Emergency of International Concern. In Pakistan, the spread of the virus is on the rise with the number of infected people and causalities rapidly increasing. In the absence of proper vaccination and treatment, to reduce the number of infections and casualties, the only option so far is to educate people regarding preventive measures and to enforce countrywide lock-down. Any …
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 …
Since early 2020, the world has been dealing with a raging pandemic outbreak: COVID-19. A year later, vaccines have become accessible, but in limited quantities, so that governments needed to devise a strategy to decide which part of the population to prioritize when assigning the available doses, and how to manage the interval between doses for multi-dose vaccines. In this paper, we present an optimization framework to address the dynamic double-dose vaccine allocation problem whereby the available vaccine doses must be administered to different age-groups to minimize specific societal object…
Background: The ongoing COVID-19 epidemic dilated rapidly throughout India. To end the global COVID-19 pandemic major behavioral, social distancing, contact tracing, and state interventions has been undertaken to reduce the outbreak and avert the persistence of the coronavirus in humans in India and worldwide. In absence of any vaccine or therapeutics, forecasting is of utmost priority for health care planning and control the transmission of COVID-19. Methods: We have proposed a mathematical model that explain the transmission dynamics of COVID-19 in India. Based on the estimated data our mode…
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 SIR pandemic model suffers from an unrealistic assumption: The rate of removal from the infectious class of individuals is assumed to be proportional to the number of infectious individuals. This means that a change in the rate of infection is simultaneous with an equal change in the rate of removal. A more realistic assumption is that an individual is removed at a certain time interval after having been infected. A simple modified SIR model is proposed which implements this delay, resulting in a single delay differential equation which comprises the model. A solution to this equation whic…
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…
University of Rochester（罗切斯特大学）；University of Rochester Medical Center（罗切斯特大学医学中心）；Ludwig Maximilian University（路德维希-马克西米利安大学）
Objective: To introduce a method for tracking results and utilization of Artificial Intelligence (tru-AI) in radiology. By tracking both large-scale utilization and AI results data, the tru-AI approach is designed to calculate surrogates for measuring important disease-related observational quantities over time, such as the prevalence of intracranial hemorrhage during the COVID-19 pandemic outbreak. Methods: To quantitatively investigate the clinical applicability of the tru-AI approach, we analyzed service requests for automatically identifying intracranial hemorrhage (ICH) on head CT using a…
The two-step contagion model is a simple toy model for understanding pandemic outbreaks that occur in the real world. The model takes into account that a susceptible person either gets immediately infected or weakened when getting into contact with an infectious one. As the number of weakened people increases, they eventually can become infected in a short time period and a pandemic outbreak occurs. The time required to reach such a pandemic outbreak allows for intervention and is often called golden time. Understanding the size-dependence of the golden time is useful for controlling pandemic …
As the outbreak of COVID-19 enters its third year, we have now enough data to analyse the behavior of the pandemic with mathematical models over a long period of time. The pandemic alternates periods of high and low infections, in a way that sheds a light on the nature of mathematical model that can be used for reliable predictions. The main hypothesis of the model presented here is that the oscillatory behavior is a structural feature of the outbreak, even without postulating a time-dependence of the coefficients. As such, it should be reflected by the presence of limit cycles as asymptotic s…
As Europe is facing the second wave of the CoViD-19 pandemic, each country should carefully review how it dealt with the first wave of outbreak. Lessons from the first experience should be useful to avoid indiscriminate closures and, above all, to determine universal (understandable) parameters to guide the introduction of containment measures to reduce the spreading of the virus. The use of few (effective) parameters is indeed of extreme importance to create a link between authorities and population, allowing the latter to understand the reason for some restrictions and, consequently, to allo…
For the last few years there has been a resurgence in the use of phenomenological growth models for predicting the early dynamics of infectious diseases. These models assume that time is a continuous variable whereas in the present contribution, the discrete versions of Gompertz and Generalized Logistic models are used for early monitoring and short-term forecasting of the spread of an epidemic in a region. The time-continuous models are represented mathematically by first-order differential equations while their discrete versions are represented by first-order difference equations that involv…
COVID-19 pandemic has been raging all around the world for almost a year now, as of November 1, 2020. In this paper, we try to analyze the variation of the COVID-19 pandemic in different countries in the light of some modifications to the susceptible-infected-recovered (SIR) model. The SIR model was modified by taking time-dependent rate parameters. From this modified SIR model, the basic reproduction number, effective reproduction number, herd immunity, and herd immunity threshold are redefined. The re-outbreak of the COVID-19 is a real threat to various countries. We have used the above-ment…
In late-2020, many countries around the world faced another surge in number of confirmed cases of COVID-19, including United Kingdom, Canada, Brazil, United States, etc., which resulted in a large nationwide and even worldwide wave. While there have been indications that precaution fatigue could be a key factor, no scientific evidence has been provided so far. We used a stochastic metapopulation model with a hierarchical structure and fitted the model to the positive cases in the US from the start of outbreak to the end of 2020. We incorporated non-pharmaceutical interventions (NPIs) into this…
Residential colleges and universities face unique challenges in providing in-person instruction during the COVID-19 pandemic. Administrators are currently faced with decisions about whether to open during the pandemic and what modifications of their normal operations might be necessary to protect students, faculty and staff. There is little information, however, on what measures are likely to be most effective and whether existing interventions could contain the spread of an outbreak on campus. We develop a full-scale stochastic agent-based model to determine whether in-person instruction coul…
We show that the COVID-19 pandemic under social distancing exhibits universal dynamics. The cumulative numbers of both infections and deaths quickly cross over from exponential growth at early times to a longer period of power law growth, before eventually slowing. In agreement with a recent statistical forecasting model by the IHME, we show that this dynamics is well described by the erf function. Using this functional form, we perform a data collapse across countries and US states with very different population characteristics and social distancing policies, confirming the universal behavior…
We study the reported data from the COVID-19 pandemic outbreak in January - May 2020 in 119 countries. We observe that the time series of active cases in individual countries (the difference of the total number of confirmed infections and the sum of the total number of reported deaths and recovered cases) display a strong agreement with polynomial growth and at a later epidemic stage also with a combined polynomial growth with exponential decay. Our results are also formulated in terms of compartment type mathematical models of epidemics. Within these models the universal scaling characterizin…
One of the central tools to control the COVID-19 pandemics is the knowledge of its spreading dynamics. Here we develop a fractal model capable of describe this dynamics, in term of daily new cases, and provide quantitative criteria for some predictions. We propose a fractal dynamical model using conformed derivative and fractal time scale. A Burr-XII shaped solution of the fractal-like equation is obtained. The model is tested using data from several countries, showing that a single function is able to describe very different shapes of the outbreak. The diverse behavior of the outbreak on thos…
For nearly a century, the initial reproduction number (R0) has been used as a one number summary to compare outbreaks of infectious disease, yet there is no `standard' estimator for R0. Difficulties in estimating R0 arise both from how a disease transmits through a population as well as from differences in statistical estimation method. We describe eight methods used to estimate R0 and provide a thorough simulation study of how these estimates change in the presence of different disease parameters. As motivation, we analyze the 2009 outbreak of the H1N1 pandemic influenza in the USA and compar…
The Richards family models comprise a well-known set of models with useful parameters to describe several aspects of disease outbreaks. Some of these models have been used to study the current Covid-19 pandemic. However, there seems to be confusion regarding the discrimination among competing models. In this paper a detailed application of Akaikes information approach is used to discern among models using data from The European Union, The United States and The United Kingdom. We argue that the epidemiological characteristics derived from competing models should be examined to complement the se…
Purpose: In this study we propose to identify significant economic, political, and social factors that helped contribute to the incidence and mortality of SARS-CoV-2 around the world during the first seven months of the COVID-19 pandemic. Methods: Retrospective analyses were conducted using data acquired by the World Health Organization regarding the number of new cases and deaths from 76 countries from January through July 2020. Hierarchical cluster and principal component analyses were used to categorize different countries based on their ability to control the outbreak based on number of ca…
The infectious diseases are spreading due to human interactions enabled by various social networks. Therefore, when a new pathogen such as SARS-CoV-2 causes an outbreak, the non-pharmaceutical isolation strategies (e.g., social distancing) are the only possible response to disrupt its spreading. To this end, we introduce the new epidemic model (SICARS) and compare the centralized (C), decentralized (D), and combined (C+D) social distancing strategies, and analyze their efficiency to control the dynamics of COVID-19 on heterogeneous complex networks. Our analysis shows that the centralized soci…
At the time of this writing, the novel coronavirus (COVID-19) pandemic outbreak has already put tremendous strain on many countries' citizens, resources and economies around the world. Social distancing measures, travel bans, self-quarantines, and business closures are changing the very fabric of societies worldwide. With people forced out of public spaces, much conversation about these phenomena now occurs online, e.g., on social media platforms like Twitter. In this paper, we describe a multilingual coronavirus (COVID-19) Twitter dataset that we have been continuously collecting since Januar…
COVID-19 pandemic has become a major threat to the country. Till date, well tested medication or antidote is not available to cure this disease. According to WHO reports, COVID-19 is a severe acute respiratory syndrome which is transmitted through respiratory droplets and contact routes. Analysis of this disease requires major attention by the Government to take necessary steps in reducing the effect of this global pandemic. In this study, outbreak of this disease has been analysed for India till 30th March 2020 and predictions have been made for the number of cases for the next 2 weeks. SEIR …
The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modeling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive an explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega functi…
In the present article a mathematical model is proposed to research the current coronavirus outbreak (SARS-CoV-2) in Paraguay, describing the multiple transmission paths in the infection dynamics, following the susceptible, exposed, infectious, hospitalized, with lost immunity and recovered individuals, as well as the role of the virus in the environment and deaths from COVID-19 or other reasons. In order to reflect the impact of the control measures adopted by the government and the population, the model employs variable transmission rates that change with the epidemiological status and envir…
Witnessing its first case in late January 2020 India has seen a sharp rise in the number of positive cases of COVID-19. 34 States/UT (s) of the country have been found to be affected by the pandemic to date. We in this work, study the progress of COVID-19 pandemic in India. We aim to create transmission network visualization (s) of COVID-19 in India and perform analysis upon them. Using the transmission networks obtained we attempt to find the possible Super Spreader Individual (s) and Super Spreader Events (SSE) responsible for the outbreak in their respective regions. We discuss the potentia…
Objective: The COVID-19 pandemic has created many challenges that need immediate attention. Various epidemiological and deep learning models have been developed to predict the COVID-19 outbreak, but all have limitations that affect the accuracy and robustness of the predictions. Our method aims at addressing these limitations and making earlier and more accurate pandemic outbreak predictions by (1) using patients' EHR data from different counties and states that encode local disease status and medical resource utilization condition; (2) considering demographic similarity and geographical proxi…
One of the many unresolved questions that revolves around the Covid-19 pandemic is whether local outbreaks can depend on ambient conditions like temperature and relative humidity. In this paper, we develop a model that tries to explain and describe the temperature and relative humidity sensitivity of respiratory droplets and their possible connection in determining viral outbreaks. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism - the final equations of which are similar to the well-known SIR model. The advantage of modeling the…
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…
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…
Sweden has adopted far less restrictive social distancing policies than most countries following the COVID-19 pandemic. This paper uses data on all mobile phone users, from one major Swedish mobile phone network, to examine the impact of the Coronavirus outbreak under the Swedish mild recommendations and restrictions regime on individual mobility and if changes in geographical mobility vary over different socio-economic strata. Having access to data for January-March in both 2019 and 2020 enables the estimation of causal effects of the COVID-19 outbreak by adopting a Difference-in-Differences …
During the early stage of the COVID-19 pandemic, many countries implemented non-pharmaceutical interventions (NPIs) to control the transmission of SARS-CoV-2, the causative pathogen of COVID-19. Among those NPIs, quarantine measures were widely adopted and enforced through stay-at-home and shelter-in-place orders. Understanding the effectiveness of quarantine measures can inform decision-making and control planning during the ongoing COVID-19 pandemic and for future disease outbreaks. In this study, we use mathematical models to evaluate the impact of quarantine measures on COVID-19 spread in …
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…
More and more countries show a significant slowdown in the number of new COVID-19 infections due to effective governmentally instituted lockdown and social distancing measures. We have analyzed the growth behavior of the top 25 most affected countries by means of a local slope analysis and found three distinct patterns that individual countries follow depending on the strictness of the lockdown protocols: exponential rise and fall, power law, or logistic. For countries showing power law growth we have determined the scaling exponents. For countries that showed a strong slowdown in the rate of …
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…
The COVID-19 pandemic began over two years ago, yet schools, businesses, and other organizations are still struggling to keep the risk of disease outbreak low while returning to (near) normal functionality. Observations from these past years suggest that this goal can be achieved through the right balance of mitigation strategies, which may include some combination of mask use, vaccinations, viral testing, and contact tracing. The choice of mitigation measures will be uniquely based on the needs and available resources of each organization. This article presents practical guidance for creating…
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…
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…
A well-known characteristic of pandemics such as COVID-19 is the high level of transmission heterogeneity in the infection spread: not all infected individuals spread the disease at the same rate and some individuals (superspreaders) are responsible for most of the infections. To quantify this phenomenon requires the analysis of the effect of the variance and higher moments of the infection distribution. Working in the framework of stochastic branching processes, we derive an approximate analytical formula for the probability of an outbreak in the high variance regime of the infection distribu…
Novel coronavirus-19 (2019-nCoV or COVID-19) is by far the most dangerous coronavirus ever identified for the third time in the three decades capable of infecting not only the animals but also the humans across the globe. Nearly 6000 deaths have been recorded due mainly to COVID-19 outbreak worldwide and more than 50% of these deaths appeared to have evolved from China where the virus was thought to originate. The endemicity of COVID-19 dramatically surpassed severe acute respiratory syndrome coronavirus (SARS-CoV) and Middle East respiratory syndrome coronavirus (MERS-CoV) that were so far di…
Within a short period of time, COVID-19 grew into a world-wide pandemic. Transmission by pre-symptomatic and asymptomatic viral carriers rendered intervention and containment of the disease extremely challenging. Based on reported infection case studies, we construct an epidemiological model that focuses on transmission around the symptom onset. The model is calibrated against incubation period and pairwise transmission statistics during the initial outbreaks of the pandemic outside Wuhan with minimal non-pharmaceutical interventions. Mathematical treatment of the model yields explicit express…
Some of the key questions of interest during the COVID-19 pandemic (and all outbreaks) include: where did the disease start, how is it spreading, who is at risk, and how to control the spread. There are a large number of complex factors driving the spread of pandemics, and, as a result, multiple modeling techniques play an increasingly important role in shaping public policy and decision making. As different countries and regions go through phases of the pandemic, the questions and data availability also changes. Especially of interest is aligning model development and data collection to suppo…
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…
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…
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 …
By the end of 2020, a year since the first cases of infection by the Covid-19 virus have been reported, there is a light at the end of the tunnel. Several pharmaceutical companies made significant progress in developing effective vaccines against the Covid-19 virus that has claimed the lives of more than a million people over the world. On the other hand, there is growing evidence of re-infection by the virus, which can cause further outbreaks. In this paper, we apply statistical physics tools to examine the vaccination rate required to control the pandemic for three different vaccine efficien…
