It is of vital importance to understand and track the dynamics of rapidly unfolding epidemics. The health and economic consequences of the current COVID-19 pandemic provide a poignant case. Here we point out that since they are based on differential equations, the most widely used models of epidemic spread are plagued by an approximation that is not justified in the case of the current COVID-19 pandemic. Taking the example of data from New York City, we show that currently used models significantly underestimate the initial basic reproduction number ($R_0$). The correct description, based on integral equations, can be implemented in most of the reported models and it much more accurately accounts for the dynamics of the epidemic after sharp changes in $R_0$ due to restrictive public congregation measures. It also provides a novel way to determine the incubation period, and most importantly, as we demonstrate for several countries, this method allows an accurate monitoring of $R_0$ and thus a fine-tuning of any restrictive measures. Integral equation based models do not only provide the conceptually correct description, they also have more predictive power than differential equation based models, therefore we do not see any reason for using the latter.
In this work we combing models of disease dynamics and economic production, and we show the potential implications of this for demonstrating the importance of savings for buffering an economy during the period of an epidemic. Finding an explicit function that relates poverty and the production of a community is an almost impossible task because of the number of variables and parameters that should be taken into account. However, studying the dynamics of an endemic disease in a region that affects its population, and therefore its ability to work, is an honest approach to understanding this fun…
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 …
One of the main challenges of the measures against the COVID-19 epidemic is to reduce the amplitude of the epidemic peak without increasing without control its timescale. We investigate this problem using the SIR model for the epidemic dynamics, for which reduction of the epidemic peak $I_P$ can be achieved only at the price of increasing the time $t_P$ of its occurrence and its entire time-span $t_E$. By means of a time reparametrization we linearize the equations for the SIR dynamics. This allows us to solve exactly the dynamics in the time domain and to derive the scaling behaviour of the s…
Different ways of calculating mortality ratios during epidemics have yielded very different results, particularly during the current COVID-19 pandemic. We formulate both a survival probability model and an associated infection duration-dependent SIR model to define individual- and population-based estimates of dynamic mortality ratios. The key parameters that affect the dynamics of the different mortality estimates are the incubation period and the time individuals were infected before confirmation of infection. We stress that none of these ratios are accurately represented by the often misint…
Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts often grossly wrong, concerning the numbers of people who get infected or die? The purpose of this study is to better understand the stochastic nature of an epidemic disease, and answer the above questions. Much of the work on infectious diseases has been based on "SIR deterministic models," (Kermack and McKendrick:1927.) We will explore stochastic models that…
The contact structure between hosts has a critical influence on disease spread. However, most networkbased models used in epidemiology tend to ignore heterogeneity in the weighting of contacts. This assumption is known to be at odds with the data for many contact networks (e.g. sexual contact networks) and to have a strong effect on the predictions of epidemiological models. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framew…
High impact epidemics constitute one of the largest threats humanity is facing in the 21st century. Testing, contact tracing and quarantining are critical in slowing down epidemic dynamics, but may prove insufficient for highly contagious diseases. In the absence of pharmaceutical interventions, physical distancing measures remain as the last resort to avoid a widespread outbreak. Here we show that such combined countermeasures drastically change the rules of the epidemic transition if testing capacities are limited: Instead of continuous the response to countermeasures becomes discontinuous a…
The data of the 2009 A(H1N1) epidemic in Istanbul, Turkey is unique in terms of the collected data, which include not only the hospitalization but also the fatality information recorded during the pandemic. The analysis of this data displayed an unexpected time shift between the hospital referrals and fatalities. This time shift, which does not conform to the SIR and SEIR models, was explained by multi-stage SIR and SEIR models [21]. In this study we prove that the delay for these models is half of the infectious period within a quadratic approximation, and we determine the epidemic parameters…
The outbreak of severe acute respiratory syndrome (SARS) is still threatening the world because of a possible resurgence. In the current situation that effective medical treatments such as antiviral drugs are not discovered yet, dynamical features of the epidemics should be clarified for establishing strategies for tracing, quarantine, isolation, and regulating social behavior of the public at appropriate costs. Here we propose a network model for SARS epidemics and discuss why superspreaders emerged and why SARS spread especially in hospitals, which were key factors of the recent outbreak. We…
Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model considering the two key ingredients, in which the contacts are grouped into two classes: strong contacts and normal ones. Next, we present a unified edge-based compartmental approach to the spread dynamics on Erdös-Rényi (ER) networks and validate its results by extensive numerical simulations. In case that epidemic is totally drug-resistant, we both numeric…
${\bf Background:}$ The early growth dynamics of the West African Ebola virus epidemic has been qualitatively different for Guinea, Sierra Leone and Liberia. However, it is important to understand these disparate dynamics as trends of a single epidemic spread over regions with similar geographic and cultural aspects, with likely common parameters for transmission rates and the reproduction number $R_0$. ${\bf Methods:}$ We combine a discrete, stochastic SEIR model with a two-scale community network model to demonstrate that the different regional trends may be explained by different community …
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 …
Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of non-pharmaceutical interventions that pushed the growth rate below the recovery rate. In this new phase of the pandemic many countries show an almost linear growth of confirmed cases for extended time-periods. This new containment regime is hard to explain by traditional models where infection numbers either grow explosively until herd immunity is reached, or the epidemic is completely suppressed (zero new cases). Here we offer an explanation of this puzzling observati…
Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume mass-action contact patterns and undirected contact networks, meaning that the individuals most likely to spread the disease are also the most at risk to receive it from others. Here, we review results from the theory of random directed graphs which show that many important quantities, including the reproduction number and the epidemic size, depend sensitively on the joint distribution of in- and out-degrees ("risk" and "spread"), including their heterogeneity and the correlation between them. …
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in…
The outbreak of the novel coronavirus, COVID-19, has been declared a pandemic by the WHO. The structures of social contact critically determine the spread of the infection and, in the absence of vaccines, the control of these structures through large-scale social distancing measures appears to be the most effective means of mitigation. Here we use an age-structured SIR model with social contact matrices obtained from surveys and Bayesian imputation to study the progress of the COVID-19 epidemic in India. The basic reproductive ratio R0 and its time-dependent generalization are computed based o…
University of Minnesota（明尼苏达大学）；IQVIA（艾昆纬）；University of Virginia（弗吉尼亚大学）；Temple University（天普大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Accurate prediction of the transmission of epidemic diseases such as COVID-19 is crucial for implementing effective mitigation measures. In this work, we develop a tensor method to predict the evolution of epidemic trends for many regions simultaneously. We construct a 3-way spatio-temporal tensor (location, attribute, time) of case counts and propose a nonnegative tensor factorization with latent epidemiological model regularization named STELAR. Unlike standard tensor factorization methods which cannot predict slabs ahead, STELAR enables long-term prediction by incorporating latent temporal …
Background: To prevent future outbreaks of COVID-19, Australia is pursuing a mass-vaccination approach in which a targeted group of the population comprising healthcare workers, aged-care residents and other individuals at increased risk of exposure will receive a highly effective priority vaccine. The rest of the population will instead have access to a less effective vaccine. Methods: We apply a large-scale agent-based model of COVID-19 in Australia to investigate the possible implications of this hybrid approach to mass-vaccination. The model is calibrated to recent epidemiological and demo…
COVID-19 is an emerging respiratory infectious disease caused by the coronavirus SARS-CoV-2. It was first reported on in early December 2019 in Wuhan, China and within three month spread as a pandemic around the whole globe. Here, we study macro-epidemiological patterns along the time course of the pandemic. We compute the distribution of confirmed COVID-19 cases and deaths for countries worldwide and for counties in the US, and show that both distributions follow a truncated power-law over five orders of magnitude. We are able to explain the origin of this scaling behavior as a dual-scale pro…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of ordinary differential equations. When dealing with populations with space structure the relevant quantities are spatial densities, whose evolution in time requires nonlinear partial differential equations, which are known as reaction-diffusion systems. Here we present an (historical) outline of mathematical epidemiology, with a particular attention to the role …
The pandemic of COVID-19 has caused severe public health consequences around the world. Many interventions of COVID-19 have been implemented. It is of great public health and societal importance to evaluate the effects of interventions in the pandemic of COVID-19. In this paper, with help of synthetic control method, regression discontinuity and a Susceptible-Infected and infectious without isolation-Hospitalized in isolation-Removed (SIHR) model, we evaluate the horizontal and longitudinal effects of stringent interventions implemented in Wenzhou, a representative urban city of China, where s…
To control the current outbreak of the Coronavirus Disease 2019, constant monitoring of the epidemic is required since, as of today, no vaccines or antiviral drugs against it are known. We provide daily updated estimates of the reproduction number over time at https://stochastik-tu-ilmenau.github.io/COVID-19/. In this document, we describe the estimator we are using which was developed in (Fraser 2007), derive its asymptotic properties, and we give details on its implementation. Furthermore, we validate the estimator on simulated data, demonstrate that estimates on real data lead to plausible …
