In this article, we develop a data assimilation procedure to predict the evolution of epidemics with data uncertainty, with application to the Covid-19 pandemic. We construct a vademecum of solutions by solving the SIR epidemic model for a set of data neighboring the estimated real (or official) ones. A reduced basis is constructed from this vademecum through Proper Orthogonal Decomposition (POD). The reduced POD base is then applied to assimilate the pandemic data (infected, recovered, deceased) during the period in which data are known, by a least squares procedure. The fitted curves are then used to predict the evolution of the pandemic in the next days. Validation tests for Andalusia region (Spain), Italy and Spain show accurate predictions for 7 days that improve as the number of assimilated data increases.
Predicting the spread of vector-borne diseases in response to incursions requires knowledge of both host and vector demographics in advance of an outbreak. Whereas host population data is typically available, for novel disease introductions there is a high chance of the pathogen utilising a vector for which data is unavailable. This presents a barrier to estimating the parameters of dynamical models representing host-vector-pathogen interaction, and hence limits their ability to provide quantitative risk forecasts. The Theileria orientalis (Ikeda) outbreak in New Zealand cattle demonstrates th…
We introduce a Bayesian sequential data assimilation method for COVID-19 forecasting. It is assumed that suitable transmission, epidemic and observation models are available and previously validated and the transmission and epidemic models are coded into a dynamical system. The observation model depends on the dynamical system state variables and parameters, and is cast as a likelihood function. We elicit prior distributions of the effective population size, the dynamical system initial conditions and infectious contact rate, and use Markov Chain Monte Carlo sampling to make inference and pred…
The evolution of epidemiological parameters, such as instantaneous reproduction number Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to Rt estimation, resulting in the state-of-the-art DARt system. With DARt, time misalignment …
In this work, we analyze and model the cholera epidemics that affected South Sudan, the newest country in the world, during 2014 and 2015. South Sudan possibly represents one of the most difficult context in which adapt the deterministic mathematical cholera model, due to the unstable social and political situation that clearly affects the fluxes of people and the sanitary conditions, increasing the risk of large outbreaks. Despite the limitation of a static gravity model in describing the chaotic human mobility of South Sudan, the SIRB model, calibrated with a data assimilation technique (Ens…
An analysis of the COVID-19 epidemic is proposed on the basis of the epiMOX dashboard (publicly accessible at https://www.epimox.polimi.it) that deals with data of the epidemic trends and outbreaks in Italy from late February 2020. Our analysis provides an immediate appreciation of the past epidemic development, together with its current trends by fostering a deeper interpretation of available data through several critical epidemic indicators. In addition, we complement the epiMOX dashboard with a predictive tool based on an epidemiological compartmental model, named SUIHTER, for the forecast …
IMT School for Advanced Studies Lucca（卢cca高等研究院）；TREE-TOWER S.R.L.（TREE-TOWER有限责任公司）
Computational models for the simulation of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic evolution would be extremely useful to support authorities in designing healthcare policies and lockdown measures to contain its impact on public health and economy. In Italy, the devised forecasts have been mostly based on a pure data-driven approach, by fitting and extrapolating open data on the epidemic evolution collected by the Italian Civil Protection Center. In this respect, SIR epidemiological models, which start from the description of the nonlinear interactions between…
Contact tracing data collected from disease outbreaks has received relatively little attention in the epidemic modelling literature because it is thought to be unreliable: infection sources might be wrongly attributed, or data might be missing due to resource contraints in the questionnaire exercise. Nevertheless, these data might provide a rich source of information on disease transmission rate. This paper presents novel methodology for combining contact tracing data with rate-based contact network data to improve posterior precision, and therefore predictive accuracy. We present an advanceme…
In this paper we develop a predictive model for the spread of COVID-19 infection at a provincial (i.e. EU NUTS-3) level in Italy by using official data from the Italian Ministry of Health integrated with data extracted from daily official press conferences of regional authorities and from local newspaper websites. This integration is mainly concerned with COVID-19 cause specific death data which are not available at NUTS-3 level from open official data data channels. An adjusted time-dependent SIRD model is used to predict the behavior of the epidemic, specifically the number of susceptible, i…
For practical reasons, many forecasts of case, hospitalization and death counts in the context of the current COVID-19 pandemic are issued in the form of central predictive intervals at various levels. This is also the case for the forecasts collected in the COVID-19 Forecast Hub (https://covid19forecasthub.org/). Forecast evaluation metrics like the logarithmic score, which has been applied in several infectious disease forecasting challenges, are then not available as they require full predictive distributions. This article provides an overview of how established methods for the evaluation o…
The seasonality of respiratory diseases (common cold, influenza, etc.) is a well-known phenomenon studied from ancient times. The development of predictive models is still not only an actual unsolved problem of mathematical epidemiology but also is very important for the safety of public health. Here we show that SIRS (Susceptible-Infected-Recovered-Susceptible) model accurately enough reproduces real curves of flu activity. It contains variable reaction rate, which is a function of mean daily temperature. The proposed alternation of variables represents SIRS equations as the second-order ODE …
Epidemiological models contain a set of parameters that must be adjusted based on available observations. Once a model has been calibrated, it can be used as a forecasting tool to make predictions and to evaluate contingency plans. It is customary to employ only point estimators for such predictions. However, some models may fit the same data reasonably well for a broad range of parameter values, and this flexibility means that predictions stemming from such models will vary widely, depending on the particular parameter values employed within the range that give a good fit. When data are poor …
Sheep pox is a highly transmissible disease which can cause serious loss of livestock and can therefore have major economic impact. We present data from sheep pox epidemics which occurred between 1994 and 1998. The data include weekly records of infected farms as well as a number of covariates. We implement Bayesian stochastic regression models which, in addition to various explanatory variables like seasonal and environmental/meteorological factors, also contain serial correlation structure based on variants of the Ornstein-Uhlenbeck process. We take a predictive view in model selection by ut…
In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model …
The correct evaluation of the reproductive number $R$ for COVID-19 -- which characterizes the average number of secondary cases generated by each typical primary case -- is central in the quantification of the potential scope of the pandemic and the selection of an appropriate course of action. In most models, $R$ is modeled as a universal constant for the virus across outbreak clusters and individuals -- effectively averaging out the inherent variability of the transmission process due to varying individual contact rates, population densities, demographics, or temporal factors amongst many. Y…
The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modelling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the re…
Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system is a straightforward mathematical formulation to model the dissemination of many infectious diseases. The present paper reports novel theoretical and analytical results for a perturbed version of an SIR model with Gamma-distributed delay. Notably, our epidemic model is represented by Itô-L'evy stochastic differential equations in order to simulate sudden an…
Epidemic models play a key role in understanding and responding to the emerging COVID-19 pandemic. Widely used compartmental models are static and are of limited use to evaluate intervention strategies with the emerging pandemic. Applying the technology of data assimilation, we propose a Bayesian updating approach for estimating epidemiological parameters using observable information for the purpose of assessing the impacts of different intervention strategies. We adopt a concise renewal model and propose new parameters by disentangling the reduction of instantaneous reproduction number Rt int…
Genotype networks drive oscillating endemicity and epidemic trajectories in viral evolution
University of Zaragoza（萨拉戈萨大学）；Institute of Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza（萨拉戈萨大学复杂系统生物计算与物理研究所 (BIFI)）；Universitat Rovira i Virgili（罗维拉-伊-维尔吉利大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of Kobe（神户大学）
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 …
The United States has an opioid epidemic, and Pennsylvania's Allegheny County is among the worst. This motivates a deeper exploration of what characterizes the epidemic, such as what are risk factors for people who ultimately overdose and die due to opioids. We show that some interesting trends and factors can be identified from openly available autopsy data, and demonstrate the power of building an interactive data exploration tool for policy makers. However, there is still a pressing need to incorporate further demographic factors. We show this by using synthetic Electronic Medical Record (E…
Whole genome sequencing of pathogens from multiple hosts in an epidemic offers the potential to investigate who infected whom with unparalleled resolution, potentially yielding important insights into disease dynamics and the impact of control measures. We considered disease outbreaks in a setting with dense genomic sampling, and formulated stochastic epidemic models to investigate person-to-person transmission, based on observed genomic and epidemiological data. We constructed models in which the genetic distance between sampled genotypes depends on the epidemiological relationship between th…
