The evolution of the COVID-19 epidemic has been accompanied by accumulating evidence on the underlying epidemiological parameters. Hence there is potential for models providing mid-term forecasts of the epidemic trajectory using such information. The effectiveness of lockdown interventions can also be assessed by modelling later epidemic stages, possibly using a multiphase epidemic model. Commonly applied methods to analyze epidemic trajectories include phenomenological growth models (e.g. the Richards), and variants of the susceptible-infected-recovered (SIR) compartment model. Here we focus on a practical forecasting approach, applied to interim UK COVID data, using a bivariate Reynolds model (cases and deaths). We show the utility of informative priors in developing and estimating the model, and compare error densities (Poisson-gamma, Poisson-lognormal, Poisson-logStudent) for overdispersed data on new cases and deaths. We use cross-validation to assess medium term forecasts. We also consider the longer term post-lockdown epidemic profile to assess epidemic containment, using a two phase model. Fit to mid-epidemic data shows better fit to training data and better cross validation performance for a Poisson-logStudent model. Estimation of longer term epidemic data after lockdown relaxation, characterised by protracted slow downturn and then upturn in cases, casts doubt on effective containment. Many applications of phenomenological models have been to complete epidemics. However, evaluation of such models based simply on their fit to observed data may give only a partial picture, and cross-validation against actual trends is also useful. Similarly, it may be preferable to model incidence rather than cumulative data, though this raises questions about suitable error densities for modelling often erratic fluctuations. Hence there may be utility in evaluating alternative error assumptions.
The Adult Changes in Thought (ACT) study is a long-running prospective study of incident all-cause dementia and Alzheimer's disease (AD). As the cohort ages, death (a terminal event) is a prominent competing risk for AD (a non-terminal event), although the reverse is not the case. As such, analyses of data from ACT can be placed within the semi-competing risks framework. Central to semi-competing risks, and in contrast to standard competing risks, is that one can learn about the dependence structure between the two events. To-date, however, most methods for semi-competing risks treat dependenc…
The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible-infected-removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid d…
Predictability of undesired events is a question of great interest in many scientific disciplines including seismology, economy, and epidemiology. Here, we focus on the predictability of invasion of a broad class of epidemics caused by diseases that lead to permanent immunity of infected hosts after recovery or death. We approach the problem from the perspective of the science of complexity by proposing and testing several strategies for the estimation of important characteristics of epidemics, such as the probability of invasion. Our results suggest that parsimonious approximate methodologies…
Civil registration vital statistics (CRVS) data are used to produce national estimates of maternal mortality, but are often subject to substantial reporting errors due to misclassification of maternal deaths. The accuracy of CRVS systems can be assessed by comparing CRVS-based counts of maternal and non-maternal deaths to those obtained from specialized studies, which are rigorous assessments of maternal mortality for a given country-period. We developed a Bayesian bivariate random walk model to estimate sensitivity and specificity of the reporting on maternal mortality in CRVS data, and assoc…
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 recent Covid-19 epidemic has lead to comparisons of the countries suffering from it. These are based on the number of excess deaths attributed either directly or indirectly to the epidemic. Unfortunately the data on which such comparisons rely are often incomplete and unreliable. This article discusses problems of interpretation of data even when the data is largely accurate and delayed by at most two to three weeks. This applies to the Office of National Statistics in the UK, the Statistisches Bundesamt in Germany and the Belgian statistical office Statbel. The data in the article is take…
Background: Opioid misuse is a major public health issue in the United States and in particular Ohio. However, the burden of the epidemic is challenging to quantify as public health surveillance measures capture different aspects of the problem. Here we synthesize county-level death and treatment counts to compare the relative burden across counties and assess associations with social environmental covariates. Methods: We construct a generalized spatial factor model to jointly model death and treatment rates for each county. For each outcome, we specify a spatial rates parameterization for a P…
Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected numb…
This study proposes a nonhomogeneous birth--death model which captures the dynamics of a directly transmitted infectious disease. Our model accounts for an important aspect of observed epidemic data in which only symptomatic infecteds are observed. The nonhomogeneous birth--death process depends on survival distributions of reproduction and removal, which jointly yield an estimate of the effective reproduction number $R(t)$ as a function of epidemic time. We employ the Burr distribution family for the survival functions and, as special cases, proportional rate and accelerated event-time models…
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…
The COVID-19 outbreak is asynchronous in US counties. Mitigating the COVID-19 transmission requires not only the state and federal level order of protective measures such as social distancing and testing, but also public awareness of time-dependent risk and reactions at county and community levels. We propose a robust approach to estimate the heterogeneous progression of SARS-CoV-2 at all US counties having no less than 2 COVID-19 associated deaths, and we use the daily probability of contracting (PoC) SARS-CoV-2 for a susceptible individual to quantify the risk of SARS-CoV-2 transmission in a…
Background: Following the outbreak of the coronavirus epidemic in early 2020, municipalities, regional governments and policymakers worldwide had to plan their Non-Pharmaceutical Interventions (NPIs) amidst a scenario of great uncertainty. At this early stage of an epidemic, where no vaccine or medical treatment is in sight, algorithmic prediction can become a powerful tool to inform local policymaking. However, when we replicated one prominent epidemiological model to inform health authorities in a region in the south of Brazil, we found that this model relied too heavily on manually predeter…
Emerging at the end of 2019, COVID-19 has become a public health threat to people worldwide. Apart from the deaths who tested positive for COVID-19, many others have died from causes indirectly related to COVID-19. Therefore, the COVID-19 confirmed deaths underestimate the influence of the pandemic on the society; instead, the measure of `excess deaths' is a more objective and comparable way to assess the scale of the epidemic and formulate lessons. One common practical issue in analyzing the impact of COVID-19 is to determine the `pre-COVID-19' period and the `post-COVID-19' period. We apply …
Objective: To estimate the number of deaths in Peru due to COVID-19. Design: With a priori information obtained from the daily number of deaths due to CODIV-19 in China and data from the Peruvian authorities, we constructed a predictive Bayesian non-linear model for the number of deaths in Peru. Exposure: COVID-19. Outcome: Number of deaths. Results: Assuming an intervention level similar to the one implemented in China, the total number of deaths in Peru is expected to be 612 (95%CI: 604.3 - 833.7) persons. Sixty four days after the first reported death, the 99% of expected deaths will be obs…
Coronavirus disease (COVID-2019) is a severe ongoing novel pandemic that is spreading quickly across the world. Italy, that is widely considered one of the main epicenters of the pandemic, has registered the highest COVID-2019 death rates and death toll in the world, to the present day. In this article I estimate an autoregressive integrated moving average (ARIMA) model to forecast the epidemic trend over the period after April 4, 2020, by using the Italian epidemiological data at national and regional level. The data refer to the number of daily confirmed cases officially registered by the It…
In this article, we deal with COVID-19 data to study the trend of the epidemic at the global situation. Choosing the mortality rate as an appropriate metric which measures the relative relation between the cumulative confirmed cases and death cases, we utilize the modified kernel estimator for random density function (Petersen and Muller, 2016) to obtain the density of the mortality rate, and apply Frechet change point detection (Dubey and Muller, 2020) to check if there is any significant change on the dynamic pattern of COVID-19 deaths. The analysis shows that the pattern of global COVID-19 …
In this paper we develop statistical methods for causal inference in epidemics. Our focus is in estimating the effect of social mobility on deaths in the Covid-19 pandemic. We propose a marginal structural model motivated by a modified version of a basic epidemic model. We estimate the counterfactual time series of deaths under interventions on mobility. We conduct several types of sensitivity analyses. We find that the data support the idea that reduced mobility causes reduced deaths, but the conclusion comes with caveats. There is evidence of sensitivity to model misspecification and unmeasu…
Since the beginning of the COVID-19 pandemic, many dashboards have emerged as useful tools to monitor the evolution of the pandemic, inform the public, and assist governments in decision making. Our goal is to develop a globally applicable method, integrated in a twice daily updated dashboard that provides an estimate of the trend in the evolution of the number of cases and deaths from reported data of more than 200 countries and territories, as well as a seven-day forecast. One of the significant difficulties to manage a quickly propagating epidemic is that the details of the dynamic needed t…
The crisis caused by COVID-19 revealed the global unpreparedness to handle the impact of a pandemic. In this paper, we present a statistical analysis of the data related to the COVID-19 outbreak in China, specifically the infection speed, death and fatality rates in Hubei province. By fitting distributions of these quantities we design a parametric reinsurance contract whose trigger and cap are based on the probability distributions of the infection speed, death and fatality rates. In particular, fitting the distribution for the infection speed and death rates we provide a measure of the effec…
Infectious disease forecasting for ongoing epidemics has been traditionally performed, communicated, and evaluated as numerical targets - 1, 2, 3, and 4 week ahead cases, deaths, and hospitalizations. While there is great value in predicting these numerical targets to assess the burden of the disease, we argue that there is also value in communicating the future trend (description of the shape) of the epidemic -- for instance, if the cases will remain flat or a surge is expected. To ensure what is being communicated is useful we need to be able to evaluate how well the predicted shape matches …
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 COVID-19 pandemic has caused severe public health consequences in the United States. In this study, we use a hierarchical Bayesian model to estimate the age-specific COVID-19 attributable deaths over time in the United States. The model is specified by a novel non-parametric spatial approach, a low-rank Gaussian Process (GP) projected by regularised B-splines. We show that this projection defines a new GP with attractive smoothness and computational efficiency properties, derive its kernel function, and discuss the penalty terms induced by the projected GP. Simulation analyses and benchmar…
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…
The coronavirus disease 2019 (COVID-19) pandemic has exerted a profound impact on patients with end-stage renal disease relying on kidney dialysis to sustain their lives. Motivated by a request by the U.S. Centers for Medicare & Medicaid Services, our analysis of their postdischarge hospital readmissions and deaths in 2020 revealed that the COVID-19 effect has varied significantly with postdischarge time and time since the onset of the pandemic. However, the complex dynamics of the COVID-19 effect trajectories cannot be characterized by existing varying coefficient models. To address this issu…
We analyze the data about casualties in Italy in the period 01/01/2015 to 30/09/2020 released by the Italian National Institute of Statistics (ISTAT). The data exhibit a clear sinusoidal behavior, whose fit allows for a robust subtraction of the baseline trend of casualties in Italy, with a surplus of mortality in correspondence to the flu epidemics in winter and to the hottest periods in summer. While these peaks are symmetric in shape, the peak in coincidence with the COVID-19 pandemics is asymmetric and more pronounced. We fit the former with a Gaussian function and the latter with a Gomper…
In this report we fit a semi-mechanistic Bayesian hierarchical model to describe the Mexican COVID-19 epidemic. We obtain two epidemiological measures: the number of infections and the reproduction number. Estimations are based on death data. Hence, we expect our estimates to be more accurate than the attack rates estimated from the reported number of cases.
Testing, contact tracing, and isolation (TTI) is an epidemic management and control approach that is difficult to implement at scale because it relies on manual tracing of contacts. Exposure notification apps have been developed to digitally scale up TTI by harnessing contact data obtained from mobile devices; however, exposure notification apps provide users only with limited binary information when they have been directly exposed to a known infection source. Here we demonstrate a scalable improvement to TTI and exposure notification apps that uses data assimilation (DA) on a contact network.…
Since the beginning of the epidemic, daily reports of CoViD-19 cases, hospitalizations, and deaths from around the world have been publicly available. This paper describes methods to characterize broad features of the spread of the disease, with relatively long periods of constant transmission rates, using a new population modeling framework based on discrete-time difference equations. Comparative parameters are chosen for their weak dependence on model assumptions. Approaches for their point and interval estimation, accounting for additional sources of variance in the case data, are presented…
