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Incarcerated individuals are a highly vulnerable population for infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Understanding the transmission of respiratory infections within prisons and between prisons and surrounding communities is a crucial component of pandemic preparedness and response. Here, we use mathematical and statistical models to analyze publicly available data on the spread of SARS-CoV-2 reported by the Ohio Department of Rehabilitation and Corrections (ODRC). Results from mass testing conducted on April 16, 2020 were analyzed together with time of first reported SARS-CoV-2 infection among Marion Correctional Institution (MCI) inmates. Extremely rapid, widespread infection of MCI inmates was reported, with nearly 80% of inmates infected within 3 weeks of the first reported inmate case. The dynamical survival analysis (DSA) framework that we use allows the derivation of explicit likelihoods based on mathematical models of transmission. We find that these data are consistent with three non-exclusive possibilities: (i) a basic reproduction number >14 with a single initially infected inmate, (ii) an initial superspreading event resulting in several hundred initially infected inmates with a reproduction number of approximately three, or (iii) earlier undetected circulation of virus among inmates prior to April. All three scenarios attest to the vulnerabilities of prisoners to COVID-19, and the inability to distinguish among these possibilities highlights the need for improved infection surveillance and reporting in prisons. 

Abstract The 2018–2020 Ebola virus disease epidemic in Democratic Republic of the Congo (DRC) resulted in 3481 cases (probable and confirmed) and 2299 deaths. In this paper, we use a novel statistical method to analyze the individual-level incidence and hospitalization data on DRC Ebola victims. Our analysis suggests that an increase in the rate of quarantine and isolation that has shortened the infectiousness period by approximately one day during the epidemic’s third and final wave was likely responsible for the eventual containment of the outbreak. The analysis further reveals that the total effective population size or the average number of individuals at risk for the disease exposure in three epidemic waves over the period of 24 months was around 16,000–a much smaller number than previously estimated and likely an evidence of at least partial protection of the population at risk through ring vaccination and contact tracing as well as adherence to strict quarantine and isolation policies. 

We study a stochastic compartmental susceptible–infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph vertices into two compartments, namely, S and I, denoting susceptible and infected vertices, respectively. In addition to the sizes of these two compartments, we keep track of the counts of SI-edges (those connecting a susceptible and an infected vertex) and SS-edges (those connecting two susceptible vertices). We describe the dynamical process in terms of these counts and present a functional central limit theorem (FCLT) for them as the number of vertices in the random graph grows to infinity. The FCLT asserts that the counts, when appropriately scaled, converge weakly to a continuous Gaussian vector semimartingale process in the space of vector-valued càdlàg functions endowed with the Skorokhod topology. We discuss applications of the FCLT in percolation theory and in modelling the spread of computer viruses. We also provide simulation results illustrating the FCLT for some common degree distributions.

 

We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method’s versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach. 

Abstract Background Estimating real-world vaccine effectiveness is challenging as a variety of population factors can impact vaccine effectiveness. We aimed to assess the population-level reduction in cumulative severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases, hospitalizations, and mortality due to the BNT162b2 mRNA coronavirus disease 2019 (COVID-19) vaccination campaign in Israel during January–February 2021. Methods A susceptible-infected-recovered/removed (SIR) model and a Dynamic Survival Analysis (DSA) statistical approach were used. Daily counts of individuals who tested positive and of vaccine doses administered, obtained from the Israeli Ministry of Health, were used to calibrate the model. The model was parameterized using values derived from a previous phase of the pandemic during which similar lockdown and other preventive measures were implemented in order to take into account the effect of these prevention measures on COVID-19 spread. Results Our model predicted for the total population a reduction of 648 585 SARS-CoV-2 cases (75% confidence interval [CI], 25 877–1 396 963) during the first 2 months of the vaccination campaign. The number of averted hospitalizations for moderate to severe conditions was 16 101 (75% CI, 2010–33 035), and reduction of death was estimated at 5123 (75% CI, 388–10 815) fatalities. Among children aged 0–19 years, we estimated a reduction of 163 436 (75% CI, 0–433 233) SARS-CoV-2 cases, which we consider to be an indirect effect of the vaccine. Conclusions Our results suggest that the rapid vaccination campaign prevented hundreds of thousands of new cases as well as thousands of hospitalizations and fatalities and has probably averted a major health care crisis. 

The Dynamical Survival Analysis (DSA) is a framework for modeling epidemics based on mean field dynamics applied to individual (agent) level history of infection and recovery. Recently, the Dynamical Survival Analysis (DSA) method has been shown to be an effective tool in analyzing complex non-Markovian epidemic processes that are otherwise difficult to handle using standard methods. One of the advantages of Dynamical Survival Analysis (DSA) is its representation of typical epidemic data in a simple although not explicit form that involves solutions of certain differential equations. In this work we describe how a complex non-Markovian Dynamical Survival Analysis (DSA) model may be applied to a specific data set with the help of appropriate numerical and statistical schemes. The ideas are illustrated with a data example of the COVID-19 epidemic in Ohio.