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This article considers the minimization of the total number of infected individuals over the course of an epidemic in which the rate of infectious contacts can be reduced by timedependent nonpharmaceutical interventions. The societal and economic costs of interventions are taken into account using a linear budget constraint which imposes a trade-off between short-term heavy interventions and long-term light interventions. We search for an optimal intervention strategy in an infinite-dimensional space of controls containing multiple consecutive lockdowns, gradually imposed and lifted restrictions, and various heuristic controls based, for example, on tracking the effective reproduction number. Mathematical analysis shows that among all such strategies, the global optimum is achieved by a single constant-level lockdown of maximum possible magnitude. Numerical simulations highlight the need for careful timing of such interventions and illustrate their benefits and disadvantages compared to strategies designed for minimizing peak prevalence. Rather counterintuitively, adding restrictions prior to the start of a well-planned intervention strategy may even increase the total incidence. [ABSTRACT FROM AUTHOR]

The real-time analysis of infectious disease surveillance data is essential in obtaining situational awareness about the current dynamics of a major public health event such as the COVID-19 pandemic. This analysis of e.g., time-series of reported cases or fatalities is complicated by reporting delays that lead to under-reporting of the complete number of events for the most recent time points. This can lead to misconceptions by the interpreter, for instance the media or the public, as was the case with the time-series of reported fatalities during the COVID-19 pandemic in Sweden. Nowcasting methods provide real-time estimates of the complete number of events using the incomplete time-series of currently reported events and information about the reporting delays from the past. In this paper we propose a novel Bayesian nowcasting approach applied to COVID-19-related fatalities in Sweden. We incorporate additional information in the form of time-series of number of reported cases and ICU admissions as leading signals. We demonstrate with a retrospective evaluation that the inclusion of ICU admissions as a leading signal improved the nowcasting performance of case fatalities for COVID-19 in Sweden compared to existing methods. Author summary: Nowcasting methods are an essential tool to provide situational awareness in a pandemic. The methods aim to provide real-time estimates of the complete number of events using the incomplete time-series of currently reported events and the information about the reporting delays from the past. In this paper, we propose a Bayesian approach applied to COVID-19 fatalities in Sweden. We incorporate regression components into the Bayesian hierarchical model to accommodate additional information provided by leading indicators such as time-series of the number of reported cases and ICU admissions. We use a retrospective evaluation covering the second (alpha) and third (delta) wave of COVID-19 in Sweden to assess the performance of the proposed method. We demonstrate that the inclusion of ICU admissions as a regression component improved the nowcasting performance (measured by the CRPS score) of case fatalities for COVID-19 in Sweden by 3.9% compared to when this information was not incorporated into the model. [ABSTRACT FROM AUTHOR]

The transmission heterogeneity of an epidemic is associated with a complex mixture of host, pathogen and environmental factors. And it may indicate superspreading events to reduce the efficiency of population-level control measures and to sustain the epidemic over a larger scale and a longer duration. Methods have been proposed to identify significant transmission heterogeneity in historic epidemics based on several data sources, such as contact history, viral genomes and spatial information, which may not be available, and more importantly ignore the temporal trend of transmission heterogeneity. Here we attempted to establish a convenient method to estimate real-time heterogeneity over an epidemic. Within the branching process framework, we introduced an instant-individualheterogenous infectiousness model to jointly characterize the variation in infectiousness both between individuals and among different times. With this model, we could simultaneously estimate the transmission heterogeneity and the reproduction number from incidence time series. We validated the model with data of both simulated and real outbreaks. Our estimates of the overall and real-time heterogeneities of the six epidemics were consistent with those presented in the literature. Additionally, our model is robust to the ubiquitous bias of under-reporting and misspecification of serial interval. By analyzing recent data from South Africa, we found evidence that the Omicron might be of more significant transmission heterogeneity than Delta. Our model based on incidence data was proved to be reliable in estimating the real-time transmission heterogeneity. Author Summary: The transmission of many infectious diseases is usually heterogeneous in time and space. Such transmission heterogeneity may indicate superspreading events (where some infected individuals transmit to disproportionately more susceptibles than others), reduce the efficiency of the population-level control measures, and sustain the epidemic over a larger scale and a longer duration. Classical methods of monitoring epidemic spread centered on the reproduction number which represent the average transmission potential of the epidemic at the population level, but failed to reflect the systematic variation in transmission. Several recent methods have been proposed to identify significant transmission heterogeneity in the epidemics such as Ebola, MERS, COVID-19. However, these methods are developed based on some sophisticated information such as contact history, viral genome and spatial information, of the confirmed cases, which are typically field-specific and not easy to generalize. In this study, we proposed a simple and generic method of estimating transmission heterogeneity from incidence time series, which provided consistent estimation of heterogeneity with those records with detailed data. It also helps in exploring the transmission heterogeneity of the newly emerging variant of Omicron. Our model enhances current understanding of epidemic dynamics, and highlight the potential importance of targeted control measures. [ABSTRACT FROM AUTHOR]

A stochastic SIR (susceptible → infective → recovered) model is considered for the spread of an epidemic on a network, described initially by an Erdős–Rényi random graph, in which susceptible individuals connected to infectious neighbors may drop or rewire such connections. A novel construction of the model is used to derive a deterministic model for epidemics started with a positive fraction initially infected and prove convergence of the scaled stochastic model to that deterministic model as the population size n→∞. For epidemics initiated by a single infective that take off, we prove that for part of the parameter space, in the limit as n→∞, the final fraction infected τ(λ) is discontinuous in the infection rate λ at its threshold λc, thus not converging to 0 as λ↓λc. The discontinuity is particularly striking when rewiring is necessarily to susceptible individuals in that τ(λ) jumps from 0 to 1 as λ passes through λc. [ABSTRACT FROM AUTHOR]