Disentangling the causes of mumps reemergence in the United States.

Over the past two decades, multiple countries with high vaccine coverage have experienced resurgent outbreaks of mumps. Worryingly, in these countries, a high proportion of cases have been among those who have completed the recommended vaccination schedule, raising alarm about the effectiveness of existing vaccines. Two putative mechanisms of vaccine failure have been proposed as driving observed trends: 1) gradual waning of vaccine-derived immunity (necessitating additional booster doses) and 2) the introduction of novel viral genotypes capable of evading vaccinal immunity. Focusing on the United States, we conduct statistical likelihood-based hypothesis testing using a mechanistic transmission model on age-structured epidemiological, demographic, and vaccine uptake time series data. We find that the data are most consistent with the waning hypothesis and estimate that 32.8% (32%, 33.5%) of individuals lose vaccine-derived immunity by age 18 y. Furthermore, we show using our transmission model how waning vaccine immunity reproduces qualitative and quantitatively consistent features of epidemiological data, namely 1) the shift in mumps incidence toward older individuals, 2) the recent recurrence of mumps outbreaks, and 3) the high proportion of mumps cases among previously vaccinated individuals.

Charting the spatial dynamics of early SARS-CoV-2 transmission in Washington state.

The spread of SARS-CoV-2 has been geographically uneven. To understand the drivers of this spatial variation in SARS-CoV-2 transmission, in particular the role of stochasticity, we used the early stages of the SARS-CoV-2 invasion in Washington state as a case study. We analysed spatially-resolved COVID-19 epidemiological data using two distinct statistical analyses. The first analysis involved using hierarchical clustering on the matrix of correlations between county-level case report time series to identify geographical patterns in the spread of SARS-CoV-2 across the state. In the second analysis, we used a stochastic transmission model to perform likelihood-based inference on hospitalised cases from five counties in the Puget Sound region. Our clustering analysis identifies five distinct clusters and clear spatial patterning. Four of the clusters correspond to different geographical regions, with the final cluster spanning the state. Our inferential analysis suggests that a high degree of connectivity across the region is necessary for the model to explain the rapid inter-county spread observed early in the pandemic. In addition, our approach allows us to quantify the impact of stochastic events in determining the subsequent epidemic. We find that atypically rapid transmission during January and February 2020 is necessary to explain the observed epidemic trajectories in King and Snohomish counties, demonstrating a persisting impact of stochastic events. Our results highlight the limited utility of epidemiological measures calculated over broad spatial scales. Furthermore, our results make clear the challenges with predicting epidemic spread within spatially extensive metropolitan areas, and indicate the need for high-resolution mobility and epidemiological data.

Anomalous influenza seasonality in the United States and the emergence of novel influenza B viruses.

The 2019/2020 influenza season in the United States began earlier than any season since the 2009 H1N1 pandemic, with an increase in influenza-like illnesses observed as early as August. Also noteworthy was the numerical domination of influenza B cases early in this influenza season, in contrast to their typically later peak in the past. Here, we dissect the 2019/2020 influenza season not only with regard to its unusually early activity, but also with regard to the relative dynamics of type A and type B cases. We propose that the recent expansion of a novel influenza B/Victoria clade may be associated with this shift in the composition and kinetics of the influenza season in the United States. We use epidemiological transmission models to explore whether changes in the effective reproduction number or short-term cross-immunity between these viruses can explain the dynamics of influenza A and B seasonality. We find support for an increase in the effective reproduction number of influenza B, rather than support for cross-type immunity-driven dynamics. Our findings have clear implications for optimal vaccination strategies.

Dynamical footprints enable detection of disease emergence.

Developing methods for anticipating the emergence or reemergence of infectious diseases is both important and timely; however, traditional model-based approaches are stymied by uncertainty surrounding the underlying drivers. Here, we demonstrate an operational, mechanism-agnostic detection algorithm for disease (re-)emergence based on early warning signals (EWSs) derived from the theory of critical slowing down. Specifically, we used computer simulations to train a supervised learning algorithm to detect the dynamical footprints of (re-)emergence present in epidemiological data. Our algorithm was then challenged to forecast the slowly manifesting, spatially replicated reemergence of mumps in England in the mid-2000s and pertussis post-1980 in the United States. Our method successfully anticipated mumps reemergence 4 years in advance, during which time mitigation efforts could have been implemented. From 1980 onwards, our model identified resurgent states with increasing accuracy, leading to reliable classification starting in 1992. Additionally, we successfully applied the detection algorithm to 2 vector-transmitted case studies, namely, outbreaks of dengue serotypes in Puerto Rico and a rapidly unfolding outbreak of plague in 2017 in Madagascar. Taken together, these findings illustrate the power of theoretically informed machine learning techniques to develop early warning systems for the (re-)emergence of infectious diseases.

Transmission dynamics reveal the impracticality of COVID-19 herd immunity strategies.

The rapid growth rate of COVID-19 continues to threaten to overwhelm healthcare systems in multiple countries. In response, severely affected countries have had to impose a range of public health strategies achieved via nonpharmaceutical interventions. Broadly, these strategies have fallen into two categories: 1) "mitigation," which aims to achieve herd immunity by allowing the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus to spread through the population while mitigating disease burden, and 2) "suppression," aiming to drastically reduce SARS-CoV-2 transmission rates and halt endogenous transmission in the target population. Using an age-structured transmission model, parameterized to simulate SARS-CoV-2 transmission in the United Kingdom, we assessed the long-term prospects of success using both of these approaches. We simulated a range of different nonpharmaceutical intervention scenarios incorporating social distancing applied to differing age groups. Our modeling confirmed that suppression of SARS-CoV-2 transmission is possible with plausible levels of social distancing over a period of months, consistent with observed trends. Notably, our modeling did not support achieving herd immunity as a practical objective, requiring an unlikely balancing of multiple poorly defined forces. Specifically, we found that 1) social distancing must initially reduce the transmission rate to within a narrow range, 2) to compensate for susceptible depletion, the extent of social distancing must be adaptive over time in a precise yet unfeasible way, and 3) social distancing must be maintained for an extended period to ensure the healthcare system is not overwhelmed.

Detecting critical slowing down in high-dimensional epidemiological systems.

Despite medical advances, the emergence and re-emergence of infectious diseases continue to pose a public health threat. Low-dimensional epidemiological models predict that epidemic transitions are preceded by the phenomenon of critical slowing down (CSD). This has raised the possibility of anticipating disease (re-)emergence using CSD-based early-warning signals (EWS), which are statistical moments estimated from time series data. For EWS to be useful at detecting future (re-)emergence, CSD needs to be a generic (model-independent) feature of epidemiological dynamics irrespective of system complexity. Currently, it is unclear whether the predictions of CSD-derived from simple, low-dimensional systems-pertain to real systems, which are high-dimensional. To assess the generality of CSD, we carried out a simulation study of a hierarchy of models, with increasing structural complexity and dimensionality, for a measles-like infectious disease. Our five models included: i) a nonseasonal homogeneous Susceptible-Exposed-Infectious-Recovered (SEIR) model, ii) a homogeneous SEIR model with seasonality in transmission, iii) an age-structured SEIR model, iv) a multiplex network-based model (Mplex) and v) an agent-based simulator (FRED). All models were parameterised to have a herd-immunity immunization threshold of around 90% coverage, and underwent a linear decrease in vaccine uptake, from 92% to 70% over 15 years. We found evidence of CSD prior to disease re-emergence in all models. We also evaluated the performance of seven EWS: the autocorrelation, coefficient of variation, index of dispersion, kurtosis, mean, skewness, variance. Performance was scored using the Area Under the ROC Curve (AUC) statistic. The best performing EWS were the mean and variance, with AUC > 0.75 one year before the estimated transition time. These two, along with the autocorrelation and index of dispersion, are promising candidate EWS for detecting disease emergence.

The statistics of epidemic transitions.

Emerging and re-emerging pathogens exhibit very complex dynamics, are hard to model and difficult to predict. Their dynamics might appear intractable. However, new statistical approaches-rooted in dynamical systems and the theory of stochastic processes-have yielded insight into the dynamics of emerging and re-emerging pathogens. We argue that these approaches may lead to new methods for predicting epidemics. This perspective views pathogen emergence and re-emergence as a "critical transition," and uses the concept of noisy dynamic bifurcation to understand the relationship between the system observables and the distance to this transition. Because the system dynamics exhibit characteristic fluctuations in response to perturbations for a system in the vicinity of a critical point, we propose this information may be harnessed to develop early warning signals. Specifically, the motion of perturbations slows as the system approaches the transition.

Anticipating epidemic transitions with imperfect data.

Epidemic transitions are an important feature of infectious disease systems. As the transmissibility of a pathogen increases, the dynamics of disease spread shifts from limited stuttering chains of transmission to potentially large scale outbreaks. One proposed method to anticipate this transition are early-warning signals (EWS), summary statistics which undergo characteristic changes as the transition is approached. Although theoretically predicted, their mathematical basis does not take into account the nature of epidemiological data, which are typically aggregated into periodic case reports and subject to reporting error. The viability of EWS for epidemic transitions therefore remains uncertain. Here we demonstrate that most EWS can predict emergence even when calculated from imperfect data. We quantify performance using the area under the curve (AUC) statistic, a measure of how well an EWS distinguishes between numerical simulations of an emerging disease and one which is stationary. Values of the AUC statistic are compared across a range of different reporting scenarios. We find that different EWS respond to imperfect data differently. The mean, variance and first differenced variance all perform well unless reporting error is highly overdispersed. The autocorrelation, autocovariance and decay time perform well provided that the aggregation period of the data is larger than the serial interval and reporting error is not highly overdispersed. The coefficient of variation, skewness and kurtosis are found to be unreliable indicators of emergence. Overall, we find that seven of ten EWS considered perform well for most realistic reporting scenarios. We conclude that imperfect epidemiological data is not a barrier to using EWS for many potentially emerging diseases.

Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system.

We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.

Maternal pertussis immunization and the blunting of routine vaccine effectiveness: a meta-analysis and modeling study.

A key goal of pertussis control is to protect infants too young to be vaccinated, the age group most vulnerable to this highly contagious respiratory infection. In the last decade, maternal immunization has been deployed in many countries, successfully reducing pertussis in this age group. Because of immunological blunting, however, this strategy may erode the effectiveness of primary vaccination at later ages. Here, we systematically reviewed the literature on the relative risk (RR) of pertussis after primary immunization of infants born to vaccinated vs. unvaccinated mothers. The four studies identified had ≤6 years of follow-up and large statistical uncertainty (meta-analysis weighted mean RR: 0.71, 95% CI: 0.38-1.32). To interpret this evidence, we designed a new mathematical model with explicit blunting mechanisms and evaluated maternal immunization's short- and long-term impact on pertussis transmission dynamics. We show that transient dynamics can mask blunting for at least a decade after rolling out maternal immunization. Hence, the current epidemiological evidence may be insufficient to rule out modest reductions in the effectiveness of primary vaccination. Irrespective of this potential collateral cost, we predict that maternal immunization will remain effective at protecting unvaccinated newborns, supporting current public health recommendations.

Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation.

We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.

Containing novel SARS-CoV-2 variants at source is possible with high-intensity sequencing.

Throughout the COVID-19 pandemic, control of transmission has been repeatedly thwarted by the emergence of variants of concern (VOC) and their geographic spread. Key questions remain regarding effective means of minimizing the impact of VOC, in particular the feasibility of containing them at source, in light of global interconnectedness. By analysing a stochastic transmission model of COVID-19, we identify the appropriate monitoring requirements that make containment at source feasible. Specifically, precise risk assessment informed primarily by epidemiological indicators (e.g. accumulated hospitalization or mortality reports), is unlikely prior to VOC escape. Consequently, decision makers will need to make containment decisions without confident severity estimates. In contrast, successfully identifying and containing variants via genomic surveillance is realistic, provided sequence processing and dissemination is prompt.

Early warning signals of infectious disease transitions: a review.

Early warning signals (EWSs) are a group of statistical time-series signals which could be used to anticipate a critical transition before it is reached. EWSs are model-independent methods that have grown in popularity to support evidence of disease emergence and disease elimination. Theoretical work has demonstrated their capability of detecting disease transitions in simple epidemic models, where elimination is reached through vaccination, to more complex vector transmission, age-structured and metapopulation models. However, the exact time evolution of EWSs depends on the transition; here we review the literature to provide guidance on what trends to expect and when. Recent advances include methods which detect when an EWS becomes significant; the earlier an upcoming disease transition is detected, the more valuable an EWS will be in practice. We suggest that future work should firstly validate detection methods with synthetic and historical datasets, before addressing their performance with real-time data which is accruing. A major challenge to overcome for the use of EWSs with disease transitions is to maintain the accuracy of EWSs in data-poor settings. We demonstrate how EWSs behave on reported cases for pertussis in the USA, to highlight some limitations when detecting disease transitions with real-world data.

Ignoring spatial heterogeneity in drivers of SARS-CoV-2 transmission in the US will impede sustained elimination.

To dissect the transmission dynamics of SARS-CoV-2 in the United States, we integrate parallel streams of high-resolution data on contact, mobility, seasonality, vaccination and seroprevalence within a metapopulation network. We find the COVID-19 pandemic in the US is characterized by a geographically localized mosaic of transmission along an urban-rural gradient, with many outbreaks sustained by between-county transmission. We detect a dynamic tension between the spatial scale of public health interventions and population susceptibility as pre-pandemic contact is resumed. Further, we identify regions rendered particularly at risk from invasion by variants of concern due to spatial connectivity. These findings emphasize the public health importance of accounting for the hierarchy of spatial scales in transmission and the heterogeneous impacts of mobility on the landscape of contagion risk.

COVID-19 herd immunity strategies: walking an elusive and dangerous tightrope.

The rapid growth in cases of COVID-19 has threatened to overwhelm healthcare systems in multiple countries. In response, severely affected countries have had to consider a range of public health strategies achieved by implementing non-pharmaceutical interventions. Broadly, these strategies have fallen into two categories: i) "mitigation", which aims to achieve herd immunity by allowing the SARS-CoV-2 virus to spread through the population while mitigating disease burden, and ii) "suppression", aiming to drastically reduce SARS-CoV-2 transmission rates and halt endogenous transmission in the target population. Using an age-structured transmission model, parameterised to simulate SARS-CoV-2 transmission in the UK, we assessed the prospects of success using both of these approaches. We simulated a range of different non-pharmaceutical intervention scenarios incorporating social distancing applied to differing age groups. We found that it is possible to suppress SARS-CoV-2 transmission if social distancing measures are sustained at a sufficient level for a period of months. Our modelling did not support achieving herd immunity as a practical objective, requiring an unlikely balancing of multiple poorly-defined forces. Specifically, we found that: i) social distancing must initially reduce the transmission rate to within a narrow range, ii) to compensate for susceptible depletion, the extent of social distancing must be vary over time in a precise but unfeasible way, and iii) social distancing must be maintained for a long duration (over 6 months).

Anticipating the emergence of infectious diseases.

In spite of medical breakthroughs, the emergence of pathogens continues to pose threats to both human and animal populations. We present candidate approaches for anticipating disease emergence prior to large-scale outbreaks. Through use of ideas from the theories of dynamical systems and stochastic processes we develop approaches which are not specific to a particular disease system or model, but instead have general applicability. The indicators of disease emergence detailed in this paper can be classified into two parallel approaches: a set of early-warning signals based around the theory of critical slowing down and a likelihood-based approach. To test the reliability of these two approaches we contrast theoretical predictions with simulated data. We find good support for our methods across a range of different model structures and parameter values.

Generating functionals and Gaussian approximations for interruptible delay reactions.

We develop a generating functional description of the dynamics of non-Markovian individual-based systems in which delay reactions can be terminated before completion. This generalizes previous work in which a path-integral approach was applied to dynamics in which delay reactions complete with certainty. We construct a more widely applicable theory, and from it we derive Gaussian approximations of the dynamics, valid in the limit of large, but finite, population sizes. As an application of our theory we study predator-prey models with delay dynamics due to gestation or lag periods to reach the reproductive age. In particular, we focus on the effects of delay on noise-induced cycles.

Publisher's Note: Generating functionals and Gaussian approximations for interruptible delay reactions [Phys. Rev. E 92, 042105 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.92.042105.