Modeling the spread of Middle East respiratory syndrome coronavirus in Saudi Arabia

Middle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. Abundant scientific evidence showed that dromedary camels are the primary host of the virus. Majority of human cases (i.e., 75% or 88%) are due to human-to-human transmission, while the others are due to camel-to-human transmission. Mathematical modeling of Middle East respiratory syndrome coronavirus camel-to-camel transmission was lacking. Using the plug-and-play likelihood-based inference framework, we fitted a susceptible-exposed-infectious-recovered-susceptible model of camels to the reported human cases with a constant proportion of human cases from camels (i.e., either 25% or 12%). We considered two scenarios: (i) the transmission rate among camels is time-varying with a constant spill-over rate from camels to human or (ii) the spill-over rate is time-varying with a constant transmission rate among camels. Our estimated loss-of-immunity rate and prevalence of Middle East respiratory syndrome coronavirus infections among camels largely matched with previous serological or virological studies, shedding light on this issue. We recommended including dromedary camels in animal surveillance and control of Middle East respiratory syndrome coronavirus in Saudi Arabia which could help reduce their sporadic introductions to humans.

Evaluating consumptive and nonconsumptive predator effects on prey density using field time-series data

Determining the degree to which predation affects prey abundance in natural communities constitutes a key goal of ecological research. Predators can affect prey through both consumptive effects (CEs) and nonconsumptive effects (NCEs), although the contributions of each mechanism to the density of prey populations remain largely hypothetical in most systems. Common statistical methods applied to time-series data cannot elucidate the mechanisms responsible for hypothesized predator effects on prey density (e.g., differentiate CEs from NCEs), nor can they provide parameters for predictive models. State-space models (SSMs) applied to time-series data offer a way to meet these goals. Here, we employ SSMs to assess effects of an invasive predatory zooplankter, Bythotrephes longimanus, on an important prey species, Daphnia mendotae, in Lake Michigan. We fit mechanistic models in an SSM framework to seasonal time series (1994-2012) using a recently developed, maximum-likelihood-based optimization method, iterated filtering, which can overcome challenges in ecological data (e.g., nonlinearities, measurement error, and irregular sampling intervals). Our results indicate that B. longimanus strongly influences D. mendotae dynamics, with mean annual peak densities of B. longimanus observed in Lake Michigan estimated to cause a 61% reduction in D. mendotae population growth rate and a 59% reduction in peak biomass density. Further, the observed B. longimanus effect is most consistent with an NCE via reduced birth rates. The SSM approach also provided estimates for key biological parameters (e.g., demographic rates) and the contribution of dynamic stochasticity and measurement error. Our study therefore provides evidence derived directly from survey data that the invasive zooplankter B. longimanus is affecting zooplankton demographics and offer parameter estimates needed to inform predictive models that explore the effect of B. longimanus under different scenarios, such as climate change.

Modeling and inference for infectious disease dynamics: a likelihood-based approach

Likelihood-based statistical inference has been considered in most scientific fields involving stochastic modeling. This includes infectious disease dynamics, where scientific understanding can help capture biological processes in so-called mechanistic models and their likelihood functions. However, when the likelihood of such mechanistic models lacks a closed-form expression, computational burdens are substantial. In this context, algorithmic advances have facilitated likelihood maximization, promoting the study of novel data-motivated mechanistic models over the last decade. Reviewing these models is the focus of this paper. In particular, we highlight statistical aspects of these models like overdispersion, which is key in the interface between nonlinear infectious disease modeling and data analysis. We also point out potential directions for further model exploration.

Infectious Disease Dynamics Inferred from Genetic Data via Sequential Monte Carlo

Genetic sequences from pathogens can provide information about infectious disease dynamics that may supplement or replace information from other epidemiological observations. Most currently available methods first estimate phylogenetic trees from sequence data, then estimate a transmission model conditional on these phylogenies. Outside limited classes of models, existing methods are unable to enforce logical consistency between the model of transmission and that underlying the phylogenetic reconstruction. Such conflicts in assumptions can lead to bias in the resulting inferences. Here, we develop a general, statistically efficient, plug-and-play method to jointly estimate both disease transmission and phylogeny using genetic data and, if desired, other epidemiological observations. This method explicitly connects the model of transmission and the model of phylogeny so as to avoid the aforementioned inconsistency. We demonstrate the feasibility of our approach through simulation and apply it to estimate stage-specific infectiousness in a subepidemic of human immunodeficiency virus in Detroit, Michigan. In a supplement, we prove that our approach is a valid sequential Monte Carlo algorithm. While we focus on how these methods may be applied to population-level models of infectious disease, their scope is more general. These methods may be applied in other biological systems where one seeks to infer population dynamics from genetic sequences, and they may also find application for evolutionary models with phenotypic rather than genotypic data.

Pertussis immunity and epidemiology: mode and duration of vaccine-induced immunity

The resurgence of pertussis in some countries that maintain high vaccination coverage has drawn attention to gaps in our understanding of the epidemiological effects of pertussis vaccines. In particular, major questions surround the nature, degree and durability of vaccine protection. To address these questions, we used mechanistic transmission models to examine regional time series incidence data from Italy in the period immediately following the introduction of acellular pertussis (aP) vaccine. Our results concur with recent animal-challenge experiments wherein infections in aP-vaccinated individuals proved as transmissible as those in naive individuals but much less symptomatic. On the other hand, the data provide evidence for vaccine-driven reduction in susceptibility, which we quantify via a synthetic measure of vaccine impact. As to the precise nature of vaccine failure, the data do not allow us to distinguish between leakiness and waning of vaccine immunity, or some combination of these. Across the range of well-supported models, the nature and duration of vaccine protection, the age profile of incidence and the range of projected epidemiological futures differ substantially, underscoring the importance of the remaining unknowns. We identify key data gaps: sources of data that can supply the information needed to eliminate these remaining uncertainties.

Dynamic Variation in Sexual Contact Rates in a Cohort of HIV-Negative Gay Men

Human immunodeficiency virus (HIV) transmission models that include variability in sexual behavior over time have shown increased incidence, prevalence, and acute-state transmission rates for a given population risk profile. This raises the question of whether dynamic variation in individual sexual behavior is a real phenomenon that can be observed and measured. To study this dynamic variation, we developed a model incorporating heterogeneity in both between-person and within-person sexual contact patterns. Using novel methodology that we call iterated filtering for longitudinal data, we fitted this model by maximum likelihood to longitudinal survey data from the Centers for Disease Control and Prevention's Collaborative HIV Seroincidence Study (1992-1995). We found evidence for individual heterogeneity in sexual behavior over time. We simulated an epidemic process and found that inclusion of empirically measured levels of dynamic variation in individual-level sexual behavior brought the theoretical predictions of HIV incidence into closer alignment with reality given the measured per-act probabilities of transmission. The methods developed here provide a framework for quantifying variation in sexual behaviors that helps in understanding the HIV epidemic among gay men.

Inferring the causes of the three waves of the 1918 influenza pandemic in England and Wales

Past influenza pandemics appear to be characterized by multiple waves of incidence, but the mechanisms that account for this phenomenon remain unclear. We propose a simple epidemic model, which incorporates three factors that might contribute to the generation of multiple waves: (i) schools opening and closing, (ii) temperature changes during the outbreak, and (iii) changes in human behaviour in response to the outbreak. We fit this model to the reported influenza mortality during the 1918 pandemic in 334 UK administrative units and estimate the epidemiological parameters. We then use information criteria to evaluate how well these three factors explain the observed patterns of mortality. Our results indicate that all three factors are important but that behavioural responses had the largest effect. The parameter values that produce the best fit are biologically reasonable and yield epidemiological dynamics that match the observed data well.