Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics

Infectious diseases provide a particularly clear illustration of the spatiotemporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics and, depending on the nature of spatial contagion, may result in traveling waves. Measles epidemics are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatiotemporal variations in population structure and demography. On the basis of a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatiotemporal properties in prevaccination epidemics of measles in England and Wales.     

Parasite consumption and host interference can inhibit disease spread in dense populations

Disease dynamics hinge on parasite transmission among hosts. However, canonical models for transmission often fit data poorly, limiting predictive ability. One solution involves building mechanistic yet general links between host behaviour and disease spread. To illustrate, we focus on the exposure component of transmission for hosts that consume their parasites, combining experiments, models and field data. Models of transmission that incorporate parasite consumption and foraging interference among hosts vastly outperformed alternatives when fit to experimental data using a zooplankton host (Daphnia dentifera) that consumes spores of a fungus (Metschnikowia bicuspidata). Once plugged into a fully dynamic model, both mechanisms inhibited epidemics overall. Foraging interference further depressed parasite invasion and prevalence at high host density, creating unimodal (hump‐shaped) relationships between host density and these indices. These novel results qualitatively matched a unimodal density–prevalence relationship in natural epidemics. Ultimately, a mechanistic approach to transmission can reveal new insights into disease outbreaks.     

Predicting seasonal influenza using supermarket retail records

Increased availability of epidemiological data, novel digital data streams, and the rise of powerful machine learning approaches have generated a surge of research activity on real-time epidemic forecast systems. In this paper, we propose the use of a novel data source, namely retail market data to improve seasonal influenza forecasting. Specifically, we consider supermarket retail data as a proxy signal for influenza, through the identification of sentinel baskets, i.e., products bought together by a population of selected customers. We develop a nowcasting and forecasting framework that provides estimates for influenza incidence in Italy up to 4 weeks ahead. We make use of the Support Vector Regression (SVR) model to produce the predictions of seasonal flu incidence. Our predictions outperform both a baseline autoregressive model and a second baseline based on product purchases. The results show quantitatively the value of incorporating retail market data in forecasting models, acting as a proxy that can be used for the real-time analysis of epidemics.     

Small amplitude,long period outbreaks in seasonally driven epidemics

It is now documented that childhood diseases such as measles, mumps, and chickenpox exhibit a wide range of recurrent behavior (periodic as well as chaotic) in large population centers in the first world. Mathematical models used in the past (such as the SEIR model with seasonal forcing) have been able to predict the onset of both periodic and chaotic sustained epidemics using parameters of childhood diseases. Although these models possess stable solutions which appear to have the correct frequency content, the corresponding outbreaks require extremely large populations to support the epidemic. This paper shows that by relaxing the assumption of uniformity in the supply of susceptibles, simple models predict stable long period oscillatory epidemics having small amplitude. Both coupled and single population models are considered.     

The interplay between determinism and stochasticity in childhood diseases

An important issue in the history of ecology has been the study of the relative importance of deterministic forces and processes noise in shaping the dynamics of ecological populations. We address this question by exploring the temporal dynamics of two childhood infections, measles and whooping cough, in England and Wales. We demonstrate that epidemics of whooping cough are strongly influenced by stochasticity; fully deterministic approaches cannot achieve even a qualitative fit to the observed data. In contrast, measles dynamics are extremely well explained by a deterministic model. These differences are shown to be caused by their contrasting responses to dynamical noise due to different infectious periods.     

Evidence of recombination among early-vaccination era measles virus strains

Background  

The advent of live-attenuated vaccines against measles virus during the 1960'ies changed the circulation dynamics of the virus. Earlier the virus was indigenous to countries worldwide, but now it is mediated by a limited number of evolutionary lineages causing sporadic outbreaks/epidemics of measles or circulating in geographically restricted endemic areas of Africa, Asia and Europe. We expect that the evolutionary dynamics of measles virus has changed from a situation where a variety of genomic variants co-circulates in an epidemic with relatively high probabilities of co-infection of the individual to a situation where a co-infection with strains from evolutionary different lineages is unlikely.     

Shear Bond Strength and Fracture Analysis of Human vs. Bovine Teeth

Purpose

To evaluate if bovine enamel and dentin are appropriate substitutes for the respective human hard tooth tissues to test shear bond strength (SBS) and fracture analysis.

Materials and Methods

80 sound and caries-free human erupted third molars and 80 freshly extracted bovine permanent central incisors (10 specimens for each group) were used to investigate enamel and dentine adhesion of one 2-step self-etch (SE) and one 3-step etch and rinse (E&R) product. To test SBS the buccal or labial areas were ground plane to obtain appropriate enamel or dentine areas. SE and E&R were applied and SBS was measured prior to and after 500 thermocycles between +5 and +55°C. Fracture analysis was performed for all debonded areas.

Results

ANOVA revealed significant differences of enamel and dentin SBS prior to and after thermocycling for both of the adhesives. SBS- of E&R-bonded human enamel increased after thermocycling but SE-bonded did not. Bovine enamel SE-bonded showed higher SBS after TC but E&R-bonded had lower SBS. No differences were found for human dentin SE- or E&R-bonded prior to or after thermocycling but bovine dentin SE-bonded increased whereas bovine dentine E&R-bonded decreased. Considering the totalized and adhesive failures, fracture analysis did not show significances between the adhesives or the respective tooth tissues prior to or after thermocycling.

Conclusion

Although SBS was different on human and bovine teeth, no differences were found for fracture analysis. This indicates that solely conducted SBS on bovine substrate are not sufficient to judge the perfomance of adhesives, thus bovine teeth are questionnable as a substrate for shear bond testing.     

Using Hawkes Processes to model imported and local malaria cases in near-elimination settings

Developing new methods for modelling infectious diseases outbreaks is important for monitoring transmission and developing policy. In this paper we propose using semi-mechanistic Hawkes Processes for modelling malaria transmission in near-elimination settings. Hawkes Processes are well founded mathematical methods that enable us to combine the benefits of both statistical and mechanistic models to recreate and forecast disease transmission beyond just malaria outbreak scenarios. These methods have been successfully used in numerous applications such as social media and earthquake modelling, but are not yet widespread in epidemiology. By using domain-specific knowledge, we can both recreate transmission curves for malaria in China and Eswatini and disentangle the proportion of cases which are imported from those that are community based.     

Toxic gas dispersion prediction for point source emission using deep learning method

Abstract

Accurate and rapid toxic gas concentration prediction model plays an important role in emergency aid of sudden gas leak. However, it is difficult for existing dispersion model to achieve accuracy and efficiency requirements at the same time. Although some researchers have considered developing new forecasting models with traditional machine learning, such as back propagation (BP) neural network, support vector machine (SVM), the prediction results obtained from such models need to be improved still in terms of accuracy. Then new prediction models based on deep learning are proposed in this paper. Deep learning has obvious advantages over traditional machine learning in prediction and classification. Deep belief networks (DBNs) as well as convolution neural networks (CNNs) are used to build new dispersion models here. Both models are compared with Gaussian plume model, computation fluid dynamics (CFD) model and models based on traditional machine learning in terms of accuracy, prediction time, and computation time. The experimental results turn out that CNNs model performs better considering all evaluation indexes.     

Multi-locus Analysis of Genomic Time Series Data from Experimental Evolution

Genomic time series data generated by evolve-and-resequence (E&R) experiments offer a powerful window into the mechanisms that drive evolution. However, standard population genetic inference procedures do not account for sampling serially over time, and new methods are needed to make full use of modern experimental evolution data. To address this problem, we develop a Gaussian process approximation to the multi-locus Wright-Fisher process with selection over a time course of tens of generations. The mean and covariance structure of the Gaussian process are obtained by computing the corresponding moments in discrete-time Wright-Fisher models conditioned on the presence of a linked selected site. This enables our method to account for the effects of linkage and selection, both along the genome and across sampled time points, in an approximate but principled manner. We first use simulated data to demonstrate the power of our method to correctly detect, locate and estimate the fitness of a selected allele from among several linked sites. We study how this power changes for different values of selection strength, initial haplotypic diversity, population size, sampling frequency, experimental duration, number of replicates, and sequencing coverage depth. In addition to providing quantitative estimates of selection parameters from experimental evolution data, our model can be used by practitioners to design E&R experiments with requisite power. We also explore how our likelihood-based approach can be used to infer other model parameters, including effective population size and recombination rate. Then, we apply our method to analyze genome-wide data from a real E&R experiment designed to study the adaptation of D. melanogaster to a new laboratory environment with alternating cold and hot temperatures.     

Human birth seasonality: latitudinal gradient and interplay with childhood disease dynamics

More than a century of ecological studies have demonstrated the importance of demography in shaping spatial and temporal variation in population dynamics. Surprisingly, the impact of seasonal recruitment on infectious disease systems has received much less attention. Here, we present data encompassing 78 years of monthly natality in the USA, and reveal pronounced seasonality in birth rates, with geographical and temporal variation in both the peak birth timing and amplitude. The timing of annual birth pulses followed a latitudinal gradient, with northern states exhibiting spring/summer peaks and southern states exhibiting autumn peaks, a pattern we also observed throughout the Northern Hemisphere. Additionally, the amplitude of United States birth seasonality was more than twofold greater in southern states versus those in the north. Next, we examined the dynamical impact of birth seasonality on childhood disease incidence, using a mechanistic model of measles. Birth seasonality was found to have the potential to alter the magnitude and periodicity of epidemics, with the effect dependent on both birth peak timing and amplitude. In a simulation study, we fitted an susceptible-exposed-infected-recovered model to simulated data, and demonstrated that ignoring birth seasonality can bias the estimation of critical epidemiological parameters. Finally, we carried out statistical inference using historical measles incidence data from New York City. Our analyses did not identify the predicted systematic biases in parameter estimates. This may be owing to the well-known frequency-locking between measles epidemics and seasonal transmission rates, or may arise from substantial uncertainty in multiple model parameters and estimation stochasticity.     

Spatial and temporal invasion dynamics of the 2014–2017 Zika and chikungunya epidemics in Colombia

Zika virus (ZIKV) and chikungunya virus (CHIKV) were recently introduced into the Americas resulting in significant disease burdens. Understanding their spatial and temporal dynamics at the subnational level is key to informing surveillance and preparedness for future epidemics. We analyzed anonymized line list data on approximately 105,000 Zika virus disease and 412,000 chikungunya fever suspected and laboratory-confirmed cases during the 2014–2017 epidemics. We first determined the week of invasion in each city. Out of 1,122, 288 cities met criteria for epidemic invasion by ZIKV and 338 cities by CHIKV. We analyzed risk factors for invasion using linear and logistic regression models. We also estimated that the geographic origin of both epidemics was located in Barranquilla, north Colombia. We assessed the spatial and temporal invasion dynamics of both viruses to analyze transmission between cities using a suite of (i) gravity models, (ii) Stouffer’s rank models, and (iii) radiation models with two types of distance metrics, geographic distance and travel time between cities. Invasion risk was best captured by a gravity model when accounting for geographic distance and intermediate levels of density dependence; Stouffer’s rank model with geographic distance performed similarly well. Although a few long-distance invasion events occurred at the beginning of the epidemics, an estimated distance power of 1.7 (95% CrI: 1.5–2.0) from the gravity models suggests that spatial spread was primarily driven by short-distance transmission. Similarities between the epidemics were highlighted by jointly fitted models, which were preferred over individual models when the transmission intensity was allowed to vary across arboviruses. However, ZIKV spread considerably faster than CHIKV.     

Impact of the topology of metapopulations on the resurgence of epidemics rendered by a new multiscale hybrid modeling approach

Simulating epidemics in metapopulations is a challenging issue due to the large demographic and geographic scales to incorporate. Traditional epidemiologic models choose to simplify reality by ignoring both the spatial distribution of populations and possible intrapopulation heterogeneities, whereas more recent solutions based on Individual-Based Modeling (IBM) can achieve high precision but are costly to compute and analyze. We introduce here an original alternative to these two approaches, which relies on a novel hybrid modeling framework and incarnates a multiscale view of epidemics. The model relies on a technical fusion of two modeling paradigms: System Dynamics (SD) and Individual-Based Modeling. It features an aggregated representation of local outbreaks rendered in SD, and at the same time a spatially-explicit simulation of the spread between populations simulated in IBM. We first present the design of this deterministic model, show that it can reproduce the dynamics of real resurgent epidemics, and infer from the sensitivity of several spatial factors absent in compartmental models the importance of having large-scale epidemiological processes represented inside of an explicitly disaggregated metapopulation. After discussing the implications of results obtained from simulation runs and the applicability of this model, we conclude that SD–IB hybrid modeling can be an interesting choice to represent epidemics in a spatially-explicit way without necessarily taking into account individual heterogeneities, and therefore it can be considered as a valuable alternative to simple compartmental models suffering from detrimental effects of the well-mixed assumption.     

Empirical determinants of measles metapopulation dynamics in England and Wales.

A key issue in metapopulation dynamics is the relative impact of internal patch dynamics and coupling between patches. This problem can be addressed by analysing large spatiotemporal data sets, recording the local and global dynamics of metapopulations. In this paper, we analyse the dynamics of measles meta-populations in a large spatiotemporal case notification data set, collected during the pre-vaccination era in England and Wales. Specifically, we use generalized linear statistical models to quantify the relative importance of local influences (birth rate and population size) and regional coupling on local epidemic dynamics. Apart from the proportional effect of local population size on case totals, the models indicate patterns of local and regional dynamic influences which depend on the current state of epidemics. Birth rate and geographic coupling are not associated with the size of major epidemics. By contrast, minor epidemics--and especially the incidence of local extinction of infection--are influenced both by birth rate and geographical coupling. Birth rate at a lag of four years provides the best fit, reflecting the delayed recruitment of susceptibles to school cohorts. A hierarchical index of spatial coupling to large centres provides the best spatial model. The model also indicates that minor epidemics and extinction patterns are more strongly influenced by this regional effect than the local impact of birth rate.     

Flexible Modeling of Epidemics with an Empirical Bayes Framework

Seasonal influenza epidemics cause consistent, considerable, widespread loss annually in terms of economic burden, morbidity, and mortality. With access to accurate and reliable forecasts of a current or upcoming influenza epidemic’s behavior, policy makers can design and implement more effective countermeasures. This past year, the Centers for Disease Control and Prevention hosted the “Predict the Influenza Season Challenge”, with the task of predicting key epidemiological measures for the 2013–2014 U.S. influenza season with the help of digital surveillance data. We developed a framework for in-season forecasts of epidemics using a semiparametric Empirical Bayes framework, and applied it to predict the weekly percentage of outpatient doctors visits for influenza-like illness, and the season onset, duration, peak time, and peak height, with and without using Google Flu Trends data. Previous work on epidemic modeling has focused on developing mechanistic models of disease behavior and applying time series tools to explain historical data. However, tailoring these models to certain types of surveillance data can be challenging, and overly complex models with many parameters can compromise forecasting ability. Our approach instead produces possibilities for the epidemic curve of the season of interest using modified versions of data from previous seasons, allowing for reasonable variations in the timing, pace, and intensity of the seasonal epidemics, as well as noise in observations. Since the framework does not make strict domain-specific assumptions, it can easily be applied to some other diseases with seasonal epidemics. This method produces a complete posterior distribution over epidemic curves, rather than, for example, solely point predictions of forecasting targets. We report prospective influenza-like-illness forecasts made for the 2013–2014 U.S. influenza season, and compare the framework’s cross-validated prediction error on historical data to that of a variety of simpler baseline predictors.     

Mathematical Model of Mouse Embryonic Cardiomyocyte Excitation–Contraction Coupling

Excitation–contraction (E–C) coupling is the mechanism that connects the electrical excitation with cardiomyocyte contraction. Embryonic cardiomyocytes are not only capable of generating action potential (AP)-induced Ca²⁺ signals and contractions (E–C coupling), but they also can induce spontaneous pacemaking activity. The spontaneous activity originates from spontaneous Ca²⁺ releases from the sarcoplasmic reticulum (SR), which trigger APs via the Na⁺/Ca²⁺ exchanger (NCX). In the AP-driven mode, an external stimulus triggers an AP and activates voltage-activated Ca²⁺ intrusion to the cell. These complex and unique features of the embryonic cardiomyocyte pacemaking and E–C coupling have never been assessed with mathematical modeling. Here, we suggest a novel mathematical model explaining how both of these mechanisms can coexist in the same embryonic cardiomyocytes. In addition to experimentally characterized ion currents, the model includes novel heterogeneous cytosolic Ca²⁺ dynamics and oscillatory SR Ca²⁺ handling. The model reproduces faithfully the experimentally observed fundamental features of both E–C coupling and pacemaking. We further validate our model by simulating the effect of genetic modifications on the hyperpolarization-activated current, NCX, and the SR Ca²⁺ buffer protein calreticulin. In these simulations, the model produces a similar functional alteration to that observed previously in the genetically engineered mice, and thus provides mechanistic explanations for the cardiac phenotypes of these animals. In general, this study presents the first model explaining the underlying cellular mechanism for the origin and the regulation of the heartbeat in early embryonic cardiomyocytes.     

Optimising predictive modelling of Ross River virus using meteorological variables

BackgroundStatistical models are regularly used in the forecasting and surveillance of infectious diseases to guide public health. Variable selection assists in determining factors associated with disease transmission, however, often overlooked in this process is the evaluation and suitability of the statistical model used in forecasting disease transmission and outbreaks. Here we aim to evaluate several modelling methods to optimise predictive modelling of Ross River virus (RRV) disease notifications and outbreaks in epidemiological important regions of Victoria and Western Australia.Methodology/Principal findingsWe developed several statistical methods using meteorological and RRV surveillance data from July 2000 until June 2018 in Victoria and from July 1991 until June 2018 in Western Australia. Models were developed for 11 Local Government Areas (LGAs) in Victoria and seven LGAs in Western Australia. We found generalised additive models and generalised boosted regression models, and generalised additive models and negative binomial models to be the best fit models when predicting RRV outbreaks and notifications, respectively. No association was found with a model’s ability to predict RRV notifications in LGAs with greater RRV activity, or for outbreak predictions to have a higher accuracy in LGAs with greater RRV notifications. Moreover, we assessed the use of factor analysis to generate independent variables used in predictive modelling. In the majority of LGAs, this method did not result in better model predictive performance.Conclusions/SignificanceWe demonstrate that models which are developed and used for predicting disease notifications may not be suitable for predicting disease outbreaks, or vice versa. Furthermore, poor predictive performance in modelling disease transmissions may be the result of inappropriate model selection methods. Our findings provide approaches and methods to facilitate the selection of the best fit statistical model for predicting mosquito-borne disease notifications and outbreaks used for disease surveillance.     

Implications of vaccination and waning immunity

For infectious diseases where immunization can offer lifelong protection, a variety of simple models can be used to explain the utility of vaccination as a control method. However, for many diseases, immunity wanes over time and is subsequently enhanced (boosted) by asymptomatic encounters with the infection. The study of this type of epidemiological process requires a model formulation that can capture both the within-host dynamics of the pathogen and immune system as well as the associated population-level transmission dynamics. Here, we parametrize such a model for measles and show how vaccination can have a range of unexpected consequences as it reduces the natural boosting of immunity as well as reducing the number of naive susceptibles. In particular, we show that moderate waning times (40–80 years) and high levels of vaccination (greater than 70%) can induce large-scale oscillations with substantial numbers of symptomatic cases being generated at the peak. In addition, we predict that, after a long disease-free period, the introduction of infection will lead to far larger epidemics than that predicted by standard models. These results have clear implications for the long-term success of any vaccination campaign and highlight the need for a sound understanding of the immunological mechanisms of immunity and vaccination.