Oscillations and chaos in epidemics: A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark

Using traditional spectral analysis and recently developed non-linear methods, we analyze the incidence of six childhood diseases in Copenhagen, Denmark. In three cases, measles, mumps, rubella, the dynamics suggest low dimensional chaos. Outbreaks of chicken pox, on the other hand, conform to an annual cycle with noise superimposed. The remaining diseases, pertussis and scarlet fever, remain problematic. The real epidemics are compared with the output of a Monte Carlo analog of the SEIR model for childhood infections. For measles, mumps, rubella, and chicken pox, we find substantial agreement between the model simulations and the data.     

Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns

Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics.     

Assessing the reporting of Dengue,Chikungunya and Zika to the National Surveillance System in Colombia from 2014–2017: A Capture-recapture analysis accounting for misclassification of arboviral diagnostics

BackgroundChikungunya, dengue, and Zika are three different arboviruses which have similar symptoms and are a major public health issue in Colombia. Despite the mandatory reporting of these arboviruses to the National Surveillance System in Colombia (SIVIGILA), it has been reported that the system captures less than 10% of diagnosed cases in some cities.Methodology/Principal findingsTo assess the scope and degree of arboviruses reporting in Colombia between 2014–2017, we conducted an observational study of surveillance data using the capture-recapture approach in three Colombian cities. Using healthcare facility registries (capture data) and surveillance-notified cases (recapture data), we estimated the degree of reporting by clinical diagnosis. We fit robust Poisson regressions to identify predictors of reporting and estimated the predicted probability of reporting by disease and year. To account for the potential misclassification of the clinical diagnosis, we used the simulation extrapolation for misclassification (MC-SIMEX) method. A total of 266,549 registries were examined. Overall arboviruses’ reporting ranged from 5.3% to 14.7% and varied in magnitude according to age and year of diagnosis. Dengue was the most notified disease (21–70%) followed by Zika (6–45%). The highest reporting rate was seen in 2016, an epidemic year. The MC-SIMEX corrected rates indicated underestimation of the reporting due to the potential misclassification bias.ConclusionsThese findings reflect challenges on arboviruses’ reporting, and therefore, potential challenges on the estimation of arboviral burden in Colombia and other endemic settings with similar surveillance systems.     

Impact of Birth Seasonality on Dynamics of Acute Immunizing Infections in Sub-Saharan Africa

We analyze the impact of birth seasonality (seasonal oscillations in the birth rate) on the dynamics of acute, immunizing childhood infectious diseases. Previous research has explored the effect of human birth seasonality on infectious disease dynamics using parameters appropriate for the developed world. We build on this work by including in our analysis an extended range of baseline birth rates and amplitudes, which correspond to developing world settings. Additionally, our analysis accounts for seasonal forcing both in births and contact rates. We focus in particular on the dynamics of measles. In the absence of seasonal transmission rates or stochastic forcing, for typical measles epidemiological parameters, birth seasonality induces either annual or biennial epidemics. Changes in the magnitude of the birth fluctuations (birth amplitude) can induce significant changes in the size of the epidemic peaks, but have little impact on timing of disease epidemics within the year. In contrast, changes to the birth seasonality phase (location of the peak in birth amplitude within the year) significantly influence the timing of the epidemics. In the presence of seasonality in contact rates, at relatively low birth rates (20 per 1000), birth amplitude has little impact on the dynamics but does have an impact on the magnitude and timing of the epidemics. However, as the mean birth rate increases, both birth amplitude and phase play an important role in driving the dynamics of the epidemic. There are stronger effects at higher birth rates.     

Effect of thermal environment on the temporal,spatial and seasonal occurrence of measles in Ondo state,Nigeria

We investigated the temporal and spatial dynamics, as well as the seasonal occurrence of measles in Ondo state, Nigeria, to better understand the role of the thermal environment in the occurrence of the childhood killer disease measles, which ranks among the top ten leading causes of child deaths worldwide. The linkages between measles and atmospheric environmental factors were examined by correlating human-biometeorological parameters in the study area with reported clinical cases of measles for the period 1998–2008. We also applied stepwise regression analysis in order to determine the human-biometeorological parameters that lead to statistical changes in reported clinical cases of measles. We found that high reported cases of measles are associated with the least populated areas, where rearing and cohabitation of livestock/domestic animals within human communities are common. There was a significant correlation (P < 0.01) between monthly cases of measles and human-biometeorological parameters except wind speed and vapour pressure. High transmission of measles occurred in the months of January to May during the dry season when human thermal comfort indices are very high. This highlights the importance of the thermal environment in disease demographics since it accounted for more than 40% variation in measles transmission within the study period.     

Protein structural features predict responsiveness to pharmacological chaperone treatment for three lysosomal storage disorders

Three-dimensional structures of proteins can provide important clues into the efficacy of personalized treatment. We perform a structural analysis of variants within three inherited lysosomal storage disorders, comparing variants responsive to pharmacological chaperone treatment to those unresponsive to such treatment. We find that predicted ΔΔG of mutation is higher on average for variants unresponsive to treatment, in the case of datasets for both Fabry disease and Pompe disease, in line with previous findings. Using both a single decision tree and an advanced machine learning approach based on the larger Fabry dataset, we correctly predict responsiveness of three Gaucher disease variants, and we provide predictions for untested variants. Many variants are predicted to be responsive to treatment, suggesting that drug-based treatments may be effective for a number of variants in Gaucher disease. In our analysis, we observe dependence on a topological feature reporting on contact arrangements which is likely connected to the order of folding of protein residues, and we provide a potential justification for this observation based on steady-state cellular kinetics.     

Bias in Markov models of disease

We examine bias in Markov models of diseases, including both chronic and infectious diseases. We consider two common types of Markov disease models: ones where disease progression changes by severity of disease, and ones where progression of disease changes in time or by age. We find sufficient conditions for bias to exist in models with aggregated transition probabilities when compared to models with state/time dependent transition probabilities. We also find that when aggregating data to compute transition probabilities, bias increases with the degree of data aggregation. We illustrate by examining bias in Markov models of Hepatitis C, Alzheimer’s disease, and lung cancer using medical data and find that the bias is significant depending on the method used to aggregate the data. A key implication is that by not incorporating state/time dependent transition probabilities, studies that use Markov models of diseases may be significantly overestimating or underestimating disease progression. This could potentially result in incorrect recommendations from cost-effectiveness studies and incorrect disease burden forecasts.     

Probabilistic measures of persistence and extinction in measles (meta)populations

Persistence and extinction are fundamental processes in ecological systems that are difficult to accurately measure due to stochasticity and incomplete observation. Moreover, these processes operate on multiple scales, from individual populations to metapopulations. Here, we examine an extensive new data set of measles case reports and associated demographics in pre‐vaccine era US cities, alongside a classic England & Wales data set. We first infer the per‐population quasi‐continuous distribution of log incidence. We then use stochastic, spatially implicit metapopulation models to explore the frequency of rescue events and apparent extinctions. We show that, unlike critical community size, the inferred distributions account for observational processes, allowing direct comparisons between metapopulations. The inferred distributions scale with population size. We use these scalings to estimate extinction boundary probabilities. We compare these predictions with measurements in individual populations and random aggregates of populations, highlighting the importance of medium‐sized populations in metapopulation persistence.     

我们离麻疹消除还有多远?

中国麻疹发病率自2008年起出现大幅度下降,但2012年底以来麻疹发病疫情呈上升趋势,部分城市出现了以成人为主的疫情暴发。导致麻疹疫情再次上升的一个可能原因是中国的麻疹疫苗实际接种率低于报告接种率,常规免疫有不到位的情况。同时,中国存在部分麻疹免疫空缺人群,既未接种过麻疹常规疫苗,也没有参加过2004—2010年的补充免疫活动。这类人群积累到一定程度后,可引起聚集性的疫情暴发。中国在消除麻疹方面虽已取得显著进展,但近年来疫情再次抬头值得警惕。进一步增加常规麻疹两剂疫苗接种率,对重点地区和人群适当增加补充免疫活动,更好地落实麻疹应急预案等,将有助于控制并消除麻疹疫情。     

Modelling seasonal variations in the age and incidence of Kawasaki disease to explore possible infectious aetiologies

The average age of infection is expected to vary during seasonal epidemics in a way that is predictable from the epidemiological features, such as the duration of infectiousness and the nature of population mixing. However, it is not known whether such changes can be detected and verified using routinely collected data. We examined the correlation between the weekly number and average age of cases using data on pre-vaccination measles and rotavirus. We show that age-incidence patterns can be observed and predicted for these childhood infections. Incorporating additional information about important features of the transmission dynamics improves the correspondence between model predictions and empirical data. We then explored whether knowledge of the age-incidence pattern can shed light on the epidemiological features of diseases of unknown aetiology, such as Kawasaki disease (KD). Our results indicate KD is unlikely to be triggered by a single acute immunizing infection, but is consistent with an infection of longer duration, a non-immunizing infection or co-infection with an acute agent and one with longer duration. Age-incidence patterns can lend insight into important epidemiological features of infections, providing information on transmission-relevant population mixing for known infections and clues about the aetiology of complex paediatric diseases.     

Analytical threshold and stability results on age-structured epidemic models with vaccination

This paper examines mathematical models for common childhood diseases such as measles and rubella and in particular the use of such models to predict whether or not an epidemic pattern of regular recurrent disease incidence will occur. We use age-structured compartmental models which divide the population amongst whom the disease is spreading into classes and use partial differential equations to model the spread of the disease. This paper is particularly concerned with an analytical investigation of the effects of different types of vaccination schemes. We examine possible equilibria and determine the stability of small oscillations about these equilibria. The results are important in predicting the long-term overall level of incidence of disease, in designing immunisation programs and in describing the variations of the incidence of disease about this equilibrium level.     

An in-host model of acute infection: measles as a case study

The epidemiology of acute infections is strongly influenced by the immune status of individuals. In-host models can provide quantitative predictions of immune status and can thus offer valuable insights into the factors that influence transmission between individuals and the effectiveness of vaccination protocols with respect to individual immunity. Here we develop an in-host model of measles infection. The model explicitly considers the effects of immune system memory and CD8 T-cells, which are key to measles clearance. The model is used to determine the effects of waning immunity through vaccination and infection, the effects of booster exposures or vaccines on the level of immunity, and the immune system characteristics that result in measles transmission (R(0)>1) even if an individual has no apparent clinical symptoms. We find that the level of immune system CD8 T-cells at the time of exposure to measles determines whether an individual will experience a measles infection or simply a boost in immunity. We also find that the infected cell dynamics are a good indicator of measles transmission and the degree of symptoms that will be experienced. Our results indicate that the degree of immunity in adults is independent of the source of exposure in early childhood, be it vaccine or natural infection.     

A DIseAse MOdule Detection (DIAMOnD) Algorithm Derived from a Systematic Analysis of Connectivity Patterns of Disease Proteins in the Human Interactome

The observation that disease associated proteins often interact with each other has fueled the development of network-based approaches to elucidate the molecular mechanisms of human disease. Such approaches build on the assumption that protein interaction networks can be viewed as maps in which diseases can be identified with localized perturbation within a certain neighborhood. The identification of these neighborhoods, or disease modules, is therefore a prerequisite of a detailed investigation of a particular pathophenotype. While numerous heuristic methods exist that successfully pinpoint disease associated modules, the basic underlying connectivity patterns remain largely unexplored. In this work we aim to fill this gap by analyzing the network properties of a comprehensive corpus of 70 complex diseases. We find that disease associated proteins do not reside within locally dense communities and instead identify connectivity significance as the most predictive quantity. This quantity inspires the design of a novel Disease Module Detection (DIAMOnD) algorithm to identify the full disease module around a set of known disease proteins. We study the performance of the algorithm using well-controlled synthetic data and systematically validate the identified neighborhoods for a large corpus of diseases.     

Interior-Point Methods for Estimating Seasonal Parameters in Discrete-Time Infectious Disease Models

Infectious diseases remain a significant health concern around the world. Mathematical modeling of these diseases can help us understand their dynamics and develop more effective control strategies. In this work, we show the capabilities of interior-point methods and nonlinear programming (NLP) formulations to efficiently estimate parameters in multiple discrete-time disease models using measles case count data from three cities. These models include multiplicative measurement noise and incorporate seasonality into multiple model parameters. Our results show that nearly identical patterns are estimated even when assuming seasonality in different model parameters, and that these patterns show strong correlation to school term holidays across very different social settings and holiday schedules. We show that interior-point methods provide a fast and flexible approach to parameterizing models that can be an alternative to more computationally intensive methods.     

When in America,do as the Americans? The evolution of health behaviors and outcomes across immigrant cohorts

This study seeks to understand US immigrants’ health-related behaviors and outcomes across arrival cohorts. We simultaneously examine risky consumption choices (smoking and drinking) and physical health conditions (asthma, diabetes, vision problems, and coronary heart diseases) using data from the National Health Interview Surveys (1989–2018). We incorporate cohort fixed-effects and the interactions between cohort effects and years since immigration into our empirical framework to capture the dynamics of immigrant health over time. For all health indicators, we find that there are important differences between arriving immigrants and natives. Despite some heterogeneity in the dynamics of unhealthy behaviors, this heterogeneity seems to dissipate as we explore longer-term health outcomes. Overall, our findings provide an interesting outlook on how the integration into the host society affects American immigrants’ health. We contribute new results to the immigrant assimilation literature, which has primarily focused on obesity and wages.