Childhood Epidemics Research Articles

Multifractal scaling in epidemics

In this work we study multifractal properties of the transmission dynamics of childhood epidemics. As a case study, the rubella epidemic in Mexico is analyzed.

Historical Associations and Geographical Distributions of Childhood Epidemics in the United States: An Exploratory, Pre-1955, Analysis at the State Level

The analysis explores possible associations among epidemic childhood diseases over time and in their geographical distributions in the United States. Diseases include diphtheria, polio, measles, scarlet fever, and whooping cough (pertussis). Analysis of their incidence rates is cross-sectional and geographical at the state level using the latitude and longitude of state centroids. All five diseases are analyzed in 1950 controlling for socio-demographic factors. Polio and measles are given an extended historical analysis from 1930 to 1954 and whooping cough from 1940 to 1954. The results show a complex relationship between measles and whooping cough where none was expected. On average, over time, states with higher measles rates also had higher whooping cough rates, and the average weekly incidence of whooping cough lags measles by a delay of two to three weeks. These findings give tentative support for the hypothesis that because of its immune suppressing effects measles causes an increase in whooping cough. The analysis shows little support for disease interference between measles and whooping cough but a possible association between scarlet fever and whooping cough. Geographical distributions of polio, measles, and whooping cough are relatively stable over time, on average, despite great seasonal and annual variations in incidence rates. The method of spatial analysis used here complements conventional metapopulation epidemic models that start in the time domain.

The Direct Estimation of Māori Vital Rates for Ruapuke Island, 1844-1845 and 1850-1885

Vital rates and cause of death for Māori on the island of Ruapuke are examined for the period 1844 to 1885. Natural decline is evident over the period, but is lower for later years. Infant mortality is higher for females. Cause of death data suggests the importance of both tuberculosis and periodic childhood epidemics for general mortality, as well as drowning for adult males.

Secular trends in new childhood epidemics: insights from evolutionary medicine

In the last few decades, pediatric medicine has observed a dramatic increase in the prevalence of hitherto rare illnesses, among which obesity, diabetes, allergies and other autoimmune diseases stand out. In addition, secular trends towards earlier onset of puberty and sexual activity contribute to the psychological problems of youth and adolescents. All this has occurred in spite of the improved health care provision for children, yet traditional concepts of medicine have failed to explain these new ?epidemics?. A recent conference and science school of the European Society of Paediatric Endocrinology (ESPE) in Acre, Israel, has taken up this challenge. Experts across disciplines including medicine, anthropology and developmental psychology discussed potential causes of childhood ill-health from an evolutionary point-of-view. Seen from an evolutionary vantage point, the ?epidemics? of childhood obesity, diabetes and psychological dysfunction appear, in part, to be related to a mismatch between ancestral adaptations and novel environmental contingencies. These include changing exposures to pathogens, which impact on the function of the immune system, as well as changing patterns of parenting, which influence the timing of puberty and the risk for developing psychopathology.

Evidence childhood epidemics of type 1 and type 2 diabetes are opposite extremes of an immune spectrum disorder induced by immune stimulants. Role of race and associated cortisol activity as a major determining factor of the type of diabetes

Design Prior publications have provided evidence that type 1 and type 2 diabetes are opposite extremes of an immune spectrum disorder. Method The risk of type 1 diabetes was correlated with the risk of type 2 diabetes in different races. Results Races with high risk of developing type 2 diabetes have an decreased risk of developing type 1 diabetes (correlation coefficients −0.5 or −0.85 depending on age, p < 0.05). Maori, American Indians, Asians, Australian Aboriginals and US Black children have a higher risk of developing type 2 diabetes but a low risk of type 1 diabetes compared to White children. Conclusion Population data is consistent with type 1 and type 2 diabetes being opposite ends of an immune spectrum disorder.

A School-Oriented, Age-Structured Epidemic Model

A model of childhood epidemics focusing on the impact of the school-year is presented. At the onset of the epidemic season, a new cohort of susceptible students enter the school, all other age-classes advance one year, while the oldest age-group leaves the mixing pool. If the susceptible pool is sufficiently large at the onset of the season, an epidemic will arise and run to its conclusion prior to the end of the school-year. The system is expressed in terms of a discrete dynamical system giving the changes in the age-dependent immunity structure on a year-to-year basis. If disease transmission is independent of age, the system settles at epidemics of constant size in each season. If disease transmission is age-dependent, more complicated dynamics may occur, including multiple stable states and chaos.

Deterministic Modeling Of Infectious Diseases: Applications To Measles And Other Similar Infections

This paper is second in our series on deterministic modeling (DM) of infectious diseases. The first paper dealt with theories and methods of DM. The current paper provides sensitivity analyses. We used the SEIR model to show how changes in the transition rate from susceptibles to infectious (force of infection), variations in the latent and infectiousness period, and alteration to the vaccination proportion can alter the profile of common childhood epidemics. Various situations are explored so that the reader may grasp the effects of interventions, i.e., altering the main model parameters, upon the size and shape of epidemics, waiting times to epidemics, spreading out of infected cases in time, and switching from an epidemic to an endemic state and to cases eradication. The paper further shows that the introduction of infectious individuals into a community of susceptibles does not automatically give rise to an epidemic outbreak. This analysis thus provides the reader with an understanding of how epidemics evolve and how they can be controlled. Vaccination has been tackled as well as other public-health interventions that may have a bearing on the rate-limiting steps of epidemics. In spite of its limitations, the SEIR model helps gain insight into the dynamics of infectious diseases.

Revisited measles and chickenpox dynamics through orthogonal transformation.

The question addressed is whether or not childhood epidemics such as measles and chickenpox are characterized by low-dimensional chaos. We propose a new method for the detection and extraction of hidden periodic components embedded in an irregular cyclical series, and study the characterization of the epidemiological series in terms of the characteristic features or periodicity attributes of the extracted components. It is shown that the measles series possesses two periodic components each having a period of one year. Both the periodic components have time-varying pattern, and the process is nonlinear and deterministic; there is no evidence of strong chaoticity in the measles dynamics. The chickenpox series has one seasonal component with stable pattern, and the process is deterministic but linear, and hence non-chaotic. We also propose surrogate generators based on null hypotheses relating to the variability of the periodicity attributes to analyse the dynamics in the epidemic series. The process dynamics is also studied using seasonally forced SEIR epidemic model, and the characterization performance of the proposed schemes is assessed.

Vaccination policies for chaos reduction in childhood epidemics.

This paper considers the problem of controlling a childhood epidemic described by a susceptible-infective-recovered (SIR) model. The epidemic has a chaotic behavior, with large outbreaks entailing considerable costs. The control problem is set up to perform a chaos reduction, namely to yield a beneficial compression of the outbreaks of infectives. A simple class of vaccination policies is considered with this aim.

Correlation models for childhood epidemics.

One of the simplest set of equations for the description of epidemics (the SEIR equations) has been much studied, and produces reasonable approximations to the dynamics of communicable disease. However, it has long been recognized that spatial and social structure are important if we are to understand the long-term persistence and detailed behaviour of disease. We will introduce three pair models which attempt to capture the underlying heterogeneous structure by studying the connections and correlations between individuals. Although modelling the correlations necessarily leads to more complex equations, this pair formulation naturally incorporates the local dynamical behaviour generating more realistic persistence. In common with other studies on childhood diseases we will focus our attention on measles, for which the case returns are particularly well documented and long running.

Chance and chaos in population biology—Models of recurrent epidemics and food chain dynamics

In spite of their complex behaviour the dynamics of some ecological systems may be explained by deterministic laws of motion. This is clearly theoretically possible, because deductive approaches to the dynamics of ecological systems lead to nonlinear models and even very simple model ecosystems generate typically a rich spectrum of dynamics, ranging from coexisting periodic regimes to chaotic behaviour. The present study analyses the complex interplay between deterministic nonlinear dynamics and demographic stochasticity using two examples. Firstly, the search for chaos in ecology has drawn much attention to the analysis of recurrent outbreaks of childhood epidemics—in particular of measles infections—in large population centres. The second example is a compartmental model of a three-species food chain, where sudden population disappearances can be observed due to transient chaos. Our analysis lends support to the plausibility of chaos in population dynamics. However, for decreasing population size (increasing fluctuations) the distinction between chaos and stochasticity becomes more and more problematic. The interplay between deterministic dynamics and stochastic fluctuations, e.g. due to the integer structure of populations or a noisy environment, suggests an analysis combining methods from the theory of nonlinear dynamical systems as well as stochastic processes.

The case for chaos in childhood epidemics. II. Predicting historical epidemics from mathematical models.

The case for chaos in childhood epidemics rests on two observations. The first is that historical epidemics show various 'fieldmarks' of chaos, such as positive Lyapunov exponents. Second, phase portraits reconstructed from real-world epidemiological time series bear a striking resemblance to chaotic solutions obtained from certain epidemiological models. Both lines of evidence are subject to dispute: the algorithms used to look for the fieldmarks can be fooled by short, noisy time series, and the same fieldmarks can be generated by stochastic models in which there is demonstrably no chaos at all. In the present paper, we compare the predictive abilities of stochastic models with those of mechanistic scenarios that admit to chaotic solutions. The main results are as follows: (i) the mechanistic models outperform their stochastic counterparts; (ii) forecasting efficacy of the deterministic models is maximized by positing parameter values that induce chaotic behaviour; (iii) simple mechanistic models are equal if not superior to more detailed schemes that include age structure; and (iv) prediction accuracy for monthly notifications declines rapidly with time, so that, from a practical standpoint, the results are of little value. By way of contrast, next amplitude maps can successfully forecast successive changes in maximum incidence one or more years into the future.

Discussion on the Meeting on Chaos

Discussion on the Meeting on Chaos

Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics

We address the question of whether or not childhood epidemics such as measles and chickenpox are chaotic, and argue that the best explanation of the observed unpredictability is that it is a manifestation of what we call chaotic stochasticity. Such chaos is driven and made permanent by the fluctuations from the mean field encountered in epidemics, or by extrinsic stochastic noise, and is dependent upon the existence of chaotic repellors in the mean field dynamics. Its existence is also a consequence of the near extinctions in the epidemic. For such systems, chaotic stochasticity is likely to be far more ubiquitous than the presence of deterministic chaotic attractors. It is likely to be a common phenomenon in biological dynamics.

Components of longevity: Developmental and genetic responses to differential childhood mortality

Childhood disease may have far-reaching effects on adult longevity in high mortality populations. It was earlier reported from demographic analysis of 19th century New England communities that survivors of high-fatality childhood epidemics lived significantly longer than their unstressed counterparts. As part of a broader survey of agricultural families of western Massachusetts, these data indicate that elevated child mortality is associated with an increase in the average age at death of survivors. This paper examines this selection process and the problem of heritable longevity using cohort data selected from historical epidemics. A series of tests of the selection hypothesis in which an attempt is made to control demographic covariates suggest that widespread childhood infectious disease strengthens survivors in a developmental manner. Whether such episodes also eliminate less fit individuals according to a simple selection model could not be determined. The influence of family formation variables on child loss, and behavioral (fertility) responses to childhood epidemics in these communities are also considered.