The dynamics of measles epidemics

Optimal Timing Regularly Outperforms Higher Coverage in Preventative Measles Supplementary Immunization Campaigns

Measles threatens the lives and livelihoods of tens of millions of children and there are countries where routine immunization systems miss enough individuals to create the risk of large outbreaks. To help address this threat, measles supplementary immunization activities are time-limited, coordinated campaigns to immunize en masse a target population. Timing campaigns to be concurrent with building outbreak risk is an important consideration, but current programmatic standards focus on campaigns achieving a high coverage of at least 95%. We show that there is a dramatic trade-off between campaign timeliness and coverage. Optimal timing at coverages as low as 50% for areas with weak routine immunization systems is shown to outperform the current standard, which is delayed by as little as 6 months. Measured coverage alone is revealed as a potentially misleading performance metric.

Raising Epidemiological Awareness: Assessment of Measles/MMR Susceptibility in Highly Vaccinated Clusters within the Hungarian and Croatian Population-A Sero-Surveillance Analysis

Perceptions of the complete eradication of vaccine-preventable diseases such as measles, mumps, and rubella (MMR) may foster complacency and compromise vaccination efforts. Decreased measles vaccination rates during the COVID-19 pandemic have heightened the risk of outbreaks, even in adequately vaccinated populations. To address this, we have aligned with ECDC recommendations, leveraging previous cross-border sero-epidemiological assessments between Pécs, Hungary, and Osijek, Croatia, to identify latent risk groups and uncover potential parallels between our nations. Testing 2680 Hungarian and 1764 Croatian serum samples for anti-MMR IgG via ELISAs revealed anti-measles seropositivity ratios below expectations in Croatian cohorts aged ~20-30 (75.7%), ~30-40 (77.5%) and ~40-50 years (73.3%). Similarly, Hungarian samples also showed suboptimal seropositivity ratios in the ~30-40 (80.9%) and ~40-50 (87.3%) age groups. Considering mumps- and rubella-associated seropositivity trends, in both examined populations, individuals aged ~30-50 years exhibited the highest vulnerability. Additionally, we noted congruent seropositivity trends across both countries, despite distinct immunization and epidemiological contexts. Therefore, we propose expanding research to encompass the intricate dynamics of vaccination, including waning long-term immunity. This understanding could facilitate targeted interventions and bolster public awareness. Our findings underscore persistent challenges in attaining robust immunity against measles despite vaccination endeavors.

Rijke tube: A nonlinear oscillator

Dynamical systems theory has emerged as an interdisciplinary area of research to characterize the complex dynamical transitions in real-world systems. Various nonlinear dynamical phenomena and bifurcations have been discovered over the decades using different reduced-order models of oscillators. Different measures and methodologies have been developed theoretically to detect, control, or suppress the nonlinear oscillations. However, obtaining such phenomena experimentally is often challenging, time-consuming, and risky mainly due to the limited control of certain parameters during experiments. With this review, we aim to introduce a paradigmatic and easily configurable Rijke tube oscillator to the dynamical systems community. The Rijke tube is commonly used by the combustion community as a prototype to investigate the detrimental phenomena of thermoacoustic instability. Recent investigations in such Rijke tubes have utilized various methodologies from dynamical systems theory to better understand the occurrence of thermoacoustic oscillations and their prediction and mitigation, both experimentally and theoretically. The existence of various dynamical behaviors has been reported in single and coupled Rijke tube oscillators. These behaviors include bifurcations, routes to chaos, noise-induced transitions, synchronization, and suppression of oscillations. Various early warning measures have been established to predict thermoacoustic instabilities. Therefore, this review article consolidates the usefulness of a Rijke tube oscillator in terms of experimentally discovering and modeling different nonlinear phenomena observed in physics, thus transcending the boundaries between the physics and the engineering communities.

Dynamical states and bifurcations in coupled thermoacoustic oscillators

The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a comprehensive theoretical study on the manifestation of these exquisite phenomena in a reduced-order model of two coupled Rijke tube oscillators, which are prototypical thermoacoustic oscillators. We characterize the dynamical behaviors of two such identical and non-identical oscillators by varying both system parameters (such as the uncoupled amplitudes and the natural frequencies of the oscillators) and coupling parameters (such as the coupling strength and the coupling delay). The present model captures all the dynamical phenomena-namely, synchronization, phase-flip bifurcation, amplitude death, and partial amplitude death-observed previously in experiments on coupled Rijke tubes. By performing numerical simulations and deriving approximate analytical solutions, we systematically decipher the conditions and the bifurcations underlying the aforementioned phenomena. The insights provided by this study can be used to understand the interactions between multiple cans in gas turbine combustors and develop control strategies to avert undesirable thermoacoustic oscillations in them.

The seasonal behaviour of COVID-19 and its galectin-like culprit of the viral spike

Seasonal behaviour is an attribute of many viral diseases. Like other 'winter' RNA viruses, infections caused by the causative agent of COVID-19, SARS-CoV-2, appear to exhibit significant seasonal changes. Here we discuss the seasonal behaviour of COVID-19, emerging viral phenotypes, viral evolution, and how the mutational landscape of the virus affects the seasonal attributes of the disease. We propose that the multiple seasonal drivers behind infectious disease spread (and the spread of COVID-19 specifically) are in 'trade-off' relationships and can be better described within a framework of a 'triangle of viral persistence' modulated by the environment, physiology, and behaviour. This 'trade-off' exists as one trait cannot increase without a decrease in another. We also propose that molecular components of the virus can act as sensors of environment and physiology, and could represent molecular culprits of seasonality. We searched for flexible protein structures capable of being modulated by the environment and identified a galectin-like fold within the N-terminal domain of the spike protein of SARS-CoV-2 as a potential candidate. Tracking the prevalence of mutations in this structure resulted in the identification of a hemisphere-dependent seasonal pattern driven by mutational bursts. We propose that the galectin-like structure is a frequent target of mutations because it helps the virus evade or modulate the physiological responses of the host to further its spread and survival. The flexible regions of the N-terminal domain should now become a focus for mitigation through vaccines and therapeutics and for prediction and informed public health decision making.

Did Hydro-climatic Extremes, Positive Checks, and Economic Fluctuations Modulate the Epidemics Outbreaks in Late Imperial China?

Empirical research has shown that climate-related variables, the decline in economic well-being, and the mutual reinforcement of positive checks are the primary drivers of epidemic outbreaks in recent human history. However, their relative importance in causing the outbreak of epidemics is rarely examined quantitatively in a single study. I sought to address this issue by analyzing the 1402 epidemic incidents in China between 1841 and 1911, which partially overlaps partly with the Third Pandemic period. Fine-grained historical big data, multiple regression, and wavelet coherence analysis were employed. Statistical results show that economic fluctuations drove the country-wide epidemics outbreaks in China in inter-annual and decadal time scales. Economic fluctuations could cause short-term hardship and long-term impoverishment to the underprivileged social groups since a large portion of the Chinese population lived at the subsistence level in the past. The fluctuations might have sustained the repeated waves of epidemic outbreaks during the Third Pandemic period.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s10745-021-00272-7.

Synchronization route to weak chimera in four candle-flame oscillators

Synchronization and chimera are examples of collective behavior observed in an ensemble of coupled nonlinear oscillators. Recent studies have focused on their discovery in systems with least possible number of oscillators. Here we present an experimental study revealing the synchronization route to weak chimera via quenching, clustering, and chimera states in a single system of four coupled candle-flame oscillators. We further report the discovery of multiphase weak chimera along with experimental evidence of the theoretically predicted states of in-phase chimera and antiphase chimera.

Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems

Oscillatory instabilities, although ubiquitous in nature, are undesirable in many situations such as biological systems, swaying of bridges and skyscrapers, aero-acoustic flutter, prey-predator and disease spread models, and thermoacoustic systems, where they exhibit large amplitude periodic oscillations. In the present study, we aim to study the suppression mechanism of such undesired oscillations in a pair of thermoacoustic oscillators, also known as horizontal Rijke tubes. These oscillators are coupled through a connecting tube whose length and diameter are varied as coupling parameters. With the variation of these parameters, we show the first experimental evidence of rich dynamical phenomena such as synchronization, amplitude death, and phase-flip bifurcation in coupled identical thermoacoustic oscillators. We discover that when frequency and amplitude mismatch are introduced between these oscillators, quenching of oscillations in one or both the oscillators occurs with further ease, through the mechanisms of amplitude death and partial amplitude death. Finally, we show that the effectiveness of coupling is sensitive to the dimensions of the connecting tube which can be directly correlated with the time delay and coupling strength of the system.

Back to the Future: Lessons Learned From the 1918 Influenza Pandemic

2018 marks the 100-year anniversary of the 1918 influenza pandemic, which killed ~50 million people worldwide. The severity of this pandemic resulted from a complex interplay between viral, host, and societal factors. Here, we review the viral, genetic and immune factors that contributed to the severity of the 1918 pandemic and discuss the implications for modern pandemic preparedness. We address unresolved questions of why the 1918 influenza H1N1 virus was more virulent than other influenza pandemics and why some people survived the 1918 pandemic and others succumbed to the infection. While current studies suggest that viral factors such as haemagglutinin and polymerase gene segments most likely contributed to a potent, dysregulated pro-inflammatory cytokine storm in victims of the pandemic, a shift in case-fatality for the 1918 pandemic toward young adults was most likely associated with the host's immune status. Lack of pre-existing virus-specific and/or cross-reactive antibodies and cellular immunity in children and young adults likely contributed to the high attack rate and rapid spread of the 1918 H1N1 virus. In contrast, lower mortality rate in in the older (>30 years) adult population points toward the beneficial effects of pre-existing cross-reactive immunity. In addition to the role of humoral and cellular immunity, there is a growing body of evidence to suggest that individual genetic differences, especially involving single-nucleotide polymorphisms (SNPs), contribute to differences in the severity of influenza virus infections. Co-infections with bacterial pathogens, and possibly measles and malaria, co-morbidities, malnutrition or obesity are also known to affect the severity of influenza disease, and likely influenced 1918 H1N1 disease severity and outcomes. Additionally, we also discuss the new challenges, such as changing population demographics, antibiotic resistance and climate change, which we will face in the context of any future influenza virus pandemic. In the last decade there has been a dramatic increase in the number of severe influenza virus strains entering the human population from animal reservoirs (including highly pathogenic H7N9 and H5N1 viruses). An understanding of past influenza virus pandemics and the lessons that we have learnt from them has therefore never been more pertinent.

Experimental Evidence of Amplitude Death and Phase-Flip Bifurcation between In-Phase and Anti-Phase Synchronization

Nonlinear phenomena emerging from the coupled behaviour of a pair of oscillators have attracted considerable research attention over the years, of which, amplitude death (AD) and phase-flip bifurcation (PFB) are two noteworthy examples. Although theoretical research has postulated the coexistence of AD and PFB upon variation of different control parameters, such an occurrence has not been reported in practical systems. Here, we provide the first experimental evidence of the coexistence of AD and PFB in a physical system, comprising of a coupled pair of candle-flame oscillators. As the strength of coupling between the oscillators is increased, we report a decrease in the span of AD region between the states of in-phase and anti-phase oscillations, leading up to a point of PFB. Understanding such a switching of phenomena between AD and PFB helps us to evade their undesirable occurrences such as AD in neuron and brain cells, oscillatory state in prey-predator systems, oscillatory spread of epidemics and so forth.

Environmental, dietary and case-control study of Nodding Syndrome in Uganda: A post-measles brain disorder triggered by malnutrition?

Nodding Syndrome (NS) is an epileptic encephalopathy characterized by involuntary vertical head nodding, other types of seizures, and progressive neurological deficits. The etiology of the east African NS epidemic is unknown. In March 2014, we conducted a case-control study of medical, nutritional and other risk factors associated with NS among children (aged 5-18years) of Kitgum District, northern Uganda (Acholiland). Data on food availability, rainfall, and prevalent disease temporally related to the NS epidemic were also analyzed. In NS Cases, the mean age of reported head nodding onset was 7.6years (range 1-17years). The epidemiologic curve of NS incidence spanned 2000-2013, with peaks in 2003 and 2008. Month of onset of head nodding was non-uniform, with all-year-aggregated peaks in April and June when food availability was low. Families with one or more NS Cases had been significantly more dependent on emergency food and, immediately prior to head nodding onset in the child, subsistence on moldy plant materials, specifically moldy maize. Medical history revealed a single significant association with NS, namely prior measles infection. NS is compared with the post-measles disorder subacute sclerosing panencephalitis, with clinical expression triggered by factors associated with poor nutrition.

Behavioral Epidemiology of Infectious Diseases: An Overview

The focus of the growing discipline of behavioral epidemiology (BE) of infectious diseases is on individual behavior as a key determinant of infection trajectories. This overview departs from the central, but static, role of human behavior in traditional mathematical models of infection to motivate the importance of including behavior into epidemiological models. Our aim is threefold. First, we attempt to motivate the historical and cultural background underpinning the BE revolution, focusing on the issue of rational opposition to vaccines as a natural endpoint of the changed relation between man and disease in modern industrialized countries. Second, we review those contributions, from both mathematical epidemiology and economics, that forerun the current “epidemic” of studies on BE. Last, we offer a more detailed overview of the current epidemic phase of BE studies and, still motivated by the issue of immunization choices, introduce some baseline ideas and models.

THRESHOLD AND STABILITY RESULTS FOR AN SIRS EPIDEMIC MODEL WITH A GENERAL PERIODIC VACCINATION STRATEGY

An SIRS epidemic model with general periodic vaccination strategy is analyzed. This periodic vaccination strategy is discussed first for an SIRS model with seasonal variation in the contact rate of period T = 1 year. We start with the case where the vaccination strategy and the contact rate have the same period and then discuss the case where the period of the vaccination strategy is LT, where L is an integer. We investigate whether a periodic vaccination strategy may force the epidemic dynamics to have periodic behavior. We prove that our SIRS model has a unique periodic disease free solution (DFS) whose period is the same as that of the vaccination strategy, which is globally asymptotically stable when the basic reproductive number R0 is less than or equal to one in value. When R0 > 1, we prove that there exists a non-trivial periodic solution of period the same as that of the vaccination strategy. Some persistence results are also discussed. Threshold conditions for these periodic vaccination strategies to ensure that R0 ≤ 1 are derived.

Diurnal temperature range and emergency room admissions for chronic obstructive pulmonary disease in Taiwan

The objective of this study was to assess the relationship between diurnal temperature range (DTR) and emergency room (ER) admissions for chronic obstructive pulmonary disease (COPD) in an ER in Taichung City, Taiwan. The design was a longitudinal study in which DTR was related to COPD admissions to the ER of the city's largest hospital. Daily ER admissions for COPD and ambient temperature were collected from 1 January 2001 to 31 December 2002. There was a significant negative association between the average daily temperature and ER admissions for COPD (r=-0.95). However, a significant positive association between DTR and COPD admissions was found (r=0.90). Using the Poisson regression model after adjusting for the effects of air pollutants and the day of the week, COPD admissions to the ER increased by 14% when DTR was over 9.6 degrees C. COPD patients must be made aware of the increased risk posed by large DTR. Hospitals and ERs should take into account the increased demand of specific facilities during periods of large temperature variations.

The effect of using different types of periodic contact rate on the behaviour of infectious diseases: A simulation study

This paper studies the effect of using different types of seasonally varying contact rate on the behaviour of the seasonally varying infectious diseases for an SEIR epidemic model. Our target is to investigate the long term behaviour of the system in response to changes in beta(1), the amplitude parameter of the seasonal contact rate, which is our bifurcation parameter. This amplitude parameter is used as a filter to plot the length in years of the period of the stable endemic periodic solution of the SEIR model. Another main aim of this simulation study is to explain how can the type of the contact rate affect the behaviour of the disease dynamics. The simulation results have indicated that using different functional forms of seasonally varying contact rate generates different patterns of solutions for each disease parameter set and type of contact rate. So prediction of the type of disease outbreaks depends on the form of contact rate. Thus it is important to determine which type of contact rate is more likely to match the actual dynamics of each disease. Also these results have shown how the dynamics of the disease depend on the amplitude of the seasonally varying contact rate. Apart from some of the results for measles with a sinusoidal periodic function the simulation results are original and give a clear and a much broader insight into the features of the dynamics of these diseases [D. Greenhalgh, I.A. Moneim, SIRS epidemic model and simulations using different types of seasonal contact rate, Syst. Anal. Modelling Simul. 43(5) (2003) 573-600; I.A. Moneim, D. Greenhalgh, Threshold and stability results for an SIRS epidemic model with a general periodic vaccination strategy, J. Biol. Syst. 13(2) (2005), to appear].

Seasonality and the persistence and invasion of measles

The critical community size (CCS) for measles, which separates persistent from extinction-prone populations, is arguably the best understood stochastic threshold in ecology. Using simple models, we explore a relatively neglected relationship of how the CCS scales with birth rate. A predominantly positive relationship of persistence with birth rate is complicated by the accompanying dynamical transitions of the underlying deterministic process. We show that these transitions imply a lower CCS for high birth rate less developed countries and contrary to the experience in lower birth rate, industrial countries, the CCS may increase after vaccination. We also consider the evolutionary implications of the CCS for the origin of measles; this analysis explores how the deterministic and stochastic thresholds for invasion and persistence set limits on the mechanism by which this highly infectious pathogen could have successfully colonized its human host.

Estimating transmission intensity for a measles epidemic in Niamey, Niger: lessons for intervention

The objective of this study is to estimate the effective reproductive ratio for the 2003-2004 measles epidemic in Niamey, Niger. Using the results of a retrospective and prospective study of reported cases within Niamey during the 2003-2004 epidemic, we estimate the basic reproductive ratio, effective reproductive ratio (RE) and minimal vaccination coverage necessary to avert future epidemics using a recent method allowing for estimation based on the epidemic case series. We provide these estimates for geographic areas within Niamey, thereby identifying neighbourhoods at high risk. The estimated citywide RE was 2.8, considerably lower than previous estimates, which may help explain the long duration of the epidemic. Transmission intensity varied during the course of the epidemic and within different neighbourhoods (RE range: 1.4-4.7). Our results indicate that vaccination coverage in currently susceptible children should be increased by at least 67% (vaccine efficacy 90%) to produce a citywide vaccine coverage of 90%. This research highlights the importance of local differences in vaccination coverage on the potential impact of epidemic control measures. The spatial-temporal spread of the epidemic from district to district in Niamey over 30 weeks suggests that targeted interventions within the city could have an impact.

An explanation for the seasonality of acute upper respiratory tract viral infections

Despite a great increase in our understanding of the molecular biology of the viruses associated with acute upper respiratory tract viral infections (URTIs) there is a remarkable lack of knowledge and ideas about why URTI should exhibit a seasonal incidence. Most publications in this area either acknowledge a complete lack of any explanation for the seasonality of URTI or put forward an explanation relating to an increased "crowding" of susceptible persons in winter. This review will discuss some of the ideas concerning the seasonality of URTI and put forward a new hypothesis for discussion, namely that seasonal exposure to cold air causes an increase in the incidence of URTI due to cooling of the nasal airway. The hypothesis is supported by literature reports demonstrating that inhalation of cold air causes cooling of the nasal epithelium, and that this reduction in nasal temperature is sufficient to inhibit respiratory defences against infection such as mucociliary clearance and the phagocytic activity of leukocytes. A case is also made to suggest that warming of the nasal airway during fever and nasal congestion may help to resolve a current URTI.

Modelling the dynamics of scarlet fever epidemics in the 19th century

Annual deaths from scarlet fever in Liverpool, UK during 1848-1900 have been used as a model system for studying the historical dynamics of the epidemics. Mathematical models are developed which include the growth of the population and the death rate from scarlet fever. Time-series analysis of the results shows that there were two distinct phases to the disease (i) 1848-1880: regular epidemics (wavelength = 3.7 years) consistent with the system being driven by an oscillation in the transmission coefficient (deltabeta) at its resonant frequency, probably associated with dry conditions in winter (ii) 1880-1900: an undriven SEIR system with a falling endemic level and decaying epidemics. This period was associated with improved nutritive levels. There is also evidence from time-series analysis that raised wheat prices in pregnancy caused increased susceptibility in the subsequent children. The pattern of epidemics and the demographic characteristics of the population can be replicated in the modelling which provides insights into the detailed epidemiology of scarlet fever in this community in the 19th century.

Interacting effects of nutrition and social class differentials on fertility and infant mortality in the pre-industrial population

Inadequate nutrition of both the mother and her offspring at each stage of its development - before pregnancy, in the womb, in infancy and during early childhod - played an important role in the patterns of subfertility and infant mortality in a saturated, marginal, preindustrial community. It is suggested that the three social classes had different diets but all were deficient in some essential constituents. Differences in nursing practices in the social groups contributed to differential exogenous mortality and to malnourishment and maternal depletion in the subsistence and (paradoxically) in the elite classes, producing an interacting web of effects and generating a vicious circle from which they could not escape for 150 years. Although the population apparently preferred daughters, the persistent generation effect of low birthweight girls bearing low birthweight daughters probably contributed to the steady-state conditions in this compromised community.