Immunological serotype interactions and their effect on the epidemiological pattern of dengue

Long-term epidemiological data reveal multi-annual fluctuations in the incidence of dengue fever and dengue haemorrhagic fever, as well as complex cyclical behaviour in the dynamics of the four serotypes of the dengue virus. It has previously been proposed that these patterns are due to the phenomenon of the so-called antibody-dependent enhancement (ADE) among dengue serotypes, whereby viral replication is increased during secondary infection with a heterologous serotype; however, recent studies have implied that this positive reinforcement cannot account for the temporal patterns of dengue and that some form of cross-immunity or external forcing is necessary. Here, we show that ADE alone can produce the observed periodicities and desynchronized oscillations of individual serotypes if its effects are decomposed into its two possible manifestations: enhancement of susceptibility to secondary infections and increased transmissibility from individuals suffering from secondary infections. This decomposition not only lowers the level of enhancement necessary for realistic disease patterns but also reduces the risk of stochastic extinction. Furthermore, our analyses reveal a time-lagged correlation between serotype dynamics and disease incidence rates, which could have important implications for understanding the irregular pattern of dengue epidemics.     

Epidemiological models with age structure,proportionate mixing,and cross-immunity

Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics. Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations.     

Stochasticity generates an evolutionary instability for infectious disease

Traditional models of disease evolution are based upon the deterministic competition between strains that confer complete cross-immunity, and predict the selection of strains with higher basic reproductive ratios ( R ₀). In contrast, evolution in a stochastic setting is determined by a complex mixture of influences. Here, to isolate the impact of stochasticity, we constrain all competing strains to have an equal basic reproductive ratio – thereby eliminating deterministic selection. The resulting stochastic models predict an evolutionary unstable strategy, which separates a region favouring the evolution of rapid-transmission (acute) strains from one favouring persistent (chronic) strains. We find this to be a generic phenomenon with strain evolution consistently driven towards extremes of epidemiological behaviour. Even in the absence of an equal R ₀ constraint, such stochastic selective pressures operate in addition to standard deterministic selection and will therefore influence the evolutionary behaviour of disease in all scenarios.     

An evolutionary computing approach for parameter estimation investigation of a model for cholera

We consider the problem of using time-series data to inform a corresponding deterministic model and introduce the concept of genetic algorithms (GA) as a tool for parameter estimation, providing instructions for an implementation of the method that does not require access to special toolboxes or software. We give as an example a model for cholera, a disease for which there is much mechanistic uncertainty in the literature. We use GA to find parameter sets using available time-series data from the introduction of cholera in Haiti and we discuss the value of comparing multiple parameter sets with similar performances in describing the data.     

Cluster formation for multi-strain infections with cross-immunity

Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of this paper is to investigate cluster formation. Computations demonstrate that clustering is independent of the model used, and is an intrinsic feature of the strain system itself. We observe that an ordered strain system, if it is sufficiently complex, admits several cluster structures of different types. Appearance of a particular cluster structure depends on levels of cross-immunity and, in some cases, on initial conditions. Clusters, once formed, are stable, and behave remarkably regularly (in contrast to the generally chaotic behaviour of the strains themselves). In general, clustering is a type of self-organisation having many features in common with pattern formation.     

On the role of cross-immunity and vaccines on the survival of less fit flu-strains

A pathogen's route to survival involves various mechanisms including its ability to invade (host's susceptibility) and its reproductive success within an invaded host ("infectiousness"). The immunological history of an individual often plays an important role in reducing host susceptibility or it helps the host mount a faster immunological response de facto reducing infectiousness. The cross-immunity generated by prior infections to influenza A strains from the same subtype provide a significant example. The results of this paper are based on the analytical study of a two-strain epidemic model that incorporates host isolation (during primary infection) and cross-immunity to study the role of invasion mediated cross-immunity in a population where a precursor related strain (within the same subtype, i.e. H3N2, H1N1) has already become established. An uncertainty and sensitivity analysis is carried out on the ability of the invading strain to survive for given cross-immunity levels. Our findings indicate that it is possible to support coexistence even in the case when invading strains are "unfit", that is, when the basic reproduction number of the invading strain is less than one. However, such scenarios are possible only in the presence of isolation. That is, appropriate increments in isolation rates and weak cross-immunity can facilitate the survival of less fit strains. The development of "flu" vaccines that minimally enhance herd cross-immunity levels may, by increasing genotype diversity, help facilitate the generation and survival of novel strains.     

Pathogen adaptation to seasonal forcing and climate change

Many diverse infectious diseases exhibit seasonal dynamics. Seasonality in disease incidence has been attributed to seasonal changes in pathogen transmission rates, resulting from fluctuations in extrinsic climate factors. Multi-strain infectious diseases with strain-specific seasonal signatures, such as cholera, indicate that a range of seasonal patterns in transmission rates is possible in identical environments. We therefore consider pathogens capable of evolving their 'seasonal phenotype', a trait that determines the sensitivity of their transmission rates to environmental variability. We introduce a theoretical framework, based on adaptive dynamics, for predicting the evolution of disease dynamics in seasonal environments. Changes in the seasonality of environmental factors are one important avenue for the effects of climate change on disease. This model also provides a framework for examining these effects on pathogen evolution and associated disease dynamics. An application of this approach gives an explanation for the recent cholera strain replacement in Bangladesh, based on changes in monsoon rainfall patterns.     

Theoretical considerations of cross-immunity, recombination and the evolution of new parasitic strains.

We explore the dynamics of multiple strains of a parasite in order to assess the conditions under which a novel strain, perhaps a mutant or migrant, may invade a population that already carries an endemic strain. Multiple strain dynamics can be modeled through coinfection or complete cross-immunity. We examine these three modes to discuss the relationships among cross-immunity, the basic reproductive rates of each strain, and the invasion of the new strain. Superinfection is more restrictive than coinfection in the proportion of parameters that allows invasion. The coinfection model is extended to allow haploid strains to undergo recombination within the host. We investigate the effects of recombination and cross-immunity on the invasion of new strains. Interestingly, although recombination is understood to generate diversity, it is not always advantageous.     

Strain Interactions as a Mechanism for Dominant Strain Alternation and Incidence Oscillation in Infectious Diseases: Seasonal Influenza as a Case Study

Background

Many human infectious diseases are caused by pathogens that have multiple strains and show oscillation in infection incidence and alternation of dominant strains which together are referred to as epidemic cycling. Understanding the underlying mechanisms of epidemic cycling is essential for forecasting outbreaks of epidemics and therefore important for public health planning. Current theoretical effort is mainly focused on the factors that are extrinsic to the pathogens themselves (“extrinsic factors”) such as environmental variation and seasonal change in human behaviours and susceptibility. Nevertheless, co-circulation of different strains of a pathogen was usually observed and thus strains interact with one another within concurrent infection and during sequential infection. The existence of these intrinsic factors is common and may be involved in the generation of epidemic cycling of multi-strain pathogens.

Methods and Findings

To explore the mechanisms that are intrinsic to the pathogens themselves (“intrinsic factors”) for epidemic cycling, we consider a multi-strain SIRS model including cross-immunity and infectivity enhancement and use seasonal influenza as an example to parameterize the model. The Kullback-Leibler information distance was calculated to measure the match between the model outputs and the typical features of seasonal flu (an outbreak duration of 11 weeks and an annual attack rate of 15%). Results show that interactions among strains can generate seasonal influenza with these characteristic features, provided that: the infectivity of a single strain within concurrent infection is enhanced 2−7 times that within a single infection; cross-immunity as a result of past infection is 0.5–0.8 and lasts 2–9 years; while other parameters are within their widely accepted ranges (such as a 2–3 day infectious period and the basic reproductive number of 1.8–3.0). Moreover, the observed alternation of the dominant strain among epidemics emerges naturally from the best fit model. Alternative modelling that also includes seasonal forcing in transmissibility shows that both external mechanisms (i.e. seasonal forcing) and the intrinsic mechanisms (i.e., strain interactions) are equally able to generate the observed time-series in seasonal flu.

Conclusions

The intrinsic mechanism of strain interactions alone can generate the observed patterns of seasonal flu epidemics, but according to Kullback-Leibler information distance the importance of extrinsic mechanisms cannot be excluded. The intrinsic mechanism illustrated here to explain seasonal flu may also apply to other infectious diseases caused by polymorphic pathogens.     

Estimation of Cross-Immunity Between Drifted Strains of Influenza A/H3N2

To determine the cross-immunity between influenza strains, we design a novel statistical method, which uses a theoretical model and clinical data on attack rates and vaccine efficacy among school children for two seasons after the 1968 A/H3N2 influenza pandemic. This model incorporates the distribution of susceptibility and the dependence of cross-immunity on the antigenic distance of drifted strains. We find that the cross-immunity between an influenza strain and the mutant that causes the next epidemic is 88%. Our method also gives estimates of the vaccine protection against the vaccinating strain, and the basic reproduction number of the 1968 pandemic influenza.     

Cross-immunity, invasion and coexistence of pathogen strains in epidemiological models with one-dimensional antigenic space

Several epidemic models with many co-circulating strains have shown that partial cross-immunity between otherwise identical strains of a pathogen can lead to exclusion of a subset of the strains. Here we examine the mechanisms behind these solutions by considering a host population in which two strains are endemic and ask when it can be invaded by a third strain. If the function relating antigenic distance to cross-immunity is strictly concave or linear invasion is always possible. If the function is strictly convex and has an initial gradient of zero invasion depends on the degree of antigenic similarity between strains and the basic reproductive number. Examining specific concave and convex functions shows that the shape of the cross-immunity function affects the role of secondary infections in invasion. The basic reproductive number affects the importance of tertiary infections. Thus the form of the relationship between antigenic distance and cross-immunity determines whether the pathogen population will consist of an unstructured cloud of strains or a limited number of strains with strong antigenic structuring. In the latter case the basic reproductive number determines the maximum number of strains that can coexist. Analysis of the evolutionary trajectory shows that attaining the maximum diversity requires large spontaneous changes in antigenic structure and cannot result from a sequence of small point mutations alone.     

Coexistence conditions for strains of influenza with immune cross-reaction

The accumulation of cross-immunity in the host population is an important factor driving the antigenic evolution of viruses such as influenza A. Mathematical models have shown that the strength of temporary non-specific cross-immunity and the basic reproductive number are both key determinants for evolutionary branching of the antigenic phenotype. Here we develop deterministic and stochastic versions of one such model. We examine how the time of emergence or introduction of a novel strain affects co-existence with existing strains and hence the initial establishment of a new evolutionary branch. We also clarify the roles of cross-immunity and the basic reproductive number in this process. We show that the basic reproductive number is important because it affects the frequency of infection, which influences the long term immune profile of the host population. The time at which a new strain appears relative to the epidemic peak of an existing strain is important because it determines the environment the emergent mutant experiences in terms of the short term immune profile of the host population. Strains are more likely to coexist, and hence to establish a new clade in the viral phylogeny, when there is a significant time overlap between their epidemics. It follows that the majority of antigenic drift in influenza is expected to occur in the earlier part of each transmission season and this is likely to be a key surveillance period for detecting emerging antigenic novelty.     

Multi-species patterns of avian cholera mortality in Nebraska's Rainwater Basin

Nebraska's Rainwater Basin (RWB) is a key spring migration area for millions of waterfowl and other avian species. Avian cholera has been endemic in the RWB since the 1970s and in some years tens of thousands of waterfowl have died from the disease. We evaluated patterns of avian cholera mortality in waterfowl species using the RWB during the last quarter of the 20th century. Mortality patterns changed between the years before (1976-1988) and coincident with (1989-1999) the dramatic increases in lesser snow goose abundance and mortality. Lesser snow geese (Chen caerulescens caerulescens) have commonly been associated with mortality events in the RWB and are known to carry virulent strains of Pasteurella multocida, the agent causing avian cholera. Lesser snow geese appeared to be the species most affected by avian cholera during 1989-1999; however, mortality in several other waterfowl species was positively correlated with lesser snow goose mortality. Coincident with increased lesser snow goose mortality, spring avian cholera outbreaks were detected earlier and ended earlier compared to 1976-1988. Dense concentrations of lesser snow geese may facilitate intraspecific disease transmission through bird-to-bird contact and wetland contamination. Rates of interspecific avian cholera transmission within the waterfowl community, however, are difficult to determine.     

Cholera Threat to Humans in Ghana Is Influenced by Both Global and Regional Climatic Variability

Cholera, an acute diarrheal illness, is caused by infection of the intestine with the bacterium Vibrio cholerae after ingestion of contaminated water or food. The disease had disappeared from most of the developed countries in the last 50 years, but cholera epidemics remain a major public health problem in many developing countries, most often localized in tropical areas. Cholera is an infectious disease for which a relationship between disease temporal patterns and climate has been demonstrated, but only in an endemic context and for local areas of Asia and South America. Until now, similar studies have not been done in an epidemic context, on the African continent, although the largest number of cholera cases has been reported for those countries by the World Health Organization. The wavelet method was used in order to explore periodicity in (i) a long-time monthly cholera incidence in Ghana, West Africa, (ii) proxy environmental variables, and (iii) climatic indices time series, from 1975 to 1995. Cross-analysis were done to explore links between these time series, i.e., between cholera and climate. Results showed strong statistical association (coherency) from the end of the 1980s, between cholera outbreak resurgences in Ghana and the climatic/environmental parameters under scrutiny. Further examination of the existence of common spatial and temporal patterns in infectious diseases on the continent of Africa will permit development of more effective treatment of disease.     

On the determinants of population structure in antigenically diverse pathogens

Many pathogens exhibit antigenic diversity and elicit strain-specific immune responses. This potential for cross-immunity structure in the host resource motivates the development of mathematical models, stressing competition for susceptible hosts in driving pathogen population dynamics and genetics. Here we establish that certain model formulations exhibit characteristics of prototype pattern-forming systems, with pathogen population structure emerging as three possible patterns: (i) incidence is steady and homogeneous; (ii) incidence is steady but heterogeneous; and (iii) incidence shows oscillatory dynamics, with travelling waves in strain-space. Results are robust to strain number, but sensitive to the mechanism of cumulative immunity.     

Localized contacts between hosts reduce pathogen diversity

We investigate the dynamics of a simple epidemiological model for the invasion by a pathogen strain of a population where another strain circulates. We assume that reinfection by the same strain is possible but occurs at a reduced rate due to acquired immunity. The rate of reinfection by a distinct strain is also reduced due to cross-immunity. Individual based simulations of this model on a 'small-world' network show that the proportion of local contacts in the host contact network structure significantly affects the outcome of such an invasion, and as a consequence will affect the patterns of pathogen evolution. In particular, hosts interacting through a 'small-world' network of contacts support lower prevalence of infection than well-mixed populations, and the region in parameter space for which an invading strain can become endemic and coexist with the circulating strain is smaller, reducing the potential to accommodate pathogen diversity. We discuss the underlying mechanisms for the reported effects, and we propose an effective mean-field model to account for the contact structure of the host population in 'small-world' networks.     

The onset of oscillatory dynamics in models of multiple disease strains

 We examine a generalised SIR model for the infection dynamics of four competing disease strains. This model contains four previously-studied models as special cases. The different strains interact indirectly by the mechanism of cross-immunity; individuals in the host population may become immune to infection by a particular strain even if they have only been infected with different but closely related strains. Several different models of cross-immunity are compared in the limit where the death rate is much smaller than the rate of recovery from infection. In this limit an asymptotic analysis of the dynamics of the models is possible, and we are able to compute the location and nature of the Takens–Bogdanov bifurcation associated with the presence of oscillatory dynamics observed by previous authors. Received: 5 December 2001 / Revised version: 5 May 2002 / Published online: 17 October 2002 Keywords or phrases: Infection – Pathogen – Epidemiology – Multiple strains – Cross-immunity – Oscillations – Dynamics – Bifurcations     

Online sequential extreme studentized deviate tests for anomaly detection in streaming data with varying patterns

In the new era of big data, numerous information and technology systems can store huge amounts of streaming data in real time, for example, in server-access logs on web application servers. The importance of anomaly detection in voluminous quantities of streaming data from such systems is rapidly increasing. One of the biggest challenges in the detection task is to carry out real-time contextual anomaly detection in streaming data with varying patterns that are visually detectable but unsuitable for a parametric model. Most anomaly detection algorithms have weaknesses in dealing with streaming time-series data containing such patterns. In this paper, we propose a novel method for online contextual anomaly detection in streaming time-series data using generalized extreme studentized deviates (GESD) tests. The GESD test is relatively accurate and efficient because it performs statistical hypothesis testing but it is unable to handle streaming time-series data. Thus, focusing on streaming time-series data, we propose an online version of the test capable of detecting outliers under varying patterns. We perform extensive experiments with simulated data, syntactic data, and real online traffic data from Yahoo Webscope, showing a clear advantage of the proposed method, particularly for analyzing streaming data with varying patterns.

     

Molecular Epidemiology of Vibrio cholerae O1 Isolated from Sporadic Cholera Cases in Okinawa,Japan

In July 1994, 6 cholera cases due to Vibrio cholerae O1 El Tor Ogawa sporadically appeared in Okinawa. All 6 patients had no history of traveling abroad. In the period of this cholera outbreak, a strain of V. cholerae O1 El Tor Ogawa was detected from an imported fish at the Naha port quarantine station. The isolates were characterized to clarify whether or not, they belonged to a common clone. Phenotypes were identical except that one strain revealed cured Celebes and the others were original Celebes in kappa phage typing. The restriction fragment patterns of DNA of the isolates hybridized with an enzyme-labeled oligonucleotide probe for cholera toxin gene (ctx) were identical. Randomly amplified polymorphic DNA of the isolates were identical when a primer was used, but 2 patterns were seen when another primer was used. Pulsed-field gel electrophoresis of the chromosomal DNA digested with NotI restriction enzyme showed 3 patterns. The DNA fragment pattern of the strain isolated from the imported fish was different from the clinical isolates. These results suggested that there was no epidemiological relation among the strains of V. cholerae O1 isolated during this period.     

The cement of medical thought. Evolutionary emergence and downward causation.

The aetio-pathogenetic sequences and the physio-pathological patterns of diabetes, emphysema, cholera, circulatory shock and thrombosis have been analysed with respect to an evolutionary interpretation. The diseases, although reflecting alterations of processes that can always be described in physico-chemical language, occur only at the level of biological systems which reflects the decodification of genomic project: the teleonomic projects that have been developed during evolution. The concepts of evolutionary emergence and of downward causation have been used to discuss the relationship between the molecular events responsible for the initiation of the disease, and the subsequent events responsible for the aetio-pathogenesis, for the systemic disarrangement and for the additional alterations of tissues and cells independent of the initial molecular events. In diabetes the systemic disarrangement, glycosuria and hyperglycemia, reflect the evolutionary emergence of the processes regulating carbohydrate metabolism, whereas the cardiovascular and neurological alterations are effects of the systemic disarrangement by a mechanism of downward causation. The complexity of the aetio-pathogenesis and of the physio-pathological patterns of diseases is due to the generation of information during the evolution of multi-hierarchical entities. The evolutionary epistemology approach is useful to explain the behaviour of complex systems.