Evolution and persistence of influenza A and other diseases

Considering humans as habitat reveals evidence of successional disease ecology among human pathogens

The realization that ecological principles play an important role in infectious disease dynamics has led to a renaissance in epidemiological theory. Ideas from ecological succession theory have begun to inform an understanding of the relationship between the individual microbiome and health but have not yet been applied to investigate broader, population-level epidemiological dynamics. We consider human hosts as habitat and apply ideas from succession to immune memory and multi-pathogen dynamics in populations. We demonstrate that ecologically meaningful life history characteristics of pathogens and parasites, rather than epidemiological features alone, are likely to play a meaningful role in determining the age at which people have the greatest probability of being infected. Our results indicate the potential importance of microbiome succession in determining disease incidence and highlight the need to explore how pathogen life history traits and host ecology influence successional dynamics. We conclude by exploring some of the implications that inclusion of successional theory might have for understanding the ecology of diseases and their hosts.

This study explores the analogy between ecological succession in terrestrial ecosystems and infections in a human-host landscape over time, showing how the ecosystem of long-term multi-pathogen dynamics within and among hosts may be a critical missing consideration in understanding epidemiology.

Pharmacometric analysis of seasonal influenza epidemics and the effect of vaccination using sentinel surveillance data

The identification of influenza epidemics and assessment of the efficacy of vaccination against this infection are major challenges for the implementation of effective public health strategies, such as vaccination programs. In this study, we developed a new pharmacometric model to evaluate the efficacy of vaccination based on infection surveillance data from the 2010/2011 to 2018/2019 influenza seasons in Japan. A novel susceptible‐infected‐removed plus vaccination model, based on an indirect response structure with the effect of vaccination, was applied to describe seasonal influenza epidemics using a preseasonal collection of data regarding serological H₁ antibody titer positivity and the fraction of virus strains. Using this model, we evaluated K_in (a parameter describing the transmission rate of symptomatic influenza infection) for different age groups. Furthermore, we defined a new parameter (prevention factor) showing the efficacy of vaccination against each viral strain and in different age groups. We found that the prevention factor of vaccination against influenza varied among age groups. Notably, children aged 5–14 years showed the highest K_in value during the 10 influenza seasons and the greatest preventive effect of vaccination (prevention factor = 70.8%). The propagation of influenza epidemics varies in different age groups. Children aged 5–14 years most likely play a leading role in the transmission of influenza. Prioritized vaccination in this age group may be the most effective strategy for reducing the prevalence of influenza in the community.

Modeling the Effectiveness of Respiratory Protective Devices in Reducing Influenza Outbreak

Outbreaks of influenza represent an important health concern worldwide. In many cases, vaccines are only partially successful in reducing the infection rate, and respiratory protective devices (RPDs) are used as a complementary countermeasure. In devising a protection strategy against influenza for a given population, estimates of the level of protection afforded by different RPDs is valuable. In this article, a risk assessment model previously developed in general form was used to estimate the effectiveness of different types of protective equipment in reducing the rate of infection in an influenza outbreak. It was found that a 50% compliance in donning the device resulted in a significant (at least 50% prevalence and 20% cumulative incidence) reduction in risk for fitted and unfitted N95 respirators, high-filtration surgical masks, and both low-filtration and high-filtration pediatric masks. An 80% compliance rate essentially eliminated the influenza outbreak. The results of the present study, as well as the application of the model to related influenza scenarios, are potentially useful to public health officials in decisions involving resource allocation or education strategies.

Global dynamics and optimal control of an influenza model with vaccination, media coverage and treatment

In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Furthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission.

Modeling transmission dynamics of Ebola virus disease

Ebola virus disease (EVD) has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynamics of EVD by formulating an SEIR-type transmission model that includes isolated individuals as well as dead individuals that are not yet buried. Dynamical systems analysis of the model is performed, and it is consequently shown that the disease-free steady state is globally asymptotically stable when the basic reproduction number, [Formula: see text] is less than unity. It is also shown that there exists a unique endemic equilibrium when [Formula: see text]. Using optimal control theory, we propose control strategies, which will help to eliminate the Ebola disease. We use data fitting on models, with and without isolation, to estimate the basic reproductive numbers for the 2014 outbreak of EVD in Liberia and Sierra Leone.

Mathematical model of plant-virus interactions mediated by RNA interference

Cross-protection, which refers to a process whereby artificially inoculating a plant with a mild strain provides protection against a more aggressive isolate of the virus, is known to be an effective tool of disease control in plants. In this paper we derive and analyse a new mathematical model of the interactions between two competing viruses with particular account for RNA interference. Our results show that co-infection of the host can either increase or decrease the potency of individual infections depending on the levels of cross-protection or cross-enhancement between different viruses. Analytical and numerical bifurcation analyses are employed to investigate the stability of all steady states of the model in order to identify parameter regions where the system exhibits synergistic or antagonistic behaviour between viral strains, as well as different types of host recovery. We show that not only viral attributes but also the propagating component of RNA-interference in plants can play an important role in determining the dynamics.

Mathematical modeling of tuberculosis data of China

This paper concentrates on the tuberculosis data of China from January 2005 to December 2012. We set up a mathematical model to fit those data with the goodness of fit and obtain the optimal parameter values of the model. By the Chi-square test of the statistical inference, the optimal parameter values of the model are reasonable. We get the effective reproductive number of the disease for each year, and also investigate the preventive measures to control the tuberculosis.

Contact between bird species of different lifespans can promote the emergence of highly pathogenic avian influenza strains

Outbreaks of highly pathogenic strains of avian influenza viruses (AIVs) cause considerable economic losses to the poultry industry and also pose a threat to human life. The possibility that one of these strains will evolve to become transmissible between humans, sparking a major influenza pandemic, is a matter of great concern. Most studies so far have focused on assessing these odds from the perspective of the intrinsic mutability of AIV rather than the ecological constraints to invasion faced by the virus population. Here we present an alternative multihost model for the evolution of AIV in which the mode and tempo of mutation play a limited role, with the emergence of strains being determined instead principally by the prevailing profile of population-level immunity. We show that (i) many of the observed differences in influenza virus dynamics among species can be captured by our model by simply varying host lifespan and (ii) increased contact between species of different lifespans can promote the emergence of potentially more virulent strains that were hitherto suppressed in one of the species.

On the role of resonance in drug failure under HIV treatment interruption

Background

The application of highly active antiretroviral therapy (HAART) against HIV can reduce and maintain viral load below detection limit in many patients. Continuous HAART, however, can have severe side effects. In this context, structured treatment interruptions (STI) were considered to be a promising strategy. However, using CD4 cell count to guide intermittent therapy starting and stopping points, the SMART study (strategies for management of antiretroviral therapy), revealed that STI were associated with increased risk of AIDS and other complications. Additionally, short-term periodic (e.g. one week on / one week off) interruption therapies have shown virus rebound exceeding a given “failure threshold”, without any evidence for the evolution of drug resistance. Currently, the only hypothesis explaining the failure of STI is the “resonance hypothesis”, which posits that treatment failure is due to a resonance effect between the drug treatment and the viral population. In the present study we used a mathematical model to analyse the parameters affecting the output of drug treatment interruption and the premises of the resonance hypothesis.

Methods

We used a population dynamic model of HIV infection. Simulations and analytical approximations of deterministic and stochastic versions of the model were studied.

Results and Conclusion

The present study examines the roles of the most important parameters affecting the viral rebound, responsible for drug failure. We related these findings to the resonance hypothesis, and showed that the degree of sustainability of damping oscillations present in the model after the acute phase is strongly linked to their amplitude, which determines the resonance level. Stochastic simulations of the same model even revealed sustained oscillations in virus population for small virus population sizes. Given that pronounced viral load oscillations have not been observed in HIV-1 patients, the link between oscillations and resonance level suggests that treatment failure due to a resonance effect is not plausible. Moreover, the failure threshold is attained before the virus population crosses the set point while growing. As the maximum virus population is reached even after the set point is crossed, the role of resonance effects in the context of treatment interruptions cannot explain drug failure.

The impact of past epidemics on future disease dynamics

Many pathogens spread primarily via direct contact between infected and susceptible hosts. Thus, the patterns of contacts or contact network of a population fundamentally shape the course of epidemics. While there is a robust and growing theory for the dynamics of single epidemics in networks, we know little about the impacts of network structure on long-term epidemic or endemic transmission. For seasonal diseases like influenza, pathogens repeatedly return to populations with complex and changing patterns of susceptibility and immunity acquired through prior infection. Here, we develop two mathematical approaches for modeling consecutive seasonal outbreaks of a partially-immunizing infection in a population with contact heterogeneity. Using methods from percolation theory we consider both leaky immunity, where all previously infected individuals gain partial immunity, and polarized immunity, where a fraction of previously infected individuals are fully immune. By restructuring the epidemiologically active portion of their host population, such diseases limit the potential of future outbreaks. We speculate that these dynamics can result in evolutionary pressure to increase infectiousness.

MATHEMATICAL MODELING AND ANALYSIS OF THE SPREAD OF CARRIER DEPENDENT INFECTIOUS DISEASES: EFFECTS OF CUMULATIVE DENSITY OF ENVIRONMENTAL FACTORS

In this paper, a nonlinear mathematical model with immigration for carrier dependent infectious diseases is proposed and analyzed by considering explicitly the cumulative effect of environmental factors, which are conducive to the growth of carrier population. It is assumed that the density of carrier population is governed by a general logistic model. It is assumed further that the growth rate per capita and the modified carrying capacity of carrier population increase as the cumulative density of environmental factors, governed by population density dependent growth equation, increases. It is shown that as the parameters governing environmental factors increase, the number of infectives in the population increases. It is also found that due to immigration, the disease becomes more endemic.

Structural basis for norovirus inhibition and fucose mimicry by citrate

Human noroviruses bind with their capsid-protruding domains to histo-blood-group antigens (HBGAs), an interaction thought to direct their entry into cells. Although human noroviruses are the major cause of gastroenteritis outbreaks, development of antivirals has been lacking, mainly because human noroviruses cannot be cultivated. Here we use X-ray crystallography and saturation transfer difference nuclear magnetic resonance (STD NMR) to analyze the interaction of citrate with genogroup II (GII) noroviruses. Crystals of citrate in complex with the protruding domain from norovirus GII.10 Vietnam026 diffracted to 1.4 Å and showed a single citrate bound at the site of HBGA interaction. The citrate interaction was coordinated with a set of capsid interactions almost identical to that involved in recognizing the terminal HBGA fucose, the saccharide which forms the primary conserved interaction between HBGAs and GII noroviruses. Citrate and a water molecule formed a ring-like structure that mimicked the pyranoside ring of fucose. STD NMR showed the protruding domain to have weak affinity for citrate (460 μM). This affinity, however, was similar to the affinities of the protruding domain for fucose (460 μM) and H type 2 trisaccharide (390 μM), an HBGA shown previously to be specifically recognized by human noroviruses. Importantly, competition STD NMR showed that citrate could compete with HBGA for norovirus binding. Together, the results suggest that citrate and other glycomimetics have the potential to block human noroviruses from binding to HBGAs.

Partial immunity and vaccination for influenza

In this article, we estimated the basic reproductive numbers by mathematical modeling and computer simulation using the hospitalization data of influenza type A (H3N2) from the United States as provided by the Centers for Disease Control and Prevention (CDC) from the 2001 to 2006 influenza seasons, respectively. The mean value of basic reproductive number from the 2001-2002 to 2005-2006 influenza seasons is 1.2440, with a 95% confidence interval of 1.1170-1.3710. Our model predicts that the proportion of vaccination of susceptible is 20% and 60 million doses of vaccines should be prepared for each influenza season in the United States. The chi-square test of goodness of fit indicates that our model fits the data reasonably well.

Prevalence of epistasis in the evolution of influenza A surface proteins

The surface proteins of human influenza A viruses experience positive selection to escape both human immunity and, more recently, antiviral drug treatments. In bacteria and viruses, immune-escape and drug-resistant phenotypes often appear through a combination of several mutations that have epistatic effects on pathogen fitness. However, the extent and structure of epistasis in influenza viral proteins have not been systematically investigated. Here, we develop a novel statistical method to detect positive epistasis between pairs of sites in a protein, based on the observed temporal patterns of sequence evolution. The method rests on the simple idea that a substitution at one site should rapidly follow a substitution at another site if the sites are positively epistatic. We apply this method to the surface proteins hemagglutinin and neuraminidase of influenza A virus subtypes H3N2 and H1N1. Compared to a non-epistatic null distribution, we detect substantial amounts of epistasis and determine the identities of putatively epistatic pairs of sites. In particular, using sequence data alone, our method identifies epistatic interactions between specific sites in neuraminidase that have recently been demonstrated, in vitro, to confer resistance to the drug oseltamivir; these epistatic interactions are responsible for widespread drug resistance among H1N1 viruses circulating today. This experimental validation demonstrates the predictive power of our method to identify epistatic sites of importance for viral adaptation and public health. We conclude that epistasis plays a large role in shaping the molecular evolution of influenza viruses. In particular, sites with , which would normally not be identified as positively selected, can facilitate viral adaptation through epistatic interactions with their partner sites. The knowledge of specific interactions among sites in influenza proteins may help us to predict the course of antigenic evolution and, consequently, to select more appropriate vaccines and drugs.

Epistasis describes non-additive interactions among genetic sites: the consequence of a mutation at one site may depend on the status of the genome at other sites. In an extreme case, a mutation may have no effect if it arises on one genetic background, but a strong effect on another background. Epistatic mutations in viruses and bacteria that live under severe conditions, such as antibiotic treatments or immune pressure, often allow pathogens to develop drug resistance or escape the immune system. In this paper we develop a new phylogenetic method for detecting epistasis, and we apply this method to the surface proteins of the influenza A virus, which are important targets of the immune system and drug treatments. The authors identify and characterize hundreds of epistatic mutations in these proteins. Among those identified, we find the specific epistatic mutations that were recently shown, experimentally, to confer resistance to the drug Tamiflu. The results of this study may help to predict the course of influenza's antigenic evolution and to select more appropriate vaccines and drugs.

A minimal model for multiple epidemics and immunity spreading

Pathogens and parasites are ubiquitous in the living world, being limited only by availability of suitable hosts. The ability to transmit a particular disease depends on competing infections as well as on the status of host immunity. Multiple diseases compete for the same resource and their fate is coupled to each other. Such couplings have many facets, for example cross-immunization between related influenza strains, mutual inhibition by killing the host, or possible even a mutual catalytic effect if host immunity is impaired. We here introduce a minimal model for an unlimited number of unrelated pathogens whose interaction is simplified to simple mutual exclusion. The model incorporates an ongoing development of host immunity to past diseases, while leaving the system open for emergence of new diseases. The model exhibits a rich dynamical behavior with interacting infection waves, leaving broad trails of immunization in the host population. This obtained immunization pattern depends only on the system size and on the mutation rate that initiates new diseases.

Sustained oscillations in an evolutionary epidemiological model of influenza A drift

Understanding the seasonal/periodic reoccurrence of influenza will be very helpful in designing successful vaccine programmes and introducing public-health interventions. However, the reasons for seasonal/periodic influenza epidemics are still not clear, even though various explanations have been proposed. In this paper, we study an age-structured type evolutionary epidemiological model of influenza A drift, in which the susceptible class is continually replenished because the pathogen changes genetically and immunologically from one epidemic to the next, causing previously immune hosts to become susceptible. Applying our recently established centre manifold theory for semi-linear equations with non-dense domain, we show that Hopf bifurcation occurs in the model. This demonstrates that the age-structured type evolutionary epidemiological model of influenza A drift has an intrinsic tendency to oscillate owing to the evolutionary and/or immunological changes of the influenza viruses.

Influenza outbreaks

Influenza is a virus that causes considerable morbidity and mortality in human populations every year. This fact, coupled with its perceived pandemic potential, means that influenza features prominently in both scientific literature and the media. In this review we focus on the biological assumptions behind theoretical attempts to understand the seasonal and evolutionary dynamics of influenza through mathematical modelling and suggest that the largely unchallenged dogma upon which most efforts are currently based is sorely lacking.

When domestic cat (Felis silvestris catus) population structures interact with their viruses

Many theoretical studies have proposed different causal mechanisms by which the structure of a host population could have important implications for life history traits of pathogens. However, little information is available from real systems to test these hypotheses. The domestic cat, Felis silvestris catus, whose populations exhibit a great variability in social and spatial structure, represent an ideal case study to assess this question. In the present article, we show how cat population structure may have influenced the evolution of feline viruses and, in return, how these viruses may have modified the genetic structure of cat populations. To cite this article: D. Pontier et al., C. R. Biologies 332 (2009).

The Widespread Evolutionary Significance of Viruses

In the last 30 years, the study of virus evolution has undergone a transformation. Originally concerned with disease and its emergence, virus evolution had not been well integrated into the general study of evolution. This chapter reviews the developments that have brought us to this new appreciation for the general significance of virus evolution to all life. We now know that viruses numerically dominate all habitats of life, especially the oceans. Theoretical developments in the 1970s regarding quasispecies, error rates, and error thresholds have yielded many practical insights into virus–host dynamics. The human diseases of HIV-1 and hepatitis C virus cannot be understood without this evolutionary framework. Yet recent developments with poliovirus demonstrate that viral fitness can be the result of a consortia, not one fittest type, a basic Darwinian concept in evolutionary biology. Darwinian principles do apply to viruses, such as with Fisher population genetics, but other features, such as reticulated and quasispecies-based evolution distinguish virus evolution from classical studies. The available phylogenetic tools have greatly aided our analysis of virus evolution, but these methods struggle to characterize the role of virus populations. Missing from many of these considerations has been the major role played by persisting viruses in stable virus evolution and disease emergence. In many cases, extreme stability is seen with persisting RNA viruses. Indeed, examples are known in which it is the persistently infected host that has better survival. We have also recently come to appreciate the vast diversity of phage (DNA viruses) of prokaryotes as a system that evolves by genetic exchanges across vast populations (Chapter 10). This has been proposed to be the “big bang” of biological evolution. In the large DNA viruses of aquatic microbes we see surprisingly large, complex and diverse viruses. With both prokaryotic and eukaryotic DNA viruses, recombination is the main engine of virus evolution, and virus host co-evolution is common, although not uniform. Viral emergence appears to be an unending phenomenon and we can currently witness a selective sweep by retroviruses that infect and become endogenized in koala bears.

On state-space reduction in multi-strain pathogen models, with an application to antigenic drift in influenza A

Many pathogens exist in phenotypically distinct strains that interact with each other through competition for hosts. General models that describe such multi-strain systems are extremely difficult to analyze because their state spaces are enormously large. Reduced models have been proposed, but so far all of them necessarily allow for coinfections and require that immunity be mediated solely by reduced infectivity, a potentially problematic assumption. Here, we suggest a new state-space reduction approach that allows immunity to be mediated by either reduced infectivity or reduced susceptibility and that can naturally be used for models with or without coinfections. Our approach utilizes the general framework of status-based models. The cornerstone of our method is the introduction of immunity variables, which describe multi-strain systems more naturally than the traditional tracking of susceptible and infected hosts. Models expressed in this way can be approximated in a natural way by a truncation method that is akin to moment closure, allowing us to sharply reduce the size of the state space, and thus to consider models with many strains in a tractable manner. Applying our method to the phenomenon of antigenic drift in influenza A, we propose a potentially general mechanism that could constrain viral evolution to a one-dimensional manifold in a two-dimensional trait space. Our framework broadens the class of multi-strain systems that can be adequately described by reduced models. It permits computational, and even analytical, investigation and thus serves as a useful tool for understanding the evolution and ecology of multi-strain pathogens.

Many important human pathogens, including HIV and influenza viruses, consist of many different “strains,” which elicit distinct immune responses in their hosts. Infection by one variant usually triggers partial cross-immunity against several other variants. This process leads to a complicated and dynamic immunity structure in the host population. Most existing models of a population with a multi-strain pathogen are either very complex, or rely on specific simplifying assumptions. Here, we suggest a new way of simplifying such models that allows for greater flexibility in underlying assumptions. This approach could lead to deeper understanding of the ecology and evolution of multi-strain pathogens. We apply our approach to a simple model of evolution of influenza A that illustrates one hypothesis about how influenza A evolution may be structured.

Stochastic model of an influenza epidemic with drug resistance

A continuous-time Markov chain (CTMC) model is formulated for an influenza epidemic with drug resistance. This stochastic model is based on an influenza epidemic model, expressed in terms of a system of ordinary differential equations (ODE), developed by Stilianakis, N.I., Perelson, A.S., Hayden, F.G., [1998. Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J. Inf. Dis. 177, 863-873]. Three different treatments-chemoprophylaxis, treatment after exposure but before symptoms, and treatment after symptoms appear, are considered. The basic reproduction number, R(0), is calculated for the deterministic-model under different treatment strategies. It is shown that chemoprophylaxis always reduces the basic reproduction number. In addition, numerical simulations illustrate that the basic reproduction number is generally reduced with realistic treatment rates. Comparisons are made among the different models and the different treatment strategies with respect to the number of infected individuals during an outbreak. The final size distribution is computed for the CTMC model and, in some cases, it is shown to have a bimodal distribution corresponding to two situations: when there is no outbreak and when an outbreak occurs. Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated.

Sustained oscillations via coherence resonance in SIR

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation. The agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. The validity criteria for this asymptotic approximation give explicit expressions for the parameter ranges in which one expects to observe this phenomenon.

The reinfection threshold regulates pathogen diversity: the case of influenza

The awareness that pathogens can adapt and evolve over relatively short time-scales is changing our view of infectious disease epidemiology and control. Research on the transmission dynamics of antigenically diverse pathogens is progressing and there is increasing recognition for the need of new concepts and theories. Mathematical models have been developed considering the modelling unit in two extreme scales: either diversity is not explicitly represented or diversity is represented at the finest scale of single variants. Here, we use an intermediate approach and construct a model at the scale of clusters of variants. The model captures essential properties of more detailed systems and is much more amenable to mathematical treatment. Specificities of pathogen clusters and the overall potential for transmission determine the reinfection rates. These are, in turn, important regulators of cluster dynamics. Ultimately, we detect a reinfection threshold (RT) that separates different behaviours along the transmissibility axis: below RT, levels of infection are low and cluster substitutions are probable; while above RT, levels of infection are high and multiple cluster coexistence is the most probable outcome.

Inter-seasonal diversity of norovirus genotypes: Emergence and selection of virus variants

This study describes a method used to determine the diversity of NoVs co-circulating in the community that consisted of the analysis of a limited number of strains collected from outbreaks occurring at different times of the NoV season. The diversity of twenty NoV strains collected from outbreaks occurring at the beginning of each NoV season (September) was compared to the diversity found in the middle (December) and at the end of the season (March). The method was validated through the characterisation of greater numbers of strains at times when novel genotypes or variants were detected. A total of 864 strains from outbreaks of gastroenteritis from the 2003/04, 2004/05 and 2005/06 seasons were genotyped, with the majority of outbreaks occurring in the UK. There was a greater diversity of NoV genotypes at the beginning of two of the three seasons, 2003/04 and 2005/06, when compared to strains circulating at the end of the seasons, and GII-4 NoV strains predominated (>90%) at the end of each season. Data from this study also identified the co-circulation and differentiation of three major GII-4 variants (v2, v3, and v4). Detailed analysis of a larger number of strains throughout each season confirmed that variants emerged, became the predominant circulating strain and were ultimately replaced with another variant selected from a pool of variants. By June 2006, GII-4 v4 (Hu/NoV/Rhyl440/2005/UK) emerged as the predominant GII-4 strain, usurping the previous GII-4 v3 strain [Hu/NoV/Hunter284E/040/AU] to become the commonest co-circulating strain, in the UK in 2006.

Spatiotemporal distributions of reported cases of the avian influenza H5N1 (bird flu) in Southern China in early 2004

This study investigates spatiotemporal distributions of reported cases of the avian influenza H5N1 (bird flu) in Southern China in early 2004. Forty-nine cases of the avian influenza H5N1 covering a 6-week period (January 19, 2004, through March 9, 2004) were compiled from the Chinese Ministry of Agriculture and the World Health Organization. Geographic information systems (GIS) techniques combined with statistical techniques were used to analyze the spatiotemporal variation of reported cases of avian influenza. Using Oden's direction method, we also explored the spatiotemporal interaction of individual-level avian influenza cases during the study duration. The peak period (temporal clustering) for the epidemiological avian influenza outbreak occurred between the third and fourth weeks. Although we observed a major northeast-southwest distribution of the avian influenza H5N1 cases, there was no significant spatiotemporal association in average "direction of advance" of these cases. The directional finding is very consistent with the major migratory bird routes in East Asia, but owing to weak surveillance and reporting systems in the region, the study findings warrant further evaluation.

Gaining insights into human viral diseases through mathematics

Mathematical models have been recognized as powerful tools for providing new insights into the understanding of viral dynamics of human diseases at both the population and cellular levels. This article briefly reviews the role of mathematical models and␣their historical precedents for creating new knowledge of the mechanisms of disease pathogenesis, transmission, and control of some human viral infections. Future research in the modelling of infectious diseases will need to rely upon incorporation of the fundamental principles that govern viral dynamics in vivo as well as in the population.

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.

Genomic classification using an information-based similarity index: application to the SARS coronavirus

Measures of genetic distance based on alignment methods are confined to studying sequences that are conserved and identifiable in all organisms under study. A number of alignment-free techniques based on either statistical linguistics or information theory have been developed to overcome the limitations of alignment methods. We present a novel alignment-free approach to measuring the similarity among genetic sequences that incorporates elements from both word rank order-frequency statistics and information theory. We first validate this method on the human influenza A viral genomes as well as on the human mitochondrial DNA database. We then apply the method to study the origin of the SARS coronavirus. We find that the majority of the SARS genome is most closely related to group 1 coronaviruses, with smaller regions of matches to sequences from groups 2 and 3. The information based similarity index provides a new tool to measure the similarity between datasets based on their information content and may have a wide range of applications in the large-scale analysis of genomic databases.

Detailed analysis of the genetic evolution of influenza virus during the course of an epidemic

The genetic variability of influenza virus is usually studied with sequences selected over numerous years and countries, and rarely within a single season. Here we examined the viral evolution and the correlation between genetic and clinical features during an epidemic. From a French prospective household-based study in 1999-2000, 99 infected patients were randomly selected. The HA1 genomic domain was sequenced. Phylogenetic analysis showed the existence of two groups of A/H3N2 viruses. We found no distinct pattern of genomic evolution within either group according to time. A spatial correlation with the nucleotide distances was shown. The average nucleotide diversity was 3.4x10-3 nucleotides per site, and did not differ between the groups. A lower number of segregating sites was observed in patients who experienced influenza-like symptoms during the previous epidemic. These results suggest that the influenza virus undergoes regular HA1 nucleotide changes, but without clonal expansion of mutant strains within a single epidemic.

A mathematical model for a new mechanism of phenotypic variation in malaria

The Py235 merozoite rhoptry protein of the rodent malaria agent Plasmodium (yoelii) yoeli is encoded by the Py235 multigene family whose members are transcribed during the parasite's asexual life-cycle in a fashion where single schizonts subsequently give rise to sets of merozoites containing distinct Py235 transcripts. Homologues of Py235 are found in other malaria species, and antibodies to both Py235 and P. falciparum homologues inhibit merozoite invasion, suggesting a unique survival strategy involving immune evasion and host adaptation. Using a mathematical approach to model this free-living stage of Plasmodium in interaction with specific antibodies and a heterogeneous red blood cell population, we investigate if, and under what conditions, this mechanism of clonal phenotypic variation can play a role in immune evasion and adaptation to a dynamic erythropoietic environment.

Characterizing the symmetric equilibrium of multi-strain host-pathogen systems in the presence of cross immunity

We investigate the population dynamics of host-pathogen systems in which the pathogen has a potentially arbitrary number of antigenically distinct strains interacting via cross-immunity. The interior equilibrium configuration of the symmetric multiple strain SIR model with cross-immunity is characterized. We develop an efficient iterative method for numerically solving the equilibrium equation together with a number of informative analytical approximations to the full solution. Equilibrium properties are studied as a function of the number of strains, reproduction number, infectious period, and cross immunity profile. We establish that the prevalence in the system increases monotonically with the number of strains and the reduction in cross immunity. Moreover, we demonstrate the existence of a phase transition separating high prevalence and low prevalence parameter regions, with the critical point being defined by sigmaR0 congruent with1, where sigma is the level of cross-immunity and R0 is the reproduction number. Above the threshold, prevalence saturates with increasing numbers of strains as a result of the inclusion of prohibition of co-infection in the model. Below the threshold, prevalence saturates much more rapidly as the number of strains increases--indicating that when cross-protection is sufficiently intense, the selective advantage for a pathogen to increase its diversity is substantially less than in the threshold region. Similarly, there is limited benefit to increased transmissibility (or decreased cross-immunity) both for the high and low diversity pathogen systems compared with systems at the threshold sigmaR0 congruent with1 where small increase in transmissibility can result in significant increase in prevalence.