Using dimension reduction to improve outbreak predictability of multistrain diseases

Multistrain diseases have multiple distinct coexisting serotypes (strains). For some diseases, such as dengue fever, the serotypes interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but contact with a second serotype leads to higher viral load and greater infectivity. We present and analyze a dynamic compartmental model for multiple serotypes exhibiting ADE. Using center manifold techniques, we show how the dynamics rapidly collapses to a lower dimensional system. Using the constructed reduced model, we can explain previously observed synchrony between certain classes of primary and secondary infectives (Schwartz et al. in Phys Rev E 72:066201, 2005). Additionally, we show numerically that the center manifold equations apply even to noisy systems. Both deterministic and stochastic versions of the model enable prediction of asymptomatic individuals that are difficult to track during an epidemic. We also show how this technique may be applicable to other multistrain disease models, such as those with cross-immunity.     

Of mice and men: asymmetric interactions between Bordetella pathogen species

In a recent experiment, we found that mice previously infected with Bordetella pertussis were not protected against a later infection with Bordetella parapertussis, while primary infection with B. parapertussis conferred cross-protection. This challenges the common assumption made in most mathematical models for pathogenic strain dynamics that cross-immunity between strains is symmetric. Here we investigate the potential consequences of this pattern on the circulation of the two pathogens in human populations. To match the empirical dominance of B. pertussis, we made the additional assumption that B. parapertussis pays a cost in terms of reduced fitness. We begin by exploring the range of parameter values that allow the coexistence of the two pathogens, with or without vaccination. We then track the dynamics of the system following the introduction of anti-pertussis vaccination. Our results suggest that (1) in order for B. pertussis to be more prevalent than B. parapertussis, the former must have a strong competitive advantage, possibly in the form of higher infectivity, and (2) because of asymmetric cross-immunity, the introduction of anti-pertussis vaccination should have little effect on the absolute prevalence of B. parapertussis. We discuss the evidence supporting these predictions, and the potential relevance of this model for other pathogens.     

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.     

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.     

Isolation and characterization of Escherichia coli strains producing microcins of B and C types

Abstract A screening of 11956 enterobacteria isolates resulted in selection of seven active microcin-producing strains. The microcins were shown to be peptides or their derivatives with a rather broad spectrum of activity, mainly against Gram-negative bacteria. According to cross-immunity criteria, the microcins studied belonged to two of the previously suggested types, B (five strains) and C (two strains). Those of type B could be further classified into two subtypes on the account of differences in the spectrum of antibacterial activity. In five cases out of seven the microcin-producing ability has been attributed to plasmids that the strains harboured. The effect of microcins on sensitive cells was shown to depend on ompR and ompF gene products.     

Evidence that colicin X is microcin B17.

The DNA replication inhibitor microcin B17 is a peptide antibiotic produced by Escherichia coli strains carrying plasmid pMccB17. Here we present evidence that antibiotic activities previously named colicin X are probably identical to microcin B17. Our results include comparison of the conditions of production of the antibiotics, their mode of action, cross-immunity of producer strains, and cross-resistance of resistant mutants. Plasmids encoding colicin X have been identified and shown to have a region of significant homology with the microcin B17-producing region of pMccB17 DNA.     

Phenotypic and genetic features of Escherichia coli strains showing simultaneous expression of localized and diffuse adherence

We have previously shown that some Escherichia coli strains isolated from children with diarrhea present the so-called 'localized and diffused adherence (LA/DA) pattern' in which both localized adherence (LA) and diffused adherence (DA) are expressed simultaneously. In the present study, we show that the LA adherence of these strains is genetically and phenotypically similar to that so far described for enteropathogenic E. coli (EPEC) as determined by DNA hybridization and electron microscopy. On the other hand, the DA is encoded by genes not homologous to the DAEC or AIDA-I DNA probes. In addition, the LA/DA strains are able to invade eukaryotic cells both in vitro and in vivo. In the rabbit ileal loop assay their invasion capacity goes beyond the enterocyte and reaches the muscularis mucosae as determined by transmission electron microscopy. These findings suggest that the LA/DA adherence pattern may be linked to a new E. coli virulence category which in the case of the strains studied may be associated to other virulence traits that enable them to more deeply invade the intestinal mucosa.     

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     

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.     

Consequences of host heterogeneity, epitope immunodominance, and immune breadth for strain competition

Consumer-resource dynamics of hosts with their pathogens are modulated by complex interactions between various branches of hosts’ immune systems and the imperfectly perceived pathogen. Multistrain SIR models tend to sweep competitive interaction terms between different pathogen strains into a single parameter representing cross-immunity. After reviewing several hypotheses about the generation of immune responses, we look into the consequences of assuming that hosts with identical immune repertoires respond to new pathogens identically. In particular, we vary the breadth of the typical immune response, or the average number of pathogen epitopes a host perceives, and the probability of perceiving a particular epitope. The latter quantity in our model is equivalent both to the degree of diversity in host responses at the population level and the relative immunodominance of different epitopes. We find that a sharp transition to strain coexistence occurs as host responses become narrow or skewed toward one epitope. Increasing the breadth of the immune response and the immunogenicity of different epitopes typically increases the range of cross-immunity values in which chaotic strain dynamics and competitive exclusion occur. Models attempting to predict the outcomes of strain competition should thus consider the potential diversity and specificity of hosts’ responses to infection.     

The impact of cross-immunity, mutation and stochastic extinction on pathogen diversity

We examine the dynamics of antigenically diverse infectious agents using a mathematical model describing the transmission dynamics of arbitrary numbers of pathogen strains, interacting via cross-immunity, and in the presence of mutations generating new strains and stochastic extinctions of existing ones. Equilibrium dynamics fall into three classes depending on cross-immunity, transmissibility and host population size: systems where global extinction is likely, stable single-strain persistence, and multiple-strain persistence with stable diversity. Where multi-strain dynamics are stable, a diversity threshold region separates a low-prevalence, low-diversity region of parameter space from a high-diversity, high-prevalence region. The location of the threshold region is determined by the reproduction number of the pathogen and the intensity of cross-immunity, with the sharpness of the transition being determined by the manner in which immunity accrues with repeated infections. Host population size and cross-immunity are found to be the most decisive factors in determining pathogen diversity. While the model framework developed is simplified, we show that it can capture essential aspects of the complex evolutionary dynamics of pathogens such as influenza.     

Wolbachia bacteria effects after experimental interspecific transfers in terrestrial isopods.

Wolbachia bacteria are intracellular parasites, vertically transmitted from mothers to offspring through the cytoplasm of the eggs. They manipulate the reproduction of their hosts to increase in frequency in host populations. In terrestrial isopods for example, Wolbachia are responsible for the full feminization of putative males, therefore increasing the proportion of females, the sex by which they are transmitted. Vertical transmission, however, is not the only means for Wolbachia propagation. Infectious (i.e., horizontal) transmission between different host species or taxa is required to explain the fact that the phylogeny of Wolbachia does not parallel that of their hosts. The aim of this study was to investigate, by experimental transinfections, whether Wolbachia strains could be successfully transferred to a different, previously uninfected isopod host. While Wolbachia survived in all the studied recipient species, vertical transmission was efficient only in cases where donor and recipient species were closely related. Even in this case, Wolbachia strains did not always keep their ability to entirely feminize their host, a deficiency that can be link to a low bacterial density in the host tissues. In addition, Wolbachia infection was associated with a decrease in host fertility, except when the bacterial strain came from the same host population as the recipient animals. This suggest that Wolbachia could be adapted to local host populations. It therefore seems that isopod Wolbachia are highly adapted to their host and can hardly infect another species of hosts. The successful infection of a given Wolbachia strain into a new isopod host species therefore probably requires a strong selection on bacterial variants.     

Influenza emergence in the face of evolutionary constraints

Different influenza subtypes can evolve at very different rates, but the causes are not well understood. In this paper, we explore whether differences in transmissibility between subtypes can play a role if there are fitness constraints on antigenic evolution. We investigate the problem using a mathematical model that separates the interaction of strains through cross-immunity from the process of emergence for new antigenic variants. Evolutionary constraints are also included with antigenic mutation incurring a fitness cost. We show that the transmissibility of a strain can become disproportionately important in dictating the rate of antigenic drift: strains that spread only slightly more easily can have a much higher rate of emergence. Further, we see that the effect continues when vaccination is considered; a small increase in the rate of transmission can make it much harder to control the frequency at which new strains emerge. Our results not only highlight the importance of considering both transmission and fitness constraints when modelling influenza evolution, but may also help in understanding the differences between the emergence of H1N1 and H3N2 subtypes.     

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.     

Immunization of guinea pigs with Neisseria gonorrhoeae: strain specificity and mechanisms of immunity.

Infection of subcutaneusly implanted chambers in guinea pigs conferred immunity against homologous infection of other chambers in the same animals. However, attempts to immunize guinea pigs by subcutaneous injection of filtered fluid from infected chambers, or with small doses of formalin-killed, chamber gonococci were not successful. Thus, neither organisms grown in vivo nor their extracellular products appeared to be exceptionally immunogenic. In immunizing tests with different isolates of gonococci adapted to growth in guinea-pig chambers, cross-immunity to chamber infection with low challenge doses was detected only between two of six isolates. The killing of gonococci in chambers of immunized animals, which occurred only after homologous challenge or with the heterologous strain showing cross-immunity, was not due primarily to humoral factors in the chamber fluid but probably to an enhanced effectiveness of phagocytosis. The serum of immunized animals was bactericidal for homologous strains and for the strain showing cross-immunity but not for strains showing no cross-immunity. Hence, serum bactericidal activity might be a useful indicator for investigating the specificity of immunity produced by different gonococcal strains.     

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.     

Widespread Wolbachia infection in terrestrial isopods and other crustaceans

Wolbachia bacteria are obligate intracellular alpha-Proteobacteria of arthropods and nematodes. Although widespread among isopod crustaceans, they have seldom been found in non-isopod crustacean species. Here, we report Wolbachia infection in fourteen new crustacean species. Our results extend the range of Wolbachia infections in terrestrial isopods and amphipods (class Malacostraca). We report the occurrence of two different Wolbachia strains in two host species (a terrestrial isopod and an amphipod). Moreover, the discovery of Wolbachia in the goose barnacle Lepas anatifera (subclass Thecostraca) establishes Wolbachia infection in class Maxillopoda. The new bacterial strains are closely related to B-supergroup Wolbachia strains previously reported from crustacean hosts. Our results suggest that Wolbachia infection may be much more widespread in crustaceans than previously thought. The presence of related Wolbachia strains in highly divergent crustacean hosts suggests that Wolbachia endosymbionts can naturally adapt to a wide range of crustacean hosts. Given the ability of isopod Wolbachia strains to induce feminization of genetic males or cytoplasmic incompatibility, we speculate that manipulation of crustacean-borne Wolbachia bacteria might represent potential tools for controlling crustacean species of commercial interest and crustacean or insect disease vectors.     

Host switching vs. host sharing in overlapping sylvatic Trypanosoma cruzi transmission cycles

ABSTRACT

The principle of competitive exclusion is well established for multiple populations competing for the same resource, and simple models for multistrain infection exhibit it as well when cross-immunity precludes coinfections. However, multiple hosts provide niches for different pathogens to occupy simultaneously. This is the case for the vector-borne parasite Trypanosoma cruzi in overlapping sylvatic transmission cycles in the Americas, where it is enzootic. This study uses cycles in the USA involving two different hosts but the same vector species as a context for the study of the mechanisms behind the communication between the two cycles. Vectors dispersing in search of new hosts may be considered to move between the two cycles (host switching) or, more simply, to divide their time between the two host types (host sharing). Analysis considers host switching as an intermediate case between isolated cycles and intermingled cycles (host sharing) in order to examine the role played by the host-switching rate in permitting coexistence of multiple strains in a single-host population. Results show that although the population dynamics (demographic equilibria) in host-switching models align well with those in the limiting models (host sharing or isolated cycles), infection dynamics differ significantly, in ways that sometimes illuminate the underlying epidemiology (such as differing host susceptibilities to infection) and sometimes reveal model limitations (such as host switching dominating the infection dynamics). Numerical work suggests that the model explains the trace presence of TcI in raccoons but not the more significant co-persistence observed in woodrats.     

Evolution of antibiotic resistance by human and bacterial niche construction

Antibiotic treatment by humans generates strong viability selection for antibiotic-resistant bacterial strains. The frequency of host antibiotic use often determines the strength of this selection, and changing patterns of antibiotic use can generate many types of behaviors in the population dynamics of resistant and sensitive bacterial populations. In this paper, we present a simple model of hosts dimorphic for their tendency to use/avoid antibiotics and bacterial pathogens dimorphic in their resistance/sensitivity to antibiotic treatment. When a constant fraction of hosts uses antibiotics, the two bacterial strain populations can coexist unless host use-frequency is above a critical value; this critical value is derived as the ratio of the fitness cost of resistance to the fitness cost of undergoing treatment. When strain frequencies can affect host behavior, the dynamics may be analyzed in the light of niche construction. We consider three models underlying changing host behavior: conformism, the avoidance of long infections, and adherence to the advice of public health officials. In the latter two, we find that the pathogen can have quite a strong effect on host behavior. In particular, if antibiotic use is discouraged when resistance levels are high, we observe a classic niche-construction phenomenon of maintaining strain polymorphism even in parameter regions where it would not be expected.