Antigenic distance and cross-immunity, invasibility and coexistence of pathogen strains in an epidemiological model with discrete antigenic space

Evolution of pathogens with cross-immunity in response to healthcare interventions

Cross-immunity, as an evolutionary driver, can contribute to pathogen evolution, particularly pathogen diversity. Healthcare interventions aimed at reducing disease severity or transmission are commonly used to control diseases and can also induce pathogen evolution. Understanding pathogen evolution in the context of cross-immunity and healthcare interventions is crucial for infection control. This study starts by modelling cross-immunity, the extent of which is determined by strain traits and host characteristics. Given that all hosts have the same characteristics, full cross-immunity between residents and mutants occurs when mutation step sizes are small enough. Cross-immunity can be partial when the step size is large. The presence of partial cross-immunity reduces pathogen load and shortens the infectious period inside hosts, reducing transmission between hosts and improving host population survival and recovery. This study focuses on how pathogens evolve through small and large mutational steps and how healthcare interventions affect pathogen evolution. Using the theory of adaptive dynamics, we found that when mutational steps are small (only full cross-immunity is present), pathogen diversity cannot occur because it maximises the basic reproduction number. This results in intermediate values for both pathogen growth and clearance rates. However, when large mutational steps are allowed (with full and partial cross-immunity present), pathogens can evolve into multiple strains and induce pathogen diversity. The study also shows that different healthcare interventions can have varying effects on pathogen evolution. Generally, low levels of intervention are more likely to induce strain diversity, while high levels are more likely to result in strain reduction.

Host immunity and pathogen diversity: A computational study

The distinctive features of human influenza A phylogeny have inspired many mathematical and computational studies of viral infections spreading in a host population, but our understanding of the mechanisms that shape the coupled evolution of host immunity, disease incidence and viral antigenic properties is far from complete. In this paper we explore the epidemiology and the phylogeny of a rapidly mutating pathogen in a host population with a weak immune response, that allows re-infection by the same strain and provides little cross-immunity. We find that mutation generates explosive diversity and that, as diversity grows, the system is driven to a very high prevalence level. This is in stark contrast with the behavior of similar models where mutation gives rise to a large epidemic followed by disease extinction, under the assumption that infection with a strain provides lifelong immunity. For low mutation rates, the behavior of the system shows the main qualitative features of influenza evolution. Our results highlight the importance of heterogeneity in the human immune response for understanding influenza A phenomenology. They are meant as a first step toward computationally affordable, individual based models including more complex host-pathogen interactions.

The coexistence or replacement of two subtypes of influenza

A pandemic subtype of influenza A sometimes replaces but sometimes coexists with the previous seasonal subtype. For example, the 1957 pandemic subtype H2N2 replaced the seasonal subtype H1N1; whereas after 1977 subtypes H1N1 (from the pandemic) and H3N2 continue to coexist. In an attempt to understand these alternatives, a hybrid model for the dynamics of influenza A is formulated. During an epidemic season the model takes into account cross-immunity of strains depending on the most recent seasonal infection. This cross-immunity reduces susceptibility to related strains of the seasonal subtype, and wanes with time due to virus drift. The population is assumed to reach an equilibrium distribution in susceptibility after several seasons, and then a pandemic subtype appears. Individuals who have been infected by the seasonal subtype all have the same cross-immunity to the pandemic subtype. A combination of theoretical and numerical analyses shows that for very strong cross-immunity between the subtypes the pandemic cannot invade, whereas for strong and weak cross-immunity there is coexistence for the season following the pandemic, and for intermediate levels of cross-immunity the pandemic may replace the seasonal subtype. This replacement depends on the basic reproduction numbers of seasonal and pandemic influenza. Vaccination against the seasonal subtype is found to slightly increase this range for pandemic replacement, with the range increasing with increasing vaccine protection and with the length of time that vaccine-induced immunity lasts.

Capturing the dynamics of pathogens with many strains

Pathogens that consist of multiple antigenic variants are a serious public health concern. These infections, which include dengue virus, influenza and malaria, generate substantial morbidity and mortality. However, there are considerable theoretical challenges involved in modelling such infections. As well as describing the interaction between strains that occurs as a result cross-immunity and evolution, models must balance biological realism with mathematical and computational tractability. Here we review different modelling approaches, and suggest a number of biological problems that are potential candidates for study with these methods. We provide a comprehensive outline of the benefits and disadvantages of available frameworks, and describe what biological information is preserved and lost under different modelling assumptions. We also consider the emergence of new disease strains, and discuss how models of pathogens with multiple strains could be developed further in future. This includes extending the flexibility and biological realism of current approaches, as well as interface with data.

Characterization of the endemic equilibrium and response to mutant injection in a multi-strain disease model

We explore a model of an antigenically diverse infection whose otherwise identical strains compete through cross-immunity. We assume that individuals may produce upon infection different numbers of antibody types, each of which matches the antigenic configuration of a particular epitope, and that one matching antibody type grants total immunity against a challenging strain. In order to reduce the number of equations involved in the analytic description of the dynamics, we follow the strategy proposed by Kryazhimskiy et al. (2007) and apply a low-order closure reminiscent of a pair approximation. Using this approximation, we go beyond the numerical studies of Kryazhimskiy et al. (2007) and explore the analytic properties of the ensuing model in the absence of mutation. We characterize its endemic equilibrium, comparing with the results of agent based simulations of the full model to assess the performance of the closure assumption. We show that a particular choice of immune response leads to a degenerate endemic equilibrium, where different strain prevalences may exist, breaking the symmetry of the model. Finally we study the behavior of the system under the injection of mutant strains. We find that the build up of diversity from a single founding strain is extremely unlikely for different choices of the population׳s immune response.

Anaplasma marginale superinfection attributable to pathogen strains with distinct genomic backgrounds

Strain superinfection occurs when a second pathogen strain infects a host already infected with a primary strain. The selective pressures that drive strain divergence, which underlies superinfection, and allow penetration of a new strain into a host population are critical knowledge gaps relevant to shifts in infectious disease epidemiology. In regions of endemicity with a high prevalence of infection, broad population immunity develops against Anaplasma marginale, a highly antigenically variant rickettsial pathogen, and creates strong selective pressure for emergence of and superinfection with strains that differ in their Msp2 variant repertoires. The strains may emerge either by msp2 locus duplication and allelic divergence on an existing genomic background or by introduction of a strain with a different msp2 allelic repertoire on a distinct genomic background. To answer this question, we developed a multilocus typing assay based on high-throughput sequencing of non-msp2 target loci to distinguish among strains with different genomic backgrounds. The technical error level was statistically defined based on the percentage of perfect sequence matches of clones of each target locus and validated using experimental single strains and strain pairs. Testing of A. marginale-positive samples from tropical regions where A. marginale infection is endemic identified individual infections that contained unique alleles for all five targeted loci. The data revealed a highly significant difference in the number of strains per animal in the tropical regions compared to infections in temperate regions and strongly supported the hypothesis that transmission of genomically distinct A. marginale strains predominates in high-prevalence areas of endemicity.

Expansion of variant diversity associated with a high prevalence of pathogen strain superinfection under conditions of natural transmission

Superinfection occurs when a second, genetically distinct pathogen strain infects a host that has already mounted an immune response to a primary strain. For antigenically variant pathogens, the primary strain itself expresses a broad diversity of variants over time. Thus, successful superinfection would require that the secondary strain express a unique set of variants. We tested this hypothesis under conditions of natural transmission in both temperate and tropical regions where, respectively, single-strain infections and strain superinfections of the tick-borne pathogen Anaplasma marginale predominate. Our conclusion that strain superinfection is associated with a significant increase in variant diversity is supported by progressive analysis of variant composition: (i) animals with naturally acquired superinfection had a statistically significantly greater number of unique variant sequences than animals either experimentally infected with single strains or infected with a single strain naturally, (ii) the greater number of unique sequences reflected a statistically significant increase in primary structural diversity in the superinfected animals, and (iii) the increase in primary structural diversity reflected increased combinations of the newly identified hypervariable microdomains. The role of population immunity in establishing temporal and spatial patterns of infection and disease has been well established. The results of the present study, which examined strain structure under conditions of natural transmission and population immunity, support that high levels of endemicity also drive pathogen divergence toward greater strain diversity.

Age profile of immunity to influenza: effect of original antigenic sin

When multiple infections are possible during an individual's lifetime, as with influenza, a host's history of infection and immunity will determine the result of future exposures. In turn, the suite of varying individual infection histories will shape the population level dynamics of the disease. Exploring the consequences of precisely how immunity is acquired using mathematical models has proven challenging though: if n strains have circulated previously, there are 2(n) combinations of past infection to consider. However, by using an age-structured mathematical model of a disease with multiple strains, we can examine the population immune profile without explicitly keeping track of all possible infection histories. This framework allows previously unknown consequences of assumptions about immune acquisition to be observed. In particular, we see that 'original antigenic sin' can reduce immunity in some age groups: these immune blind spots could be responsible for the unexpectedly high severity of certain past influenza epidemics.

The impact of seasonal and year-round transmission regimes on the evolution of influenza A virus

Punctuated antigenic change is believed to be a key element in the evolution of influenza A; clusters of antigenically similar strains predominate worldwide for several years until an antigenically distant mutant emerges and instigates a selective sweep. It is thought that a region of East-Southeast Asia with year-round transmission acts as a source of antigenic diversity for influenza A and seasonal epidemics in temperate regions make little contribution to antigenic evolution. We use a mathematical model to examine how different transmission regimes affect the evolutionary dynamics of influenza over the lifespan of an antigenic cluster. Our model indicates that, in non-seasonal regions, mutants that cause significant outbreaks appear before the peak of the wild-type epidemic. A relatively large proportion of these mutants spread globally. In seasonal regions, mutants that cause significant local outbreaks appear each year before the seasonal peak of the wild-type epidemic, but only a small proportion spread globally. The potential for global spread is strongly influenced by the intensity of non-seasonal circulation and coupling between non-seasonal and seasonal regions. Results are similar if mutations are neutral, or confer a weak to moderate antigenic advantage. However, there is a threshold antigenic advantage, depending on the non-seasonal transmission intensity, beyond which mutants can escape herd immunity in the non-seasonal region and there is a global explosion in diversity. We conclude that non-seasonal transmission regions are fundamental to the generation and maintenance of influenza diversity owing to their epidemiology. More extensive sampling of viral diversity in such regions could facilitate earlier identification of antigenically novel strains and extend the critical window for vaccine development.

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.