Demographic buffering: titrating the effects of birth rate and imperfect immunity on epidemic dynamics

Host demography can alter the dynamics of infectious disease. In the case of perfectly immunizing infections, observations of strong sensitivity to demographic variation have been mechanistically explained through analysis of the susceptible–infected–recovered (SIR) model that assumes lifelong immunity following recovery from infection. When imperfect immunity is incorporated into this framework via the susceptible–infected–recovered–susceptible (SIRS) model, with individuals regaining full susceptibility following recovery, we show that rapid loss of immunity is predicted to buffer populations against the effects of demographic change. However, this buffering is contrary to the dependence on demography recently observed for partially immunizing infections such as rotavirus and respiratory syncytial virus. We show that this discrepancy arises from a key simplification embedded in the SIR(S) framework, namely that the potential for differential immune responses to repeat exposures is ignored. We explore the minimum additional immunological information that must be included to reflect the range of observed dependencies on demography. We show that including partial protection and lower transmission following primary infection is sufficient to capture more realistic reduced levels of buffering, in addition to changes in epidemic timing, across a range of partially and fully immunizing infections. Furthermore, our results identify key variables in this relationship, including R₀.     

The control of sea lice in Atlantic salmon by selective breeding

Sea lice threaten the welfare of farmed Atlantic salmon and the sustainability of fish farming across the world. Chemical treatments are the major method of control but drug resistance means that alternatives are urgently needed. Selective breeding can be a cheap and effective alternative. Here, we combine experimental trials and diagnostics to provide a practical protocol for quantifying resistance to sea lice. We then combined quantitative genetics with epidemiological modelling to make the first prediction of the response to selection, quantified in terms of reduced need for chemical treatments. We infected over 1400 young fish with Lepeophtheirus salmonis, the most important species in the Northern Hemisphere. Mechanisms of resistance were expressed early in infection. Consequently, the number of lice per fish and the ranking of families were very similar at 7 and 17 days post infection, providing a stable window for assessing susceptibility to infection. The heritability of lice numbers within this time window was moderately high at 0.3, confirming that selective breeding is viable. We combined an epidemiological model of sea lice infection and control on a salmon farm with genetic variation in susceptibility among individuals. We simulated 10 generations of selective breeding and examined the frequency of treatments needed to control infection. Our model predicted that substantially fewer chemical treatments are needed to control lice outbreaks in selected populations and chemical treatment could be unnecessary after 10 generations of selection. Selective breeding for sea lice resistance should reduce the impact of sea lice on fish health and thus substantially improve the sustainability of Atlantic salmon production.     

The dynamic influence of genetic variation on the susceptibility of sheep to gastrointestinal nematode infection.

The interaction between sheep and the nematode Teladorsagia circumcincta is one of the best understood of all host-parasite interactions. Following infection, there is considerable variation among lambs in the number of nematode eggs produced, the number of early fourth-stage larvae and the number of adult worms in the mucosa. These traits have a high variance to mean ratio (i.e. they are overdispersed or aggregated among hosts), they are skewed and approximately negative binomially distributed. The sources of overdispersion are differences among lambs in the ingestion of infective larvae and the immune response. Both forces can produce aggregation but their relative importance is unknown. The key components of variation can be identified by variance analysis. The sum of the average effects of polymorphic genes is known as additive genetic variation and this increases essentially from zero at one month of age to quite high values at six months of age. The major mechanism underlying genetic variation appears to be the differences among individuals in immune responses. Two of the major sources of variation in immune responses are differences in antigen recognition and differences in the type of cytokines produced. Genes that influence both these sources of variation are associated with differences in resistance to nematode infection. Therefore, much of the heterogeneity among animals in parasite transmission appears to be due to genetic variation in immune responsiveness.     

The evolutionary dynamics of within-generation immune priming in invertebrate hosts

While invertebrates lack the machinery necessary for ‘acquired immunity’, there is increasing empirical evidence that exposure to low levels of disease may ‘prime’ an invertebrate''s immune response, increasing its defence to subsequent exposure. Despite this increasing empirical data, there has been little theoretical attention paid to immune priming. Here, we investigate the evolution of immune priming, focusing on the role of the unique feedbacks generated by a newly developed susceptible–primed–infected epidemiological model. Contrasting our results with previous models on the evolution of acquired immunity, we highlight that there are important implications to the evolution of immunity through priming owing to these different epidemiological feedbacks. In particular, we find that in contrast to acquired immunity, priming is strongly selected for at high as well as intermediate pathogen virulence. We also find that priming may be greatest at either intermediate or high host lifespans depending on the severity of disease. Furthermore, hosts faced with more severe pathogens are more likely to evolve diversity in priming. Finally, we show when the evolution of priming leads to the exclusion of the pathogens or hosts experiencing population cycles. Overall the model acts as a baseline for understanding the evolution of priming in host–pathogen systems.     

Rare peptide segments are found significantly more often in proto-oncoproteins than control proteins: implications for immunology and oncology

There is some evidence to suggest that peptide segments that are found rarely or never in the host proteome play a role in the immune response to disease-related proteins, both those derived from microbes and those derived from the host itself. We conjecture that this pattern may extend to human proto-oncoproteins. Our hypothesis in this study is that the frequency of rare peptide segments in sets of human proto-oncoproteins is significantly higher than in sets of control proteins, and we show that this is the case. Possible immunological implications of this observation are discussed.     

Insights into mucosal innate responses to Escherichia coli O157 : H7 colonization of cattle by mathematical modelling of excretion dynamics

Mathematical model-based statistical inference applied to within-host dynamics of infectious diseases can help dissect complex interactions between hosts and microbes. This work has applied advances in model-based inference to understand colonization of cattle by enterohaemorrhagic Escherichia coli O157 : H7 at the terminal rectum. A mathematical model was developed based on niche replication and transition rates at this site. A nested-model comparison, applied to excretion curves from 25 calves, was used to reduce complexity while maintaining integrity. We conclude that, 5–9 days post inoculation, the innate immune response negates bacterial replication on the epithelium and either reduces attachment to or increases detachment from the epithelium of the terminal rectum. Thus, we provide a broadly applicable model that gives novel insights into bacterial replication rates in vivo and the timing and impact of host responses.     

A dynamic dose–response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax

The most commonly used dose–response models implicitly assume that accumulation of dose is a time-independent process where each pathogen has a fixed risk of initiating infection. Immune particle neutralization of pathogens, however, may create strong time dependence; i.e. temporally clustered pathogens have a better chance of overwhelming the immune particles than pathogen exposures that occur at lower levels for longer periods of time. In environmental transmission systems, we expect different routes of transmission to elicit different dose–timing patterns and thus potentially different realizations of risk. We present a dose–response model that captures time dependence in a manner that incorporates the dynamics of initial immune response. We then demonstrate the parameter estimation of our model in a dose–response survival analysis using empirical time-series data of inhalational anthrax in monkeys in which we find slight dose–timing effects. Future dose–response experiments should include varying the time pattern of exposure in addition to varying the total doses delivered. Ultimately, the dynamic dose–response paradigm presented here will improve modelling of environmental transmission systems where different systems have different time patterns of exposure.     

Variation in host susceptibility and infectiousness generated by co-infection: the myxoma-Trichostrongylus retortaeformis case in wild rabbits.

One of the conditions that can affect host susceptibility and parasite transmission is the occurrence of concomitant infections. Parasites interact directly or indirectly within an individual host and often these interactions are modulated by the host immune response. We used a free-living rabbit population co-infected with the nematode Trichostrongylus retortaeformis, which appears to stimulate an acquired immune response, and the immunosuppressive poxvirus myxoma. Modelling was used to examine how myxoma infection alters the immune-mediated establishment and death/expulsion of T. retortaeformis, and consequently affects parasite intensity and duration of the infection. Simulations were based on the general TH1-TH2 immunological paradigm that proposes the polarization of the host immune response towards one of the two subsets of T helper cells. Our findings suggest that myxoma infections contribute to alter host susceptibility to the nematode, as co-infected rabbits showed higher worm intensity compared with virus negative hosts. Results also suggest that myxoma disrupts the ability of the host to clear T. retortaeformis as worm intensities were consistently high and remained high in old rabbits. However, the co-infection model has to include some immune-mediated nematode regulation to be consistent with field data, indicating that the TH1-TH2 dichotomy is not complete. We conclude that seasonal myxoma outbreaks enhance host susceptibility to the nematode and generate highly infected hosts that remain infectious for a longer time. Finally, the virus-nematode co-infection increases heterogeneities among individuals and potentially has a large effect on parasite transmission.     

Predators indirectly control vector-borne disease: linking predator–prey and host–pathogen models

Pathogens transmitted by arthropod vectors are common in human populations, agricultural systems and natural communities. Transmission of these vector-borne pathogens depends on the population dynamics of the vector species as well as its interactions with other species within the community. In particular, predation may be sufficient to control pathogen prevalence indirectly via the vector. To examine the indirect effect of predators on vectored-pathogen dynamics, we developed a theoretical model that integrates predator–prey and host–pathogen theory. We used this model to determine whether predation can prevent pathogen persistence or alter the stability of host–pathogen dynamics. We found that, in the absence of predation, pathogen prevalence in the host increases with vector fecundity, whereas predation on the vector causes pathogen prevalence to decline, or even become extinct, with increasing vector fecundity. We also found that predation on a vector may drastically slow the initial spread of a pathogen. The predator can increase host abundance indirectly by reducing or eliminating infection in the host population. These results highlight the importance of studying interactions that, within the greater community, may alter our predictions when studying disease dynamics. From an applied perspective, these results also suggest situations where an introduced predator or the natural enemies of a vector may slow the rate of spread of an emerging vector-borne pathogen.     

Towards causally cohesive genotype–phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries

A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype–phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype–phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.     

Time and dose-dependent risk of pneumococcal pneumonia following influenza: a model for within-host interaction between influenza and Streptococcus pneumoniae

A significant fraction of seasonal and in particular pandemic influenza deaths are attributed to secondary bacterial infections. In animal models, influenza virus predisposes hosts to severe infection with both Streptococcus pneumoniae and Staphylococcus aureus. Despite its importance, the mechanistic nature of the interaction between influenza and pneumococci, its dependence on the timing and sequence of infections as well as the clinical and epidemiological consequences remain unclear. We explore an immune-mediated model of the viral–bacterial interaction that quantifies the timing and the intensity of the interaction. Taking advantage of the wealth of knowledge gained from animal models, and the quantitative understanding of the kinetics of pathogen-specific immunological dynamics, we formulate a mathematical model for immune-mediated interaction between influenza virus and S. pneumoniae in the lungs. We use the model to examine the pathogenic effect of inoculum size and timing of pneumococcal invasion relative to influenza infection, as well as the efficacy of antivirals in preventing severe pneumococcal disease. We find that our model is able to capture the key features of the interaction observed in animal experiments. The model predicts that introduction of pneumococcal bacteria during a 4–6 day window following influenza infection results in invasive pneumonia at significantly lower inoculum size than in hosts not infected with influenza. Furthermore, we find that antiviral treatment administered later than 4 days after influenza infection was not able to prevent invasive pneumococcal disease. This work provides a quantitative framework to study interactions between influenza and pneumococci and has the potential to accurately quantify the interactions. Such quantitative understanding can form a basis for effective clinical care, public health policies and pandemic preparedness.     

Nonlinear signalling networks and cell-to-cell variability transform external signals into broadly distributed or bimodal responses

We show theoretically and experimentally a mechanism behind the emergence of wide or bimodal protein distributions in biochemical networks with nonlinear input–output characteristics (the dose–response curve) and variability in protein abundance. Large cell-to-cell variation in the nonlinear dose–response characteristics can be beneficial to facilitate two distinct groups of response levels as opposed to a graded response. Under the circumstances that we quantify mathematically, the two distinct responses can coexist within a cellular population, leading to the emergence of a bimodal protein distribution. Using flow cytometry, we demonstrate the appearance of wide distributions in the hypoxia-inducible factor-mediated response network in HCT116 cells. With help of our theoretical framework, we perform a novel calculation of the magnitude of cell-to-cell heterogeneity in the dose–response obtained experimentally.     

Constraint-based network model of pathogen–immune system interactions

Pathogenic bacteria such as Bordetella bronchiseptica modulate host immune responses to enable their establishment and persistence; however, the immune response is generally successful in clearing these bacteria. Here, we model the dynamic outcome of the interplay between host immune components and B. bronchiseptica virulence factors. The model extends our previously published interaction network of B. bronchiseptica and includes the existing experimental information on the relative timing of IL10 and IFNγ activation in the form of qualitative inequalities. The current model improves the previous one in two directions: (i) by augmenting the network with new nodes with specific function in T helper cell differentiation and effector mechanisms and (ii) by using a dynamic approach that allows us to quantify node states and mechanisms revealed to be important from our previous model. The model makes predictions about the time scales of each process, the activity thresholds of each node and novel regulatory interactions. For example, the model predicts that the activity threshold of IL4 is higher than that of IL12 and that pro-inflammatory cytokines regulate the activity of Th2 cells. Some of these predictions are supported by the literature, and many can serve as targets of future experiments.     

Modelling the spread of infectious salmon anaemia among salmon farms based on seaway distances between farms and genetic relationships between infectious salmon anaemia virus isolates

Infectious salmon anaemia (ISA) is an important infectious disease in Atlantic salmon farming causing recurrent epidemic outbreaks worldwide. The focus of this paper is on tracing the spread of ISA among Norwegian salmon farms. To trace transmission pathways for the ISA virus (ISAV), we use phylogenetic relationships between virus isolates in combination with space–time data on disease occurrences. The rate of ISA infection of salmon farms is modelled stochastically, where seaway distances between farms and genetic distances between ISAV isolates from infected farms play prominent roles. The model was fitted to data covering all cohorts of farmed salmon and the history of all farms with ISA between 2003 and summer 2009. Both seaway and genetic distances were significantly associated with the rate of ISA infection. The fitted model predicts that the risk of infection from a neighbourhood infectious farm decreases with increasing seaway distance between the two farms. Furthermore, for a given infected farm with a given ISAV genotype, the source of infection is significantly more likely to be ISAV of a small genetic distance than of moderate or large genetic distances. Nearly half of the farms with ISA in the investigated period are predicted to have been infected by an infectious farm in their neighbourhood, whereas the remaining half of the infected farms had unknown sources. For many of the neighbourhood infected farms, it was possible to point out one or a few infectious farms as the most probable sources of infection. This makes it possible to map probable infection pathways.     

Integrating stochasticity and network structure into an epidemic model

While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation.     

A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.     

Maintenance of phenotypic diversity within a set of virulence encoding genes of the malaria parasite Plasmodium falciparum

Infection by the human malaria parasite Plasmodium falciparum results in a broad spectrum of clinical outcomes, ranging from severe and potentially life-threatening malaria to asymptomatic carriage. In a process of naturally acquired immunity, individuals living in malaria-endemic regions build up a level of clinical protection, which attenuates infection severity in an exposure-dependent manner. Underlying this shift in the immunoepidemiology as well as the observed range in malaria pathogenesis is the var multigene family and the phenotypic diversity embedded within. The var gene-encoded surface proteins Plasmodium falciparum erythrocyte membrane protein 1 mediate variant-specific binding of infected red blood cells to a diverse set of host receptors that has been linked to specific disease manifestations, including cerebral and pregnancy-associated malaria. Here, we show that cross-reactive immune responses, which minimize the within-host benefit of each additionally expressed gene during infection, can cause selection for maximum phenotypic diversity at the genome level. We further show that differential functional constraints on protein diversification stably maintain uneven ratios between phenotypic groups, in line with empirical observation. Our results thus suggest that the maintenance of phenotypic diversity within P. falciparum is driven by an evolutionary trade-off that optimizes between within-host parasite fitness and between-host selection pressure.     

Statistical analysis of the dynamics of antibody loss to a disease-causing agent: plague in natural populations of great gerbils as an example

We propose a new stochastic framework for analysing the dynamics of the immunity response of wildlife hosts against a disease-causing agent. Our study is motivated by the need to analyse the monitoring time-series data covering the period from 1975 to 1995 on bacteriological and serological tests-samples from great gerbils being the main host of Yersinia pestis in Kazakhstan. Based on a four-state continuous-time Markov chain, we derive a generalized nonlinear mixed-effect model for analysing the serological test data. The immune response of a host involves the production of antibodies in response to an antigen. Our analysis shows that great gerbils recovered from a plague infection are more likely to keep their antibodies to plague and survive throughout the summer-to-winter season than throughout the winter-to-summer season. Provided the seasonal mortality rates are similar (which seems to be the case based on a mortality analysis with abundance data), our finding indicates that the immune function of the sampled great gerbils is seasonal.