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

Discovery and functional characterization of LncRNAs associated with inflammation and macrophage activation

Long noncoding RNAs (lncRNA) are emerging players in regulation of gene expression and cell signaling and their dysregulation has been implicated in a multitude of human diseases. Recent studies from our laboratory revealed that lncRNAs play critical roles in cytokine regulation, inflammation, and metabolism. We demonstrated that lncRNA HOTAIR, which is a well-known regulator of gene silencing, plays critical roles in modulation of cytokines and proinflammatory genes, and glucose metabolism in macrophages during inflammation. In addition, we recently discovered a series of novel lncRNAs that are closely associated with inflammation and macrophage activation. We termed these as long-noncoding inflammation associated RNAs (LinfRNAs). We are currently engaged in the functional characterization of these hLinfRNAs (human LinfRNAs) with a focus on their roles in inflammation, and we are investigating their potential implications in chronic inflammatory human diseases. Here, we have summarized experimental methods that have been utilized for the discovery and functional characterization of lncRNAs in inflammation and macrophage activation.

A speed limit on serial strain replacement from original antigenic sin

Many pathogens evolve to escape immunity, yet it remains difficult to predict whether immune pressure will lead to diversification, serial replacement of one variant by another, or more complex patterns. Pathogen strain dynamics are mediated by cross-protective immunity, whereby exposure to one strain partially protects against infection by antigenically diverged strains. There is growing evidence that this protection is influenced by early exposures, a phenomenon referred to as original antigenic sin (OAS) or imprinting. In this paper, we derive constraints on the emergence of the pattern of successive strain replacements demonstrated by influenza, SARS-CoV-2, seasonal coronaviruses, and other pathogens. We find that OAS implies that the limited diversity found with successive strain replacement can only be maintained if [Formula: see text] is less than a threshold set by the characteristic antigenic distances for cross-protection and for the creation of new immune memory. This bound implies a "speed limit" on the evolution of new strains and a minimum variance of the distribution of infecting strains in antigenic space at any time. To carry out this analysis, we develop a theoretical model of pathogen evolution in antigenic space that implements OAS by decoupling the antigenic distances required for protection from infection and strain-specific memory creation. Our results demonstrate that OAS can play an integral role in the emergence of strain structure from host immune dynamics, preventing highly transmissible pathogens from maintaining serial strain replacement without diversification.

A speed limit on serial strain replacement from original antigenic sin

Many pathogens evolve to escape immunity, yet it remains difficult to predict whether immune pressure will lead to diversification, serial replacement of one variant by another, or more complex patterns. Pathogen strain dynamics are mediated by cross-protective immunity, whereby exposure to one strain partially protects against infection by antigenically diverged strains. There is growing evidence that this protection is influenced by early exposures, a phenomenon referred to as original antigenic sin (OAS) or imprinting. In this paper, we derive new constraints on the emergence of the pattern of successive strain replacements demonstrated by influenza, SARS-CoV-2, seasonal coronaviruses, and other pathogens. We find that OAS implies that the limited diversity found with successive strain replacement can only be maintained if R 0 is less than a threshold set by the characteristic antigenic distances for cross-protection and for the creation of new immune memory. This bound implies a "speed limit" on the evolution of new strains and a minimum variance of the distribution of infecting strains in antigenic space at any time. To carry out this analysis, we develop a theoretical model of pathogen evolution in antigenic space that implements OAS by decoupling the antigenic distances required for protection from infection and strain-specific memory creation. Our results demonstrate that OAS can play an integral role in the emergence of strain structure from host immune dynamics, preventing highly transmissible pathogens from maintaining serial strain replacement without diversification.

Models of immune selection for multi-locus antigenic diversity of pathogens

It is well accepted that pathogens can evade recognition and elimination by the host immune system by varying their antigenic targets. Thus, it has become a truism that host immunity is a major driver and determinant of the antigenic diversity of pathogens. However, it remains puzzling how host immunity selects for antigenic diversity at the level of the pathogen population, given that hosts have acquired immune responses to multiple antigens of most pathogens - sometimes through multiple effectors of both humoral and cellular immunity. In this Opinion article, we address this puzzle and the related question of why pathogens often have diversity at multiple antigenic loci. Here, we describe five hypotheses to explain the polymorphism of multiple antigens in a single pathogen species and highlight research relevant to our current models of thinking about multi-locus antigenic diversity.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Analytical Exploration of Potential Pathways by which Diabetes Mellitus Impacts Tuberculosis Epidemiology

We aimed to develop a conceptual framework of diabetes mellitus (DM) effects on tuberculosis (TB) natural history and treatment outcomes, and to assess the impact of these effects on TB-transmission dynamics. The model was calibrated using TB data for India. A conceptual framework was developed based on a literature review, and then translated into a mathematical model to assess the impact of the DM-on-TB effects. The impact was analyzed using TB-disease incidence hazard ratio (HR) and population attributable fraction (PAF) measures. Evidence was identified for 10 plausible DM-on-TB effects. Assuming a flat change of 300% (meaning an effect size of 3.0) for each DM-on-TB effect, the HR ranged between 1.0 (Effect 9-Recovery) and 2.7 (Effect 2-Fast progression); most effects did not have an impact on the HR. Meanwhile, TB-disease incidence attributed directly and indirectly to each effect ranged between -4.6% (Effect 7-TB mortality) and 34.5% (Effect 2-Fast progression). The second largest impact was for Effect 6-Disease infectiousness at 29.9%. In conclusion, DM can affect TB-transmission dynamics in multiple ways, most of which are poorly characterized and difficult to assess in epidemiologic studies. The indirect (e.g. onward transmission) impacts of some DM-on-TB effects are comparable in scale to the direct impacts. While the impact of several effects on the HR was limited, the impact on the PAF was substantial suggesting that DM could be impacting TB epidemiology to a larger extent than previously thought.

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.

An approach for modeling cross-immunity of two strains, with application to variants of Bartonella in terms of genetic similarity

We developed a two-strain susceptible-infected-recovered (SIR) model that provides a framework for inferring the cross-immunity between two strains of a bacterial species in the host population with discretely sampled co-infection time-series data. Moreover, the model accounts for seasonality in host reproduction. We illustrate an approach using a dataset describing co-infections by several strains of bacteria circulating within a population of cotton rats (Sigmodon hispidus). Bartonella strains were clustered into three genetically close groups, between which the divergence is correspondent to the accepted level of separate bacterial species. The proposed approach revealed no cross-immunity between genetic clusters while limited cross-immunity might exist between subgroups within the clusters.

Computational Population Biology: Linking the inner and outer worlds of organisms

Computationally complex systems models are needed to advance research and implement policy in theoretical and applied population biology. Difference and differential equations used to build lumped dynamic models (LDMs) may have the advantage of clarity, but are limited in their inability to include fine-scale spatial information and individual-specific physical, physiological, immunological, neural and behavioral states. Current formulations of agent-based models (ABMs) are too idiosyncratic and freewheeling to provide a general, coherent framework for dynamically linking the inner and outer worlds of organisms. Here I propose principles for a general, modular, hierarchically scalable, framework for building computational population models (CPMs) designed to treat the inner world of individual agents as complex dynamical systems that take information from their spatially detailed outer worlds to drive the dynamic inner worlds of these agents, simulate their ecology and the evolutionary pathways of their progeny. All the modeling elements are in place, although improvements in software technology will be helpful; but most of all we need a cultural shift in the way population biologists communicate and share model components and the models themselves, fit, test, refute, and refine models, to make the progress needed to meet the ecosystems management challenges posed by global change biology.

Epidemics with partial immunity to reinfection

We obtain analytical results about epidemics generated by the partial immunity model of Gomes et al. [3], in which infection confers partial immunity to reinfection. When the demographic process is excluded, the behavior switches from epidemic to endemic as the basic reproduction number R0 crosses the reinfection threshold R0=1σ. We derive formulas for two quantities characterizing the size of the epidemic below the reinfection threshold: the attack rate A, which is the fraction of the population infected at least once, and the final size Z, which is the average number of infections per individual. We also derive a system of differential equations which can be used to obtain more detailed information, such as the fraction of the population infected n times throughout the epidemic, for every n.

Interactions of multiple strain pathogen diseases in the presence of coinfection, cross immunity, and arbitrary strain diversity

A model for coinfection in multiple strain infectious diseases is developed to incorporate coinfection statuses, immune and infection history, and cross immunity. It is solved for the symmetric interior equilibrium through the use of a ladder operator formalism inspired by quantum mechanical methods. We find that coinfection can fundamentally affects transmission dynamics with important epidemiologic and evolutionary consequences. It can significantly shift the distribution of age at infection for highly antigenically diverse pathogens so that in small host populations, an evolutionary strategy maximizing individual strain transmissibility might be less optimal than one which maximizes the total prevalence of all strains in the system. Alternatively, mechanisms which inhibit coinfection and thus increase total infection prevalence may be evolutionarily advantageous.

Barriers to antigenic escape by pathogens: trade-off between reproductive rate and antigenic mutability

BACKGROUND

A single measles vaccination provides lifelong protection. No antigenic variants that escape immunity have been observed. By contrast, influenza continually evolves new antigenic variants, and the vaccine has to be updated frequently with new strains. Both measles and influenza are RNA viruses with high mutation rates, so the mutation rate alone cannot explain the differences in antigenic variability.

RESULTS

We develop a new hypothesis to explain antigenic stasis versus change. We first note that the antigenically static viruses tend to have high reproductive rates and to concentrate infection in children, whereas antigenically variable viruses such as influenza tend to spread more widely across age classes. We argue that, for pathogens in a naive host population that spread more rapidly in younger individuals than in older individuals, natural selection weights more heavily a rise in reproductive rate. By contrast, pathogens that spread more readily among older individuals gain more by antigenic escape, so natural selection weights more heavily antigenic mutability.

CONCLUSION

These divergent selective pressures on reproductive rate and antigenic mutability may explain some of the observed differences between pathogens in age-class bias, reproductive rate, and antigenic variation.

Analytic insights into the population level impact of imperfect prophylactic HIV vaccines

The population level implications of imperfect HIV vaccines were studied using a mathematical model. A criterion for determining the utility of a vaccine at the population level is introduced, and 2 useful summary measures, namely, vaccine utility (phi) and vaccine infection fitness (psi), are derived and shown to characterize the population-level utility once vaccine efficacies are determined. The utility of the vaccine alone does not guarantee a substantial impact, however, because the effectiveness of partially effective vaccines also depends on the prevailing level of HIV infectious spread. Therefore, a second criterion is introduced through a third summary measure, the hazard index (xi), to describe the effectiveness of a vaccine in substantially reducing HIV incidence. The qualitative features of the impact are delineated by studying 4 distinct scenarios of HIV vaccination. Accordingly, our work delineates the link between vaccine efficacies and the impact of vaccination at the population level and provides the tools for vaccine developers to assess the utility and effectiveness of a given imperfect vaccine straightforwardly and rapidly.

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.

Instabilities in multiserotype disease models with antibody-dependent enhancement

This paper investigates the complex dynamics induced by antibody-dependent enhancement (ADE) in multiserotype disease models. ADE is the increase in viral growth rate in the presence of immunity due to a previous infection of a different serotype. The increased viral growth rate is thought to increase the infectivity of the secondary infectious class. In our models, ADE induces the onset of oscillations without external forcing. The oscillations in the infectious classes represent outbreaks of the disease. In this paper, we derive approximations of the ADE parameter needed to induce oscillations and analyze the associated bifurcations that separate the types of oscillations. We then investigate the stability of these dynamics by adding stochastic perturbations to the model. We also present a preliminary analysis of the effect of a single serotype vaccination in the model.

Fundamental processes in the evolutionary ecology of Lyme borreliosis

The evolutionary ecology of many emerging infectious diseases, particularly vector-borne zoonoses, is poorly understood. Here, we aim to develop a biological, process-based framework for vector-borne zoonoses, using Borrelia burgdorferi sensu lato (s.l.), the causative agent of Lyme borreliosis in humans, as an example. We explore the fundamental biological processes that operate in this zoonosis and put forward hypotheses on how extrinsic cues and intrinsic dynamics shape B. burgdorferi s.l. populations. Additionally, we highlight possible epidemiological parallels between B. burgdorferi s.l. and other vector-borne zoonotic pathogens, including West Nile virus.

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.

Shaping the phylogenetic tree of influenza by cross-immunity

Cross-immunity among related strains can account for the selection producing the slender phylogenetic tree of influenza A and B in humans. Using a model of seasonal influenza epidemics with drift (Andreasen, 2003. Dynamics of annual influenza A epidemics with immuno-selection. J. Math. Biol. 46, 504-536), and assuming that two mutants arrive in the host population sequentially, we determine the threshold condition for the establishment of the second mutant in the presence of partial cross-protection caused by the first mutant and their common ancestors. For fixed levels of cross-protection, the chance that the second mutant establishes increases with rho the basic reproduction ratio and some temporary immunity may be necessary to explain the slenderness of flu's phylogenetic tree. In the presence of moderate levels of temporary immunity, an asymmetric situation can arise in the season after the two mutants were introduced and established: if the offspring of the new mutant arrives before the offspring of the resident type, then the mutant-line may produce a massive epidemic suppressing the original lineage. However, if the original lineage arrives first then both strains may establish and the phylogenetic tree may bifurcate.

The SIRC model and influenza A

We develop a simple ordinary differential equation model to study the epidemiological consequences of the drift mechanism for influenza A viruses. Improving over the classical SIR approach, we introduce a fourth class (C) for the cross-immune individuals in the population, i.e., those that recovered after being infected by different strains of the same viral subtype in the past years. The SIRC model predicts that the prevalence of a virus is maximum for an intermediate value of R(0), the basic reproduction number. Via a bifurcation analysis of the model, we discuss the effect of seasonality on the epidemiological regimes. For realistic parameter values, the model exhibits a rich variety of behaviors, including chaos and multi-stable periodic outbreaks. Comparison with empirical evidence shows that the simulated regimes are qualitatively and quantitatively consistent with reality, both for tropical and temperate countries. We find that the basins of attraction of coexisting cycles can be fractal sets, thus predictability can in some cases become problematic even theoretically. In accordance with previous studies, we find that increasing cross-immunity tends to complicate the dynamics of the system.