Implications of vaccination and waning immunity

Immuno-epidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting

When the body gets infected by a pathogen the immune system develops pathogen-specific immunity. Induced immunity decays in time and years after recovery the host might become susceptible again. Exposure to the pathogen in the environment boosts the immune system thus prolonging the time in which a recovered individual is immune. Such an interplay of within host processes and population dynamics poses significant challenges in rigorous mathematical modeling of immuno-epidemiology. We propose a framework to model SIRS dynamics, monitoring the immune status of individuals and including both waning immunity and immune system boosting. Our model is formulated as a system of two ordinary differential equations (ODEs) coupled with a PDE. After showing existence and uniqueness of a classical solution, we investigate the local and the global asymptotic stability of the unique disease-free stationary solution. Under particular assumptions on the general model, we can recover known examples such as large systems of ODEs for SIRWS dynamics, as well as SIRS with constant delay.

Seven challenges in modeling pathogen dynamics within-host and across scales

The population dynamics of infectious disease is a mature field in terms of theory and to some extent, application. However for microparasites, the theory and application of models of the dynamics within a single infected host is still an open field. Further, connecting across the scales--from cellular to host level, to population level--has potential to vastly improve our understanding of pathogen dynamics and evolution. Here, we highlight seven challenges in the following areas: transmission bottlenecks, heterogeneity within host, dynamic fitness landscapes within hosts, making use of next-generation sequencing data, capturing superinfection and when and how to model more than two scales.

A large-scale immuno-epidemiological simulation of influenza A epidemics

Background

Agent based models (ABM) are useful to explore population-level scenarios of disease spread and containment, but typically characterize infected individuals using simplified models of infection and symptoms dynamics. Adding more realistic models of individual infections and symptoms may help to create more realistic population level epidemic dynamics.

Methods

Using an equation-based, host-level mathematical model of influenza A virus infection, we develop a function that expresses the dependence of infectivity and symptoms of an infected individual on initial viral load, age, and viral strain phenotype. We incorporate this response function in a population-scale agent-based model of influenza A epidemic to create a hybrid multiscale modeling framework that reflects both population dynamics and individualized host response to infection.

Results

At the host level, we estimate parameter ranges using experimental data of H1N1 viral titers and symptoms measured in humans. By linearization of symptoms responses of the host-level model we obtain a map of the parameters of the model that characterizes clinical phenotypes of influenza infection and immune response variability over the population. At the population-level model, we analyze the effect of individualizing viral response in agent-based model by simulating epidemics across Allegheny County, Pennsylvania under both age-specific and age-independent severity assumptions.

Conclusions

We present a framework for multi-scale simulations of influenza epidemics that enables the study of population-level effects of individual differences in infections and symptoms, with minimal additional computational cost compared to the existing population-level simulations.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2458-14-1019) contains supplementary material, which is available to authorized users.

A two-phase within-host model for immune response and its application to serological profiles of pertussis

We present a simple phenomenological within-host model describing both the interaction between a pathogen and the immune system and the waning of immunity after clearing of the pathogen. We implement the model into a Bayesian hierarchical framework to estimate its parameters for pertussis using Markov chain Monte Carlo methods. We show that the model captures some essential features of the kinetics of titers of IgG against pertussis toxin. We identify a threshold antibody level that separates a large increase in antibody level upon infection from a small increase and accordingly might be interpreted as a threshold separating clinical from subclinical infections. We contrast predictions of the model with observations reported in the literature and based on independent data and find a remarkable correspondence.

The arrested immunity hypothesis in an immunoepidemiological model of Chlamydia transmission

For curable infectious diseases, public health strategies such as treatment can effectively shorten an individual's infectious period, and thus limit their role in transmission. However, because treatment effectively eliminates antigen impingement, these types of control strategies may also paradoxically impair the development of adaptive immune responses. For sexually transmitted Chlamydia trachomatis infections, this latter effect has been coined the arrested immunity hypothesis, and is discussed to carry significant epidemiological implications for those individuals who return to similar sexual networks with similar sexual behavior. Here, we examine the effect of antibiotic treatment on the spread of Chlamydia infection through a simple immunoepidemiological framework that characterizes the population as a collection of dynamically evolving individuals in small, paradigmatic networks. Within each individual there is an explicit representation of pathogen replication, accumulation and persistence of an immune response, followed by a gradual waning of that response once the infection is cleared. Individuals are then nested in networks, allowing the variability in the life history of their infection to be functions of both individual immune dynamics as well as their position in the network. Model results suggest that the timing and coverage of treatment are important contributors to the development of immunity and reinfection. In particular, the impact of treatment on the spread of infection between individuals can be beneficial, have no effect, or be deleterious depending on who is treated and when. Although we use sexually transmitted Chlamydia infection as an example, the observed results arise endogenously from a basic model structure, and thus warrant consideration to understanding the interaction of infection, treatment, and spread of other infectious diseases.

EPIDEMIOLOGICAL CONSEQUENCES OF IMPERFECT VACCINES FOR IMMUNIZING INFECTIONS

The control of some childhood diseases has proven to be difficult even in countries that maintain high vaccination coverage. This may be due to the use of imperfect vaccines and there has been much discussion on the different modes by which vaccines might fail. To understand the epidemiological implications of some of these different modes, we performed a systematic analysis of a model based on the standard SIR equations with a vaccinated component that permits vaccine failure in degree ("leakiness"), take ("all-or-nothingness") and duration (waning of vaccine-derived immunity). The model was first considered as a system of ordinary differential equations, then extended to a system of partial differential equations to accommodate age structure. We derived analytic expressions for the steady states of the system and the final age distributions in the case of homogenous contact rates. The stability of these equilibria are determined by a threshold parameter R_p , a function of the vaccine failure parameters and the coverage p. The value of p for which R_p = 1 yields the critical vaccination ratio, a measure of herd immunity. Using this concept we can compare vaccines that confer the same level of herd immunity to the population but may fail at the individual level in different ways. For any fixed R_p > 1, the leaky model results in the highest prevalence of infection, while the all-or-nothing and waning models have the same steady state prevalence. The actual composition of a vaccine cannot be determined on the basis of steady state levels alone, however the distinctions can be made by looking at transient dynamics (such as after the onset of vaccination), the mean age of infection, the age distributions at steady state of the infected class, and the effect of age-specific contact rates.

Latent Tuberculosis: Models, Computational Efforts and the Pathogen's Regulatory Mechanisms during Dormancy

Latent tuberculosis is a clinical syndrome that occurs after an individual has been exposed to the Mycobacterium tuberculosis (Mtb) Bacillus, the infection has been established and an immune response has been generated to control the pathogen and force it into a quiescent state. Mtb can exit this quiescent state where it is unresponsive to treatment and elusive to the immune response, and enter a rapid replicating state, hence causing infection reactivation. It remains a gray area to understand how the pathogen causes a persistent infection and it is unclear whether the organism will be in a slow replicating state or a dormant non-replicating state. The ability of the pathogen to adapt to changing host immune response mechanisms, in which it is exposed to hypoxia, low pH, nitric oxide (NO), nutrient starvation, and several other anti-microbial effectors, is associated with a high metabolic plasticity that enables it to metabolize under these different conditions. Adaptive gene regulatory mechanisms are thought to coordinate how the pathogen changes their metabolic pathways through mechanisms that sense changes in oxygen tension and other stress factors, hence stimulating the pathogen to make necessary adjustments to ensure survival. Here, we review studies that give insights into latency/dormancy regulatory mechanisms that enable infection persistence and pathogen adaptation to different stress conditions. We highlight what mathematical and computational models can do and what they should do to enhance our current understanding of TB latency.

The epidemiological consequences of immune priming

Exposure to low doses of pathogens that do not result in the host becoming infectious may 'prime' the immune response and increase protection to subsequent challenge. There is increasing evidence that such immune priming is a widespread and important feature of invertebrate host-pathogen interactions. Immune priming clearly has implications for individual hosts but will also have population-level implications. We present a susceptible-primed-infectious model-in contrast to the classic susceptible-infectious-recovered framework-to investigate the impacts of immune priming on pathogen persistence and population stability. We describe impacts of immune priming on the epidemiology of the disease in both constant and seasonal environments. A key result is that immune priming may act to destabilize population dynamics. In particular, when the proportion of individuals becoming primed rather than infected is high, but this priming does not confer full immunity, the population may be strongly destabilized through the generation of limit cycles. We discuss the implications of our model both in the context of invertebrate immunity and more widely.

A general approach for population games with application to vaccination

Reconciling the interests of individuals with the interests of communities is a major challenge in designing and implementing health policies. In this paper, we present a technique based on a combination of mechanistic population-scale models, Markov decision process theory and game theory that facilitates the evaluation of game theoretic decisions at both individual and community scales. To illustrate our technique, we provide solutions to several variants of the simple vaccination game including imperfect vaccine efficacy and differential waning of natural and vaccine immunity. In addition, we show how path-integral approaches can be applied to the study of models in which strategies are fixed waiting times rather than exponential random variables. These methods can be applied to a wide variety of decision problems with population-dynamic feedbacks.

Influenza pandemic waves under various mitigation strategies with 2009 H1N1 as a case study

A significant feature of influenza pandemics is multiple waves of morbidity and mortality over a few months or years. The size of these successive waves depends on intervention strategies including antivirals and vaccination, as well as the effects of immunity gained from previous infection. However, the global vaccine manufacturing capacity is limited. Also, antiviral stockpiles are costly and thus, are limited to very few countries. The combined effect of antivirals and vaccination in successive waves of a pandemic has not been quantified. The effect of acquired immunity from vaccination and previous infection has also not been characterized. In times of a pandemic threat countries must consider the effects of a limited vaccine, limited antiviral use and the effects of prior immunity so as to adopt a pandemic strategy that will best aid the population. We developed a mathematical model describing the first and second waves of an influenza pandemic including drug therapy, vaccination and acquired immunity. The first wave model includes the use of antiviral drugs under different treatment profiles. In the second wave model the effects of antivirals, vaccination and immunity gained from the first wave are considered. The models are used to characterize the severity of infection in a population under different drug therapy and vaccination strategies, as well as school closure, so that public health policies regarding future influenza pandemics are better informed.

Antibodies to measles in individuals with recent onset psychosis

BACKGROUND

Measles virus is a highly prevalent neurotropic virus capable of causing persistent infections within the central nervous system.

METHODS

We measured IgG class antibodies to measles in 820 individuals including 138 with recent onset psychosis, 378 with persistent schizophrenia, and 304 non-psychiatric controls. Levels of antibodies among the groups were compared by bivariate and by multivariate analyses and correlated with clinical and demographic variables.

RESULTS

The level of measles antibodies in individuals with a recent onset of psychosis was greater than the level of antibodies in individuals with persistent schizophrenia or individuals without a history of a psychiatric disorder (p<.00001). The level of measles antibodies in the individuals with persistent schizophrenia was greater than the level of measles antibodies in the controls (p<.001). Recent onset of psychosis was associated with having elevated levels of measles antibodies, defined as the 90th percentile of the levels of the controls, with an odds ratio of 8.0 (95% CI 4.6, 14.0); persistent schizophrenia was associated with having this level with an odds ratio of 2.3 (95% CI 1.4, 3.7). Within the psychiatric groups, measles antibody levels were associated with age, race, and current treatment with the antipsychotic medication, olanzapine.

CONCLUSIONS

The reasons for elevated levels of measles antibodies in the psychiatric groups are not known with certainty and should be studied in prospective investigations.

Estimating the duration of pertussis immunity using epidemiological signatures

Case notifications of pertussis have shown an increase in a number of countries with high rates of routine pediatric immunization. This has led to significant public health concerns over a possible pertussis re-emergence. A leading proposed explanation for the observed increase in incidence is the loss of immunity to pertussis, which is known to occur after both natural infection and vaccination. Little is known, however, about the typical duration of immunity and its epidemiological implications. Here, we analyze a simple mathematical model, exploring specifically the inter-epidemic period and fade-out frequency. These predictions are then contrasted with detailed incidence data for England and Wales. We find model output to be most sensitive to assumptions concerning naturally acquired immunity, which allows us to estimate the average duration of immunity. Our results support a period of natural immunity that is, on average, long-lasting (at least 30 years) but inherently variable.

The eradication of vaccine-preventable infectious diseases remains an important public health priority. To achieve this goal, the level of immunity afforded needs to be high and long-lasting. For pertussis, one of the leading causes of mortality in infants, immunity has been shown to wane in some individuals. The epidemiological impacts of this observation depend critically on the duration of protective immunity in the entire population, which remains notoriously difficult to estimate. We approach this problem by exploring the agreement between model dynamics and case notification data from England & Wales. Our estimates suggest the average duration of immunity is much longer than is currently thought (at least 30 years), but that some individuals would lose immunity quite rapidly.

Long-term presence of memory B-cells specific for different vaccine components

Vaccination against infectious diseases ideally should provide lifelong immunity, but in many cases waning of antibody titers has been observed over time. In this study we describe the identification of antigen-specific memory B-cells in peripheral blood of persons born between 1940 and 2004 in The Netherlands. Polyclonal stimulation of either PBMCs or purified B-cells induced proliferation and differentiation of B-cells of the memory phenotype (CD19(+)/CD27(+)) into antibody secreting cells (ASC). Memory B-cells against components of bacterial vaccines (Bordetella pertussis and tetanus) as well as viral vaccines (measles and influenza) were thus identified, even in persons with low serum antibody titers. Enrichment of B-cells increased the sensitivity of memory B-cell detection when compared to PBMCs. Low, but significant correlations between numbers of antigen-specific memory B-cells and the corresponding circulating antibody titers were found for the pertussis proteins and measles virus, but not for tetanus. The identification of the numbers and specificities of peripheral memory B-cells and their relationship with circulating antibodies may be very useful to determine the long-term efficacy of vaccination.