Pathogen adaptation under imperfect vaccination: implications for pertussis

Mass vaccination campaigns have drastically reduced the burden of infectious diseases. Unfortunately, in recent years several infectious diseases have re-emerged. Pertussis poses a well-known example. Inspired by pertussis, we study, by means of an epidemic model, the population and evolutionary dynamics of a pathogen population under the pressure of vaccination. A distinction is made between infection in immunologically naive individuals (primary infection) and infection in individuals whose immune system has been primed by vaccination or infection (secondary infection). The results show that (i) vaccination with an imperfect vaccine may not succeed in reducing the infection pressure if the transmissibility of secondary infections is higher than that of primary infections; (ii) pathogen strains that are able to evade the immunity induced by vaccination can only spread if escape mutants incur no or only a modest fitness cost and (iii) the direction of evolution depends crucially on the distribution of the different types of susceptibles in the population. We discuss the implications of these results for the design and use of vaccines that provide temporary immunity.     

Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives

The SIR (susceptible-infectious-resistant) and SIS (susceptible-infectious-susceptible) frameworks for infectious disease have been extensively studied and successfully applied. They implicitly assume the upper and lower limits of the range of possibilities for host immune response. However, the majority of infections do not fall into either of these extreme categories. We combine two general avenues that straddle this range: temporary immune protection (immunity wanes over time since infection), and partial immune protection (immunity is not fully protective but reduces the risk of reinfection). We present a systematic analysis of the dynamics and equilibrium properties of these models in comparison to SIR and SIS, and analyse the outcome of vaccination programmes. We describe how the waning of immunity shortens inter-epidemic periods, and poses major difficulties to disease eradication. We identify a "reinfection threshold" in transmission when partial immunity is included. Below the reinfection threshold primary infection dominates, levels of infection are low, and vaccination is highly effective (approximately an SIR model). Above the reinfection threshold reinfection dominates, levels of infection are high, and vaccination fails to protect (approximately an SIS situation). This association between high prevalence of infection and vaccine failure emphasizes the problems of controlling recurrent infections in high-burden regions. However, vaccines that induce a better protection than natural infection have the potential to increase the reinfection threshold, and therefore constitute interventions with a surprisingly high capacity to reduce infection where reduction is most needed.     

Impact of vaccination on the infectious diseases epidemiology: example of pertussis

Several vaccines are now routinely used since fifty years in different developed countries. Their principal impact has been to decrease morbidity and mortality of the infectious diseases they are targeting. One disease, smallpox, is eradicated, poliomyelitis will be soon, diphteria is controlled in several countries but pertussis is still endemic although an efficacious vaccine was used. Why? Pertussis is an example of an infection for which the immunity of the population has changed after the introduction of generalized vaccination with killed whole cell pertussis vaccines, from a natural immunity due to infection to different types of vaccine-induced immunity. These different types of immunity have changed the protection against infection, disease and transmission. The impact of the generalized vaccination in a human population has been an important change in the epidemiology of the disease. In fact, a child-to-child transmission observed before the introduction of vaccination is now replaced by an adolescent-adult to infant transmission. The major consequence is an increase in the mortality and morbidity in non vaccinated infants mostly contaminated by their parents. Researches undertaken on the agent of the disease, the bacterium, Bordetella pertussis, conducted to the development of subunits vaccines, efficacious and better tolerated by infants than whole-cell vaccines. Many developed countries decided to change vaccines but also to add vaccine boosters for adolescents and adults in order to stop the transmission of the disease to infants. However, even after 15 years of studies in many countries, pertussis is still underestimated in adults and generalized adult vaccination remains difficult. The new goal now is to give information to medical students and health care workers in general in order to increase adolescent and adult's vaccination coverage.     

Implications of vaccination and waning immunity

For infectious diseases where immunization can offer lifelong protection, a variety of simple models can be used to explain the utility of vaccination as a control method. However, for many diseases, immunity wanes over time and is subsequently enhanced (boosted) by asymptomatic encounters with the infection. The study of this type of epidemiological process requires a model formulation that can capture both the within-host dynamics of the pathogen and immune system as well as the associated population-level transmission dynamics. Here, we parametrize such a model for measles and show how vaccination can have a range of unexpected consequences as it reduces the natural boosting of immunity as well as reducing the number of naive susceptibles. In particular, we show that moderate waning times (40–80 years) and high levels of vaccination (greater than 70%) can induce large-scale oscillations with substantial numbers of symptomatic cases being generated at the peak. In addition, we predict that, after a long disease-free period, the introduction of infection will lead to far larger epidemics than that predicted by standard models. These results have clear implications for the long-term success of any vaccination campaign and highlight the need for a sound understanding of the immunological mechanisms of immunity and vaccination.     

Predicting the impact of a nonsterilizing vaccine against human immunodeficiency virus

Studies of human immunodeficiency virus (HIV) vaccines in animal models suggest that it is difficult to induce complete protection from infection (sterilizing immunity) but that it is possible to reduce the viral load and to slow or prevent disease progression following infection. We have developed an age-structured epidemiological model of the effects of a disease-modifying HIV vaccine that incorporates the intrahost dynamics of infection, a transmission rate and host mortality that depend on the viral load, the possible evolution and transmission of vaccine escape mutant viruses, a finite duration of vaccine protection, and possible changes in sexual behavior. Using this model, we investigated the long-term outcome of a disease-modifying vaccine and utilized uncertainty analysis to quantify the effects of our lack of precise knowledge of various parameters. Our results suggest that the extent of viral load reduction in vaccinated infected individuals (compared to unvaccinated individuals) is the key predictor of vaccine efficacy. Reductions in viral load of about 1 log(10) copies ml(-1) would be sufficient to significantly reduce HIV-associated mortality in the first 20 years after the introduction of vaccination. Changes in sexual risk behavior also had a strong impact on the epidemic outcome. The impact of vaccination is dependent on the population in which it is used, with disease-modifying vaccines predicted to have the most impact in areas of low prevalence and rapid epidemic growth. Surprisingly, the extent to which vaccination alters disease progression, the rate of generation of escape mutants, and the transmission of escape mutants are predicted to have only a weak impact on the epidemic outcome over the first 25 years after the introduction of a vaccine.     

An in-host model of acute infection: measles as a case study

The epidemiology of acute infections is strongly influenced by the immune status of individuals. In-host models can provide quantitative predictions of immune status and can thus offer valuable insights into the factors that influence transmission between individuals and the effectiveness of vaccination protocols with respect to individual immunity. Here we develop an in-host model of measles infection. The model explicitly considers the effects of immune system memory and CD8 T-cells, which are key to measles clearance. The model is used to determine the effects of waning immunity through vaccination and infection, the effects of booster exposures or vaccines on the level of immunity, and the immune system characteristics that result in measles transmission (R(0)>1) even if an individual has no apparent clinical symptoms. We find that the level of immune system CD8 T-cells at the time of exposure to measles determines whether an individual will experience a measles infection or simply a boost in immunity. We also find that the infected cell dynamics are a good indicator of measles transmission and the degree of symptoms that will be experienced. Our results indicate that the degree of immunity in adults is independent of the source of exposure in early childhood, be it vaccine or natural infection.     

Serotype-Specific Transmission and Waning Immunity of Endemic Foot-and-Mouth Disease Virus in Cameroon

Foot-and-mouth disease virus (FMDV) causes morbidity and mortality in a range of animals and threatens local economies by acting as a barrier to international trade. The outbreak in the United Kingdom in 2001 that cost billions to control highlighted the risk that the pathogen poses to agriculture. In response, several mathematical models have been developed to parameterize and predict both transmission dynamics and optimal disease control. However, a lack of understanding of the multi-strain etiology prevents characterization of multi-strain dynamics. Here, we use data from FMDV serology in an endemic setting to probe strain-specific transmission and immunodynamics. Five serotypes of FMDV affect cattle in the Far North Region of Cameroon. We fit both catalytic and reverse catalytic models to serological data to estimate the force of infection and the rate of waning immunity, and to detect periods of sustained transmission. For serotypes SAT2, SAT3, and type A, a model assuming life-long immunity fit better. For serotypes SAT1 and type O, the better-fit model suggests that immunity may wane over time. Our analysis further indicates that type O has the greatest force of infection and the longest duration of immunity. Estimates for the force of infection were time-varying and indicated that serotypes SAT1 and O displayed endemic dynamics, serotype A displayed epidemic dynamics, and SAT2 and SAT3 did not sustain local chains of transmission. Since these results were obtained from the same population at the same time, they highlight important differences in transmission specific to each serotype. They also show that immunity wanes at rates specific to each serotype, which influences patterns of local persistence. Overall, this work shows that viral serotypes can differ significantly in their epidemiological and immunological characteristics. Patterns and processes that drive transmission in endemic settings must consider complex viral dynamics for accurate representation and interpretation.     

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.     

Impact of vaccination and birth rate on the epidemiology of pertussis: a comparative study in 64 countries

Bordetella pertussis infection remains an important public health problem worldwide despite decades of routine vaccination. A key indicator of the impact of vaccination programmes is the inter-epidemic period, which is expected to increase with vaccine uptake if there is significant herd immunity. Based on empirical data from 64 countries across the five continents over the past 30–70 years, we document the observed relationship between the average inter-epidemic period, birth rate and vaccine coverage. We then use a mathematical model to explore the range of scenarios for duration of immunity and transmission resulting from repeat infections that are consistent with empirical evidence. Estimates of pertussis periodicity ranged between 2 and 4.6 years, with a strong association with susceptible recruitment rate, defined as birth rate × (1 − vaccine coverage). Periodicity increased by 1.27 years on average after the introduction of national vaccination programmes (95% CI: 1.13, 1.41 years), indicative of increased herd immunity. Mathematical models suggest that the observed patterns of pertussis periodicity are equally consistent with loss of immunity that is not as rapid as currently thought, or with negligible transmission generated by repeat infections. We conclude that both vaccine coverage and birth rate drive pertussis periodicity globally and that vaccination induces strong herd immunity effects. A better understanding of the role of repeat infections in pertussis transmission is critical to refine existing control strategies.     

Circulating Vaccine Derived Polio Viruses and their Impact on Global Polio Eradication

Poliomyelitis vaccination via live Oral Polio Vaccine (OPV) suffers from the inherent problem of reversion: the vaccine may, upon replication in the human gut, mutate back to virulence and transmissibility resulting in circulating vaccine derived polio viruses (cVDPVs). We formulate a general mathematical model to assess the impact of cVDPVs on prospects for polio eradication. We find that for OPV coverage levels below a certain threshold, cVDPVs have a small impact in comparison to the expected endemic level of the disease in the absence of reversion. Above this threshold, the model predicts a small but significant endemic level of the disease, even where standard models predict eradication. In light of this, we consider and analyze three alternative eradication strategies involving a transition from continuous OPV vaccination to either continuous Inactivated Polio Vaccine (IPV), pulsed OPV vaccination, or a one-time IPV pulse vaccination. Stochastic modeling shows continuous IPV vaccination is effective at achieving eradication for moderate coverage levels, while pulsed OPV is effective if higher coverage levels are maintained. The one-time pulse IPV method may also be a viable strategy, especially in terms of the number of vaccinations required and time to eradication, provided that a sufficiently large pulse is practically feasible. More investigation is needed regarding the frequency of revertant virus infection resulting directly from vaccination, the ability of IPV to induce gut immunity, and the potential role of spatial transmission dynamics in eradication efforts. B.G. Wagner’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Doctoral Scholarship. D.J.D. Earn’s research is supported by the Canadian Institutes of Health Research (CIHR), Natural Sciences and Engineering Research Council of Canada (NSERC) and the J.S. McDonnell Foundation.     

The Dynamics of Naturally Acquired Immunity to Plasmodium falciparum Infection

Severe malaria occurs predominantly in young children and immunity to clinical disease is associated with cumulative exposure in holoendemic settings. The relative contribution of immunity against various stages of the parasite life cycle that results in controlling infection and limiting disease is not well understood. Here we analyse the dynamics of Plasmodium falciparum malaria infection after treatment in a cohort of 197 healthy study participants of different ages in order to model naturally acquired immunity. We find that both delayed time-to-infection and reductions in asymptomatic parasitaemias in older age groups can be explained by immunity that reduces the growth of blood stage as opposed to liver stage parasites. We found that this mechanism would require at least two components – a rapidly acting strain-specific component, as well as a slowly acquired cross-reactive or general immunity to all strains. Analysis and modelling of malaria infection dynamics and naturally acquired immunity with age provides important insights into what mechanisms of immune control may be harnessed by malaria vaccine strategists.     

Strategies for introducing Wolbachia to reduce transmission of mosquito-borne diseases

Certain strains of the endosymbiont Wolbachia have the potential to lower the vectorial capacity of mosquito populations and assist in controlling a number of mosquito-borne diseases. An important consideration when introducing Wolbachia-carrying mosquitoes into natural populations is the minimisation of any transient increase in disease risk or biting nuisance. This may be achieved by predominantly releasing male mosquitoes. To explore this, we use a sex-structured model of Wolbachia-mosquito interactions. We first show that Wolbachia spread can be initiated with very few infected females provided the infection frequency in males exceeds a threshold. We then consider realistic introduction scenarios involving the release of batches of infected mosquitoes, incorporating seasonal fluctuations in population size. For a range of assumptions about mosquito population dynamics we find that male-biased releases allow the infection to spread after the introduction of low numbers of females, many fewer than with equal sex-ratio releases. We extend the model to estimate the transmission rate of a mosquito-borne pathogen over the course of Wolbachia establishment. For a range of release strategies we demonstrate that male-biased release of Wolbachia-infected mosquitoes can cause substantial transmission reductions without transiently increasing disease risk. The results show the importance of including mosquito population dynamics in studying Wolbachia spread and that male-biased releases can be an effective and safe way of rapidly establishing the symbiont in mosquito populations.     

Social Contact Networks and Disease Eradicability under Voluntary Vaccination

Certain theories suggest that it should be difficult or impossible to eradicate a vaccine-preventable disease under voluntary vaccination: Herd immunity implies that the individual incentive to vaccinate disappears at high coverage levels. Historically, there have been examples of declining coverage for vaccines, such as MMR vaccine and whole-cell pertussis vaccine, that are consistent with this theory. On the other hand, smallpox was globally eradicated by 1980 despite voluntary vaccination policies in many jurisdictions. Previous modeling studies of the interplay between disease dynamics and individual vaccinating behavior have assumed that infection is transmitted in a homogeneously mixing population. By comparison, here we simulate transmission of a vaccine-preventable SEIR infection through a random, static contact network. Individuals choose whether to vaccinate based on infection risks from neighbors, and based on vaccine risks. When neighborhood size is small, rational vaccinating behavior results in rapid containment of the infection through voluntary ring vaccination. As neighborhood size increases (while the average force of infection is held constant), a threshold is reached beyond which the infection can break through partially vaccinated rings, percolating through the whole population and resulting in considerable epidemic final sizes and a large number vaccinated. The former outcome represents convergence between individually and socially optimal outcomes, whereas the latter represents their divergence, as observed in most models of individual vaccinating behavior that assume homogeneous mixing. Similar effects are observed in an extended model using smallpox-specific natural history and transmissibility assumptions. This work illustrates the significant qualitative differences between behavior–infection dynamics in discrete contact-structured populations versus continuous unstructured populations. This work also shows how disease eradicability in populations where voluntary vaccination is the primary control mechanism may depend partly on whether the disease is transmissible only to a few close social contacts or to a larger subset of the population.     

Stochastic dynamics of immunity in small populations: a general framework

Assessment of immunological status is a powerful tool in the surveillance and control of infectious pathogens in livestock and human populations. The distribution of immunity levels in the population provides information on time and age dependent transmission. A stochastic model is developed for a livestock population which relates the dynamics of the distribution of immunity levels at the population level to those of pathogen transmission. A general model with K immunity level categories is first proposed, taking into account the increase of the immunity level due to an infection or a re-exposure, the decrease of the immunity level with time since infection or exposure, and the effect of immunity level on the susceptibility and the infectivity of individuals. Numerical results are presented in the particular cases with K=2 and K=3 immunity level categories. We demonstrate that for a given distribution of the immunity levels at the population level, the model can be used to identify quantities such as most likely periods of time since introduction of infection. We discuss this approach in relation to analysis of serological data.     

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.     

Beyond Rational Decision-Making: Modelling the Influence of Cognitive Biases on the Dynamics of Vaccination Coverage

Background

Theoretical studies predict that it is not possible to eradicate a disease under voluntary vaccination because of the emergence of non-vaccinating “free-riders” when vaccination coverage increases. A central tenet of this approach is that human behaviour follows an economic model of rational choice. Yet, empirical studies reveal that vaccination decisions do not necessarily maximize individual self-interest. Here we investigate the dynamics of vaccination coverage using an approach that dispenses with payoff maximization and assumes that risk perception results from the interaction between epidemiology and cognitive biases.

Methods

We consider a behaviour-incidence model in which individuals perceive actual epidemiological risks as a function of their opinion of vaccination. As a result of confirmation bias, sceptical individuals (negative opinion) overestimate infection cost while pro-vaccines individuals (positive opinion) overestimate vaccination cost. We considered a feedback between individuals and their environment as individuals could change their opinion, and thus the way they perceive risks, as a function of both the epidemiology and the most common opinion in the population.

Results

For all parameter values investigated, the infection is never eradicated under voluntary vaccination. For moderately contagious diseases, oscillations in vaccination coverage emerge because individuals process epidemiological information differently depending on their opinion. Conformism does not generate oscillations but slows down the cultural response to epidemiological change.

Conclusion

Failure to eradicate vaccine preventable disease emerges from the model because of cognitive biases that maintain heterogeneity in how people perceive risks. Thus, assumptions of economic rationality and payoff maximization are not mandatory for predicting commonly observed dynamics of vaccination coverage. This model shows that alternative notions of rationality, such as that of ecological rationality whereby individuals use simple cognitive heuristics, offer promising new avenues for modelling vaccination behaviour.     

Mycobacterial ecology as a modulator of tuberculosis vaccine success

Natural infection with Mycobacterium tuberculosis, as well as cross-immune reactions with the constituent of standard vaccines, attenuated M. bovis, and other species of mycobacteria confer partial immunity to subsequent M. tuberculosis infection. It has been shown in the past that the immune response to mycobacteria found naturally in the environment reduces the benefit of vaccination as assessed by means of vaccine efficacy. In this paper we show that efficacy is a poor measure of the potential success of new anti-tuberculous vaccines due to its inability to account for the relative weight of reinfection in disease dynamics. We advocate instead the use of vaccine effectiveness when evaluating the impact of new control methods against infections that confer partial immunity. Through the study of a simple model that incorporates cross-reactive responses to environmental mycobacteria (EM) and reinfection, we show how the particulars of the relation between EM abundance and vaccine effectiveness depend on the degree of protection conferred respectively by natural infection, vaccination and EM. The relative importance of reinfection as a transmission mechanism comes up as the most important source of variability in vaccine effectiveness. Our results suggest that control efforts should be placed in reducing the importance of reinfection through diminishing transmission rates. Vaccines that overcome preexisting immunity to other mycobacteria will still have varying degrees of success depending on the underlying rate of TB transmission.     

Dynamics of Japanese Encephalitis Virus Transmission among Pigs in Northwest Bangladesh and the Potential Impact of Pig Vaccination

Background

Japanese encephalitis (JE) virus infection can cause severe disease in humans, resulting in death or permanent neurologic deficits among survivors. Studies indicate that the incidence of JE is high in northwestern Bangladesh. Pigs are amplifying hosts for JE virus (JEV) and a potentially important source of virus in the environment. The objectives of this study were to describe the transmission dynamics of JEV among pigs in northwestern Bangladesh and estimate the potential impact of vaccination to reduce incidence among pigs.

Methodology/Principal Findings

We conducted a comprehensive census of pigs in three JE endemic districts and tested a sample of them for evidence of previous JEV infection. We built a compartmental model to describe JEV transmission dynamics in this region and to estimate the potential impact of pig vaccination. We identified 11,364 pigs in the study area. Previous JEV infection was identified in 30% of pigs with no spatial differences in the proportion of pigs that were seropositive across the study area. We estimated that JEV infects 20% of susceptible pigs each year and the basic reproductive number among pigs was 1.2. The model suggest that vaccinating 50% of pigs each year resulted in an estimated 82% reduction in annual incidence in pigs.

Conclusions/Significance

The widespread distribution of historic JEV infection in pigs suggests they may play an important role in virus transmission in this area. Future studies are required to understand the contribution of pig infections to JE risk in humans and the potential impact of pig vaccination on human disease.     

Modeling toxoplasmosis spread in cat populations under vaccination

In this paper we present an epidemiological model to study the transmission dynamics of toxoplasmosis in a cat population under a continuous vaccination schedule. We explore the dynamics of toxoplasmosis at the population level using a mathematical model that includes the effect of oocyst, since the probability of acquisition of Toxoplasma Gondii infection depends on the environmental load of the parasite. This model considers indirectly the infection of prey through the oocyst shedding by cats. We prove that the basic reproduction number R₀ is a threshold value that completely determines the global dynamics and the outcome of the disease. Numerical computer simulations are presented to investigate different scenarios. These simulations show the effectiveness of a constant vaccination program.