Evolving public perceptions and stability in vaccine uptake

Recent vaccine scares and sudden spikes in vaccine demand remind us that the effectiveness of mass vaccination programs is governed by the public perception of vaccination. Previous work has shown that the tendency of individuals to optimize self-interest can lead to vaccination levels that are suboptimal for a community. We use game theory to relate population-level demand for vaccines to decision-making by individuals with varied beliefs about the costs of infection and vaccination. In contrast to previous work proposing that universal vaccination is impossible in a game theoretic context, we show that optimal individual behavior can vary between universal vaccination and no vaccination, depending on the relative costs and benefits to individuals. By coupling game models and epidemic models, we demonstrate that the pursuit of self-interest often leads to stable dynamics but can lead to oscillations in vaccine uptake over time. The instability is exacerbated in populations that are more homogeneous with respect to their perceptions of vaccine and infection risks. This research illustrates the importance of applying temporal models to an inherently temporal situation, namely, the time evolution of vaccine coverage in an informed population with a voluntary vaccination policy.     

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.     

Erratic flu vaccination emerges from short-sighted behavior in contact networks

The effectiveness of seasonal influenza vaccination programs depends on individual-level compliance. Perceptions about risks associated with infection and vaccination can strongly influence vaccination decisions and thus the ultimate course of an epidemic. Here we investigate the interplay between contact patterns, influenza-related behavior, and disease dynamics by incorporating game theory into network models. When individuals make decisions based on past epidemics, we find that individuals with many contacts vaccinate, whereas individuals with few contacts do not. However, the threshold number of contacts above which to vaccinate is highly dependent on the overall network structure of the population and has the potential to oscillate more wildly than has been observed empirically. When we increase the number of prior seasons that individuals recall when making vaccination decisions, behavior and thus disease dynamics become less variable. For some networks, we also find that higher flu transmission rates may, counterintuitively, lead to lower (vaccine-mediated) disease prevalence. Our work demonstrates that rich and complex dynamics can result from the interaction between infectious diseases, human contact patterns, and behavior.     

Control of emerging infectious diseases using responsive imperfect vaccination and isolation

This paper is concerned with a stochastic model for the spread of an SEIR (susceptible --> exposed (= latent) --> infective --> removed) epidemic among a population partitioned into households, featuring different rates of infection for within and between households. The model incorporates responsive vaccination and isolation policies, based upon the appearance of diagnosed cases in households. Different models for imperfect vaccine response are considered. A threshold parameter R*, which determines whether or not a major epidemic can occur, and the probability of a major epidemic are obtained for different infectious and latent period distributions. Simpler expressions for these quantities are obtained in the limiting case of infinite within-household infection rate. Numerical studies suggest that the choice of infectious period distribution and whether or not latent individuals are vaccine-sensitive have a material influence on the spread of the epidemic, while, for given vaccine efficacy, the choice of vaccine action model is less influential. They also suggest that an effective isolation policy has a more significant impact than vaccination. The results show that R* alone is not sufficient to summarise the potential for an epidemic.     

Estimation of Population Vaccination Effectiveness from HIV Vaccine Trials

Longini , Datta , and Halloran (1996) proposed to design HIV vaccine trials in a way that will permit the simultaneous estimation of the vaccine effects on susceptibility to infection and on infectiousness of vaccine brak-throughs. The main feature of their design is the inclusion of steady partners of trial participants. They estimate four parameters from the vaccine trial: the probability that a susceptible person will become infected from his/her steady partner, the probability of becoming infected from outside the partnership, the vaccine efficacy for susceptibility and the vaccine efficacy for infectiousness. We show how the estimates of these parameters can be used to predict the attack rate in a given population during a specified period following mass-vaccination. This is an iterative method, as the attack rate depends on the HIV prevalence which, in turn, depends on the number of new cases during that period. The same method is also used to estimate the attack rate in that population during the same period in the absence of vaccination. The estimated attack rates allow us to estimate the population vaccination effectiveness, defined as the fraction HIV cases prevented by a vaccination program.     

Effectiveness of Meningococcal C Conjugate Vaccine in Salvador,Brazil: A Case-Control Study

Background

During a citywide epidemic of serogroup C meningococcal disease in Salvador in 2010, Brazil, the state government initiated mass vaccination targeting two age groups with high attack rates: individuals aged <5 years and 10–24 years. More than 600,000 doses of meningococcal serogroup C conjugate vaccines were administered. We performed a case-control study to evaluate vaccine uptake, document vaccine effectiveness and identify reasons for non-vaccination.

Methods and Findings

Population-based surveillance identified patients with laboratory-confirmed invasive meningococcal C (MenC) disease during 2010. Information on MenC vaccination was obtained from case patients and age-matched individuals from the same neighborhoods. MenC vaccine effectiveness was estimated based on the exact odds ratios obtained by conditional logistic regression analysis. Of 51 laboratory-confirmed cases of serogroup C meningococcal disease among patients <5 and 10–24 years of age 50 were included in the study and matched with 240 controls. Overall case-fatality was 25%. MenC vaccine coverage among controls increased from 7.1% to 70.2% after initiation of the vaccination campaign. None of the 50 case patients but 70 (29.2%) of the 240 control individuals, including 59 (70.2%) of 84 matched with cases from the period after MenC vaccination, had received at least one MenC vaccine dose. Overall effectiveness of MenC was 98% with a lower 95% exact confidence limit of 89%.

Conclusions

MenC vaccines administered during the meningococcal epidemic were highly effective, suggesting that rapid vaccine uptake through campaigns contributed to control of meningococcal disease.     

Strain replacement in an epidemic model with super-infection and perfect vaccination

Several articles in the recent literature discuss the complexities of the impact of vaccination on competing subtypes of one micro-organism. Both with competing virus strains and competing serotypes of bacteria, it has been established that vaccination has the potential to switch the competitive advantage from one of the pathogen subtypes to the other resulting in pathogen replacement. The main mechanism behind this process of substitution is thought to be the differential effectiveness of the vaccine with respect to the two competing micro-organisms. In this article, we show that, if the disease dynamics is regulated by super-infection, strain substitution may indeed occur even with perfect vaccination. In fact we discuss a two-strain epidemic model in which the first strain can infect individuals already infected by the second and, as far as vaccination is concerned, we consider a best-case scenario in which the vaccine provides perfect protection against both strains. We find out that if the reproduction number of the first strain is smaller than the reproduction number of the second strain and the first strain dominates in the absence of vaccination then increasing vaccination levels promotes coexistence which allows the first strain to persist in the population even if its vaccine-dependent reproduction number is below one. Further increase of vaccination levels induces the domination of the second strain in the population. Thus the second strain replaces the first strain. Large enough vaccination levels lead to the eradication of the disease.     

Real-time investigation of measles epidemics with estimate of vaccine efficacy

As part of measles elimination effort, evaluation of the vaccination program and real-time assessment of the epidemic dynamics constitute two important tasks to improve and strengthen the control. The present study aimed to develop an epidemiological modeling method which can be applied to estimating the vaccine efficacy at an individual level while conducting the timely investigation of the epidemic. The multivariate renewal process model was employed to describe the temporal evolution of infection by vaccination history, jointly estimating the time-dependent reproduction number and the vaccine efficacy. Analyzing the enhanced surveillance data of measles in Aichi prefecture, Japan from 2007-08, the vaccine efficacy was estimated at 96.7% (95% confidence interval: 95.8, 97.4). Using an age structured model, the vaccine efficacy among those aged from 5-19 years was shown to be smaller than that among those from 0-4 years. The age-dependent vaccine efficacy estimate informs the age-groups to be targeted for revaccination. Because the estimation method can rest on readily available epidemiological data, the proposed model has a potential to be integrated with routine surveillance.     

Modeling HIV Vaccines in Brazil: Assessing the Impact of a Future HIV Vaccine on Reducing New Infections,Mortality and Number of People Receiving ARV

Background

The AIDS epidemic in Brazil remains concentrated in populations with high vulnerability to HIV infection, and the development of an HIV vaccine could make an important contribution to prevention. This study modeled the HIV epidemic and estimated the potential impact of an HIV vaccine on the number of new infections, deaths due to AIDS and the number of people receiving ARV treatment, under various scenarios.

Methods and Findings

The historical HIV prevalence was modeled using Spectrum and projections were made from 2010 to 2050 to study the impact of an HIV vaccine with 40% to 70% efficacy, and 80% coverage of adult population, specific groups such as MSM, IDU, commercial sex workers and their partners, and 15 year olds. The possibility of disinhibition after vaccination, neglecting medium- and high-risk groups, and a disease-modifying vaccine were also considered. The number of new infections and deaths were reduced by 73% and 30%, respectively, by 2050, when 80% of adult population aged 15–49 was vaccinated with a 40% efficacy vaccine. Vaccinating medium- and high-risk groups reduced new infections by 52% and deaths by 21%. A vaccine with 70% efficacy produced a great decline in new infections and deaths. Neglecting medium- and high-risk population groups as well as disinhibition of vaccinated population reduced the impact or even increased the number of new infections. Disease-modifying vaccine also contributed to reducing AIDS deaths, the need for ART and new HIV infections.

Conclusions

Even in a country with a concentrated epidemic and high levels of ARV coverage, such as Brazil, moderate efficacy vaccines as part of a comprehensive package of treatment and prevention could have a major impact on preventing new HIV infections and AIDS deaths, as well as reducing the number of people on ARV. Targeted vaccination strategies may be highly effective and cost-beneficial.     

Epidemiological Impact of a Genital Herpes Type 2 Vaccine for Young Females

Genital Herpes, which is caused by Herpes Simplex Virus-1 or -2 (HSV-1, -2, predominantly HSV-2) is a sexually transmitted infection (STI) that causes a chronic latent infection with outbreak episodes linked to transmission. Antiviral therapies are effective in reducing viral shedding during these episodes, but are ineffective as a whole since many outbreaks are asymptomatic or have mild symptoms. Thus, the development of a vaccine for genital herpes is needed to control this disease. The question of how to implement such a vaccine program is an important one, and may be similar to the vaccination program for Human Papilloma Virus (HPV) for young females. We have developed a mathematical model to describe the epidemiology of vaccination targeting young females against HSV-2. The model population is delineated with respect to age group, sexual activity and infection status including oral infection of HSV-1, which may affect vaccine efficacy. A threshold parameter , which determines the level of vaccine uptake needed to eradicate HSV-2, is found. Computer simulation shows that an adolescent-only vaccination program may be effective in eliminating HSV-2 disease, however, the success of extinction greatly depends on the level of vaccine uptake, the vaccine efficacy, the age of sexual maturity and safe sex practices. However, the time course of eradication would take many years. We also investigate the prevalence of infection in the total population and in women between 16–30 years of age before and after vaccination has been introduced, and show that the adolescent-only vaccination program can be effective in reducing disease prevalence in these populations depending on the level of vaccine uptake and vaccine efficacy. This will also result in a decrease of maternal-fetal transmission of HSV-2 infection. Another important, if commonsense, conclusion is that vaccination of some females reduces infection in men, which then reduces infection in women.     

Uniqueness of Nash equilibrium in vaccination games

One crucial condition for the uniqueness of Nash equilibrium set in vaccination games is that the attack ratio monotonically decreases as the vaccine coverage level increasing. We consider several deterministic vaccination models in homogeneous mixing population and in heterogeneous mixing population. Based on the final size relations obtained from the deterministic epidemic models, we prove that the attack ratios can be expressed in terms of the vaccine coverage levels, and also prove that the attack ratios are decreasing functions of vaccine coverage levels. Some thresholds are presented, which depend on the vaccine efficacy. It is proved that for vaccination games in homogeneous mixing population, there is a unique Nash equilibrium for each game.     

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.     

Optimizing vaccine allocation at different points in time during an epidemic

Background

Pandemic influenza A(H1N1) 2009 began spreading around the globe in April of 2009 and vaccination started in October of 2009. In most countries, by the time vaccination started, the second wave of pandemic H1N1 2009 was already under way. With limited supplies of vaccine, we are left to question whether it may be a good strategy to vaccinate the high-transmission groups earlier in the epidemic, but it might be a better use of resources to protect instead the high-risk groups later in the epidemic. To answer this question, we develop a deterministic epidemic model with two age-groups (children and adults) and further subdivide each age group in low and high risk.

Methods and Findings

We compare optimal vaccination strategies started at various points in time in two different settings: a population in a developed country where children account for 24% of the population, and a population in a less developed country where children make up the majority of the population, 55%. For each of these populations, we minimize mortality or hospitalizations and we find an optimal vaccination strategy that gives the best vaccine allocation given a starting vaccination time and vaccine coverage level. We find that population structure is an important factor in determining the optimal vaccine distribution. Moreover, the optimal policy is dynamic as there is a switch in the optimal vaccination strategy at some time point just before the peak of the epidemic. For instance, with 25% vaccine coverage, it is better to protect the high-transmission groups before this point, but it is optimal to protect the most vulnerable groups afterward.

Conclusions

Choosing the optimal strategy before or early in the epidemic makes an important difference in minimizing the number of influenza infections, and consequently the number of influenza deaths or hospitalizations, but the optimal strategy makes little difference after the peak.     

Analyzing effects of vaccines.

A population with (individually) varying susceptibilities to infection and a vaccine with (individually) varying protective effect are considered. A simple stochastic model is used to illustrate different effects of the vaccine on the spread of the infection. The behavior of different estimators of the vaccine efficacy using data from a clinical trial and the relation between vaccine efficacy and the effectiveness of a vaccination program are discussed.     

A game dynamic model for delayer strategies in vaccinating behaviour for pediatric infectious diseases

Several studies have found that some parents delay the age at which their children receive pediatric vaccines due to perception of higher vaccine risk at the recommended age of vaccination. This has been particularly apparently during the Measles-Mumps-Rubella scare in the United Kingdom. Under a voluntary vaccination policy, vaccine coverage in certain age groups is a potentially complex interplay between vaccinating behaviour, disease dynamics, and age-specific risk factors. Here, we construct an age-structured game dynamic model, where individuals decide whether to vaccinate according to imitation dynamics depending on age-dependent disease prevalence and perceived risk of vaccination. Individuals may be timely vaccinators, delayers, or non-vaccinators. The model exhibits multiple equilibria and a broad range of possible dynamics. For certain parameter regimes, the proportion of timely vaccinators and delayers oscillate in an anti-phase fashion in response to oscillations in infection prevalence. Under an exogenous change to the perceived risk of vaccination as might occur during a vaccine scare, the model can also capture an increase in delayer strategists similar in magnitude to that observed during the Measles-Mumps-Rubella vaccine scare in the United Kingdom. Our model also shows that number of delayers steadily increases with increasing severity of the scare, whereas it saturates to specific value with increases in duration of the scare. Finally, by comparing the model dynamics with and without the option of a delayer strategy, we show that adding a third delayer strategy can have a stabilizing effect on model dynamics. In an era where individual choice—rather than accessibility—is becoming an increasingly important determinant of vaccine uptake, more infectious disease models may need to use game theory or related techniques to determine vaccine uptake.     

Protective Vaccine Efficacy when Vaccine Response is Random

Vaccine induced protection against infection is often random because of primary vaccine failures and variation in the immune systems of hosts. We introduce a concept of protective vaccine efficacy in terms of mean relative susceptibility of vaccinated individuals and derive both a lower and an upper bound for it. These bounds apply for all distributions of the vaccine response and can be estimated from data on the size of a major epidemic. Standard errors are given for estimates of the bounds. Bounds are also given for the vaccination coverage required to prevent epidemics and these are also estimable from data on the size of a major epidemic. The results are applied to data on an outbreak of mumps.     

A Susceptible-infected Epidemic Model with Voluntary Vaccinations

An susceptible-infected epidemic model with endogenous behavioral changes is presented to analyze the impact of a prophylactic vaccine on disease prevalence. It is shown that, with voluntary vaccination, whether an endemic equilibrium exists or not does not depend on vaccine efficacy or the distribution of agent-types. Although an endemic equilibrium is unique in the absence of a vaccine, the availability of a vaccine can lead to multiple endemic equilibria that differ in disease prevalence and vaccine coverage. Depending on the distribution of agent-types, the introduction of a vaccine or, if one is available, a subsidy for vaccination can increase disease prevalence by inducing more risky behavior.I would like to thank one of the editors of the journal, Alan Hastings, for his comments and suggestions.     

Modelling the effect of a booster vaccination on disease epidemiology

Despite the effectiveness of vaccines in dramatically decreasing the number of new infectious cases and severity of illnesses, imperfect vaccines may not completely prevent infection. This is because the immunity afforded by these vaccines is not complete and may wane with time, leading to resurgence and epidemic outbreaks notwithstanding high levels of primary vaccination. To prevent an endemic spread of disease, and achieve eradication, several countries have introduced booster vaccination programs. The question of whether this strategy could eventually provide the conditions for global eradication is addressed here by developing a seasonally-forced mathematical model. The analysis of the model provides the threshold condition for disease control in terms of four major parameters: coverage of the primary vaccine; efficacy of the vaccine; waning rate; and the rate of booster administration. The results show that if the vaccine provides only temporary immunity, then the infection typically cannot be eradicated by a single vaccination episode. Furthermore, having a booster program does not necessarily guarantee the control of a disease, though the level of epidemicity may be reduced. In addition, these findings strongly suggest that the high coverage of primary vaccination remains crucial to the success of a booster strategy. Simulations using estimated parameters for measles illustrate model predictions. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). One of the authors (P.R.) acknowledges the support of the Ellison Medical Foundation.     

Modelling infectious diseases with relapse: a case study of HSV-2

Background

Herpes Simplex Virus Type 2 (HSV-2) is one of the most common sexually transmitted diseases. Although there is still no licensed vaccine for HSV-2, a theoretical investigation of the potential effects of a vaccine is considered important and has recently been conducted by several researchers. Although compartmental mathematical models were considered for each special case in the previous studies, as yet there are few global stability results.

Results

In this paper, we formulate a multi-group SVIRI epidemic model for HSV-2, which enables us to consider the effects of vaccination, of waning vaccine immunity, and of infection relapse. Since the number of groups is arbitrary, our model can be applied to various structures such as risk, sex, and age group structures. For our model, we define the basic reproduction number ?₀ and prove that if ?₀≤1, then the disease-free equilibrium is globally asymptotically stable, whereas if ?₀>1, then the endemic equilibrium is so. Based on this global stability result, we estimate ?₀ for HSV-2 by applying our model to the risk group structure and using US data from 2001 to 2014. Through sensitivity analysis, we find that ?₀ is approximately in the range of 2-3. Moreover, using the estimated parameters, we discuss the optimal vaccination strategy for the eradication of HSV-2.

Conclusions

Through discussion of the optimal vaccination strategy, we come to the following conclusions. (1) Improving vaccine efficacy is more effective than increasing the number of vaccines. (2) Although the transmission risk in female individuals is higher than that in male individuals, distributing the available vaccines almost equally between female and male individuals is more effective than concentrating them within the female population.

     

Reactive vaccination in the presence of disease hotspots

Reactive vaccination has recently been adopted as an outbreak response tool for cholera and other infectious diseases. Owing to the global shortage of oral cholera vaccine, health officials must quickly decide who and where to distribute limited vaccine. Targeted vaccination in transmission hotspots (i.e. areas with high transmission efficiency) may be a potential approach to efficiently allocate vaccine, however its effectiveness will likely be context-dependent. We compared strategies for allocating vaccine across multiple areas with heterogeneous transmission efficiency. We constructed metapopulation models of a cholera-like disease and compared simulated epidemics where: vaccine is targeted at areas of high or low transmission efficiency, where vaccine is distributed across the population, and where no vaccine is used. We find that connectivity between populations, transmission efficiency, vaccination timing and the amount of vaccine available all shape the performance of different allocation strategies. In highly connected settings (e.g. cities) when vaccinating early in the epidemic, targeting limited vaccine at transmission hotspots is often optimal. Once vaccination is delayed, targeting the hotspot is rarely optimal, and strategies that either spread vaccine between areas or those targeted at non-hotspots will avert more cases. Although hotspots may be an intuitive outbreak control target, we show that, in many situations, the hotspot-epidemic proceeds so fast that hotspot-targeted reactive vaccination will prevent relatively few cases, and vaccination shared across areas where transmission can be sustained is often best.