A game dynamic model for vaccine skeptics and vaccine believers: measles as an example

Effect of homophily on coupled behavior-disease dynamics near a tipping point

Understanding the interplay between social activities and disease dynamics is crucial for effective public health interventions. Recent studies using coupled behavior-disease models assumed homogeneous populations. However, heterogeneity in population, such as different social groups, cannot be ignored. In this study, we divided the population into social media users and non-users, and investigated the impact of homophily (the tendency for individuals to associate with others similar to themselves) and online events on disease dynamics. Our results reveal that homophily hinders the adoption of vaccinating strategies, hastening the approach to a tipping point after which the population converges to an endemic equilibrium with no vaccine uptake. Furthermore, we find that online events can significantly influence disease dynamics, with early discussions on social media platforms serving as an early warning signal of potential disease outbreaks. Our model provides insights into the mechanisms underlying these phenomena and underscores the importance of considering homophily in disease modeling and public health strategies.

Dynamical vaccination behavior with risk perception and vaccination rewards

Vaccination is the most effective way to control the epidemic spreading. However, the probability of people getting vaccinated changes with the epidemic situation due to personal psychology. Facing various risks, some people are reluctant to vaccinate and even prefer herd immunity. To encourage people to get vaccinated, many countries set up reward mechanisms. In this paper, we propose a disease transmission model combining vaccination behaviors based on the SIR (Susceptible-Infected-Recovered) model and introduce three vaccination mechanisms. We analyze the impact of the infection rate and the recovery rate on the total cost and the epidemic prevalence. Numerical simulations fit with our intuitive feelings. Then, we study the impact of vaccination rewards on the total social cost. We find that when vaccination rewards offset vaccination costs, both the total cost and the epidemic prevalence reach the lowest levels. Finally, this paper suggests that encouraging people to get vaccinated at the beginning of an epidemic has the best effect.

Exploring epidemic voluntary vaccinating behavior based on information-driven decisions and benefit-cost analysis

A complex dynamic interplay exists between epidemic transmission and vaccination, which is significantly influenced by human behavioral responses. We construct a research framework combining both the function modeling of the cumulative global COVID-19 information and limited individuals' information processing capacity employing the Gompertz model for growing processes. Meanwhile, we built a function representing the decision to get vaccinated following benefit-cost analysis considered the choices made by people in each scenario have an influence from altruism, free-riding and immunity escaping capacity. Through the mean-field calculation analysis and using a fourth-order Runge-Kutta method with constant step size, we obtain plots from numerical simulations. We found that only when the total number of infectious individuals proves sufficient to reach and exceed a certain level will the individuals face a better trade-off in determining whether to get vaccinated against the diseases based on that information. Besides, authoritative media have a higher decisive influence and efforts should be focused on extending the duration of vaccine protection, which is beneficial to inhibit the outbreaks of epidemics. Our work elucidates that reducing the negative payoff brought about by the free-riding behavior for individuals or improving the positive payoff from the altruistic motivation helps to control the disease in cultures that value social benefits, vaccination willingness is generally stronger. We also note that at a high risk of infection, the decision of vaccination is highly correlated with global epidemic information concerning COVID-19 infection, while at times of lower risk, it depends on the game theoretic vaccine strategy. The findings demonstrate that improving health literacy, ensuring open and transparent information on vaccine safety and efficacy as a public health priority can be an effective strategy for mitigating inequalities in health education, as well as alleviating the phenomenon that immunity escaping abilities is more likely to panic by populations with high levels of education. In addition, prosocial nudges are great ways to bridge these immunity gaps that can contribute to implementing government public health control measures, creating a positive feedback loop.

Imperfect vaccine can yield multiple Nash equilibria in vaccination games

As infectious diseases continue to threaten communities across the globe, people are faced with a choice to vaccinate, or not. Many factors influence this decision, such as the cost of the disease, the chance of contracting the disease, the population vaccination coverage, and the efficacy of the vaccine. While the vaccination games in which individuals decide whether to vaccinate or not based on their own interests are gaining in popularity in recent years, the vaccine imperfection has been an overlooked aspect so far. In this paper we investigate the effects of an imperfect vaccine on the outcomes of a vaccination game. We use a simple SIR compartmental model for the underlying model of disease transmission. We model the vaccine imperfection by adding vaccination at birth and maintain a possibility for the vaccinated individual to become infected. We derive explicit conditions for the existence of different Nash equilibria, the solutions of the vaccination game. The outcomes of the game depend on the complex interplay between disease transmission dynamics (the basic reproduction number), the relative cost of the infection, and the vaccine efficacy. We show that for diseases with relatively low basic reproduction numbers (smaller than about 2.62), there is a little difference between outcomes for perfect or imperfect vaccines and thus the simpler models assuming perfect vaccines are good enough. However, when the basic reproduction number is above 2.62, then, unlike in the case of a perfect vaccine, there can be multiple equilibria. Moreover, unless there is a mandatory vaccination policy in place that would push the vaccination coverage above the value of unstable Nash equilibrium, the population could eventually slip to the "do not vaccinate" state. Thus, for diseases that have relatively high basic reproduction numbers, the potential for the vaccine not being perfect should be explicitly considered in the models.

A game-theoretic model of rabies in domestic dogs with multiple voluntary preventive measures

Game theory is now routinely applied to quantitatively model the decision making of individuals presented with various voluntary actions that can prevent a given disease. Most models consider only a single preventive strategy and the case where multiple preventative actions are available is severely understudied. In our paper, we consider a very simple SI compartmental model of rabies in the domestic dog population. We study two choices of the dog owners: to vaccinate their dogs or to restrict the movements of unvaccinated dogs. We analyze the relatively rich patterns of Nash equilibria (NE). We show that there is always at least one NE at which the owners utilize only one form of prevention. However, there can be up to three different NEs at the same time: two NEs at which the owners use exclusively only the vaccination or movement restriction, and the third NE when the owners use both forms of prevention simultaneously. However, we also show that, unlike the first two types of NEs, the third kind of NE is not convergent stable.

Profiling vaccine believers and skeptics in nurses: A latent profile analysis

BACKGROUND

A tailored immunization program is deemed more successful in encouraging vaccination. Understanding the profiles of vaccine hesitancy constructs in nurses can help policymakers in devising such programs. Encouraging vaccination in nurses is an important step in building public confidence in the upcoming COVID-19 and influenza vaccination campaigns.

OBJECTIVES

Using a person-centered approach, this study aimed to reveal the profiles of the 5C psychological constructs of vaccine hesitancy (confidence, complacency, constraints, calculation, and collective responsibility) among Hong Kong nurses.

DESIGN

Cross-sectional online survey.

SETTINGS

With the promotion of a professional nursing organization, we invited Hong Kong nurses to complete an online survey between mid-March and late April 2020 during the COVID-19 outbreak.

PARTICIPANTS

1,193 eligible nurses (mean age = 40.82, SD = 10.49; with 90.0% being female) were included in the analyses.

METHODS

In the online survey, we asked the invited nurses to report their demographics, COVID-19-related work demands (including the supply of personal protective equipment, work stress, and attitudes towards workplace infection control policies), the 5C vaccine hesitancy components, seasonal influenza vaccine uptake history, and the COVID-19 vaccine uptake intention. Latent profile analysis was employed to identify distinct vaccine hesitancy antecedent subgroups.

RESULTS

Results revealed five profiles, including "believers" (31%; high confidence, collective responsibility; low complacency, constraint), "skeptics" (11%; opposite to the believers), "outsiders" (14%; low calculation, collective responsibility), "contradictors" (4%; high in all 5C constructs), and "middlers" (40%; middle in all 5C constructs). Believers were less educated, reported more long-term illnesses, greater work stress, higher perceived personal protective equipment sufficiency, and stronger trust in government than skeptics. They were older and had higher perceived personal protective equipment sufficiency than middlers. Also, believers were older and had greater work stress than outsiders. From the highest to the lowest on vaccination uptake and intention were believers and contradictors, then middlers and outsiders, and finally skeptics.

CONCLUSION

Different immunization programs can be devised based on the vaccine hesitancy profiles and their predictors. Despite both profiles being low in vaccination uptake and intention, our results distinguished between outsiders and skeptics regarding their different levels of information-seeking engagement. The profile structure reveals the possibilities in devising tailored interventions based on their 5C characteristics. The current data could serve as the reference for the identification of individual profile membership and future profiling studies. Future endeavor is needed to examine the generalizability of the profile structure in other populations and across different study sites. Tweetable abstract: Covid-19 vaccine hesitancy profiles of Hong Kong nurses (believers, sceptics, outsiders, contradictors and middlers) highlight the importance of tailored vaccine campaigns.

Effect of population heterogeneity on herd immunity and on vaccination decision making process

We study the influence of population heterogeneity on herd immunity level and on individual's vaccination decision making process. We first formulate the mathematical model in a population with two subgroups, based on different activity levels or different susceptibilities. The herd immunity threshold is derived and discussed. It is calculated that the required vaccine coverage level for herd immunity in a heterogeneous mixing population can be varied significantly. The required vaccine coverage level is lower than the classical herd immunity level, if the vaccine coverage level in the more active group or more susceptible group is higher than the other subgroup. It is suggested that the classical herd immunity levels can be misleading in the process of planning mass vaccination programs. The analysis is further extended to study the population with more subgroups. We then study the formal vaccination games to simulate the process of vaccination decision making, in either homogeneous or heterogeneous mixing populations. It is proved that the Nash equilibrium in the vaccination game is not unique if population heterogeneity is considered. Moreover, herd immunity is not achieved if individuals are solely driven by self-interests.

Persistence of anti-vaccine sentiment in social networks through strategic interactions

Vaccination is the primary intervention for controlling the spread of infectious diseases. A certain level of vaccination rate (referred to as "herd immunity") is needed for this intervention to be effective. However, there are concerns that herd immunity might not be achieved due to an increasing level of hesitancy and opposition to vaccines. One of the primary reasons for this is the cost of non-conformance with one's peers. We use the framework of network coordination games to study the persistence of anti-vaccine sentiment in a population. We extend it to incorporate the opposing forces of the pressure of conforming to peers, herd-immunity and vaccination benefits. We study the structure of the equilibria in such games, and the characteristics of unvaccinated nodes. We also study Stackelberg strategies to reduce the number of nodes with anti-vaccine sentiment. Finally, we evaluate our results on different kinds of real world social networks.

Optimal voluntary and mandatory insect repellent usage and emigration strategies to control the chikungunya outbreak on Reunion Island

In 2005, a chikungunya virus outbreak devastated the tropical island of Reunion, infecting a third of the total population. Motivated by the Reunion Island case study, we investigate the theoretic potential for two intervention measures under both voluntary and mandatory protocols to control a vector-borne disease when there is risk of the disease becoming endemic. The first measure uses insect repellent to prevent mosquito bites, while the second involves emigrating to the neighboring Mauritius Island to avoid infection. There is a threshold on the cost of using repellent above which both voluntary and mandatory regimes find it optimal to forgo usage. Below that threshold, mandatory usage protocols will eradicate the disease; however, voluntary adoption leaves the disease at a small endemic level. Emigrating from the island to avoid infection results in a tragedy-of-the-commons effect: while being potentially beneficial to specific susceptible individuals, the remaining islanders paradoxically face a higher risk of infection. Mandated relocation of susceptible individuals away from the epidemic is viable only if the cost of this relocation is several magnitudes lower than the cost of infection. Since this assumption is unlikely to hold for chikungunya, it is optimal to discourage such emigration for the benefit of the entire population. An underlying assumption about the conservation of human-vector encounter rates in mosquito biting behavior informs our conclusions and may warrant additional experimental verification.

Optimal strategies for vaccination and social distancing in a game-theoretic epidemiologic model

For various infectious diseases, vaccination has become a major intervention strategy. However, the importance of social distancing has recently been highlighted during the ongoing COVID-19 pandemic. In the absence of vaccination, or when vaccine efficacy is poor, social distancing may help to curb the spread of new virus strains. However, both vaccination and social distancing are associated with various costs. It is critical to consider these costs in addition to the benefits of these strategies when determining the optimal rates of application of control strategies. We developed a game-theoretic epidemiological model that considers vaccination and social distancing under the assumption that individuals pursue the maximization of payoffs. By using this model, we identified the individually optimal strategy based on the Nash strategy when both strategies are available and when only one strategy is available. Furthermore, we determined the relative costs of control strategies at which individuals preferentially adopt vaccination over social distancing (or vice versa).

A game-theoretic model of Monkeypox to assess vaccination strategies

Monkeypox (MPX) is a zoonotic disease similar to smallpox. Its fatality rate is about 11% and it is endemic to the Central and West African countries. In this paper, we analyze a compartmental model of MPX dynamics. Our goal is to see whether MPX can be controlled and eradicated by voluntary vaccinations. We show that there are three equilibria—disease free, fully endemic and previously neglected semi-endemic (with disease existing only among humans). The existence of semi-endemic equilibrium has severe implications should the MPX virus mutate to increased viral fitness in humans. We find that MPX is controllable and can be eradicated in a semi-endemic equilibrium by vaccination. However, in a fully endemic equilibrium, MPX cannot be eradicated by vaccination alone.

A game-theoretical analysis of poliomyelitis vaccination

Poliomyelitis is a worldwide disease that has nearly been eradicated thanks to the Global Polio Eradication Initiative. Nevertheless, the disease is currently still endemic in three countries. In this paper, we incorporate the vaccination in a two age-class model of polio dynamics. Our main objective is to see whether mandatory vaccination policy is needed or if polio could be almost eradicated by a voluntary vaccination. We perform game theoretical analysis and compare the herd immunity vaccination levels with the Nash equilibrium vaccination levels. We show that the gap between two vaccination levels is too large. We conclude that the mandatory vaccination policy is therefore needed to achieve a complete eradication.

Characterizing the impact of spatial clustering of susceptibility for measles elimination

Measles elimination efforts are primarily focused on achieving and maintaining national vaccination coverage goals, based on estimates of the critical vaccination threshold (Vc): the proportion of the population that must be immune to prevent sustained epidemics. Traditionally, Vc estimates assume evenly mixing populations, an invalid assumption. If susceptible individuals preferentially contact one another, communities may remain vulnerable to epidemics even when vaccination coverage targets are met at the national level. Here we present a simple method to estimate Vc and the effective reproductive number, R, while accounting for spatial clustering of susceptibility. For measles, assuming R0 = 15 and 95% population immunity, adjustment for high clustering of susceptibility increases R from 0.75 to 1.29, Vc from 93% to 96%, and outbreak probability after a single introduction from <1% to 23%. The impact of clustering remains minimal until vaccination coverage nears elimination levels. We illustrate our approach using Demographic and Health Survey data from Tanzania and show how non-vaccination clustering potentially contributed to continued endemic transmission of measles virus during the last two decades. Our approach demonstrates why high national vaccination coverage sometimes fails to achieve measles elimination, and that a shift from national to subnational focus is needed as countries approach elimination.

A Game-Theoretic Model of Cholera with Optimal Personal Protection Strategies

Cholera is an acute gastro-intestinal infection that affects millions of people throughout the world each year, primarily but not exclusively in developing countries. Because of its public health ramifications, considerable mathematical attention has been paid to the disease. Here we consider one neglected aspect of combating cholera: personal participation in anti-cholera interventions. We construct a game-theoretic model of cholera in which individuals choose whether to participate in either vaccination or clean water consumption programs under assumed costs. We find that relying upon individual compliance significantly lowers the incidence of the disease as long as the cost of intervention is sufficiently low, but does not eliminate it. The relative costs of the measures determined whether a population preferentially adopts a single preventative measure or employs the measure with the strongest early adoption.

Individual decisions to vaccinate one's child or oneself: A discrete choice experiment rejecting free-riding motives

It is essential for public health to understand what drives people's hesitance towards vaccination. Theoretical models of vaccination decisions are ubiquitous, often incorporating herd immunity, perceptions of vaccine-related side-effects (VRSE) and of vaccine-preventable burden of disease, but with little to no empirical exploration. Herd immunity is a (usually) positive externality where vaccinated individuals influence others' risks by their reduced capability to transmit an infectious disease to them. It is often assumed that (rational) individuals incorporate this externality in their strategic vaccination decision, from which free-riding behavior arises. We performed a Bayesian D-efficient discrete choice experiment in February-March 2017 to study vaccination behavior in 1919 Belgian respondents. Choice sets with vaccine profiles were constructed using six attributes: vaccine effectiveness, VRSE, accessibility (in terms of convenience and reimbursement), vaccine-preventable burden of disease, local (respondents' network of contacts) vaccination coverage, and population (the population at large) vaccination coverage. VRSE and accessibility are the most influential attributes, followed by vaccine effectiveness and burden of disease. Both population and local coverage are less important than the other attributes, but show a significant direct linear relationship with vaccine utility. This supports the existence of peer influence (more incentivized as more and more vaccinate), rather than free-riding on herd immunity. These findings were independent of whether respondents made vaccine choices for themselves or for their child. Around 40% of the respondents indicated accepting vaccination with little or no questioning. These 'acceptors' were less sensitive to changes in the vaccine-preventable burden of disease for their child's vaccination choices (but not for themselves). Public health institutions are critical in stimulating vaccine uptake by making vaccines conveniently available at an affordable price and by communicating pro-actively on perceived VRSEs. The free-riding assumption as a driver of individual vaccine decisions, seems inappropriate, but this observation needs confirming in other populations.

The Measles and Free Riders

This article takes up a game-theoretic perspective on California's recently passed bill (SB 277) that closes all nonmedical exemptions for school-mandated vaccination. Such a perspective characterizes parental decisions to vaccinate their children as a collective action problem and reveals the presence of an incentive to free ride-to enjoy the benefits of others' efforts to vaccinate their children without vaccinating one's own. This article defends California's legislation as a reasonable means of overcoming the free rider problem and of ensuring that the burdens of vaccination are shared equally.

Ebola could be eradicated through voluntary vaccination

Ebola virus disease (EVD) is a severe infection with an extremely high fatality rate spread through direct contact with body fluids. A promising Ebola vaccine (rVSV-ZEBOV) may soon become universally available. We constructed a game-theoretic model of Ebola incorporating individual decisions to vaccinate. We found that if a population adopts selfishly optimal vaccination strategies, then the population vaccination coverage falls negligibly short of the herd immunity level. We concluded that eradication of Ebola is feasible if voluntary vaccination programmes are coupled with focused public education efforts. We conducted uncertainty and sensitivity analysis to demonstrate that our findings do not depend on the choice of the epidemiological model parameters.

Dynamics of vaccination in a time-delayed epidemic model with awareness

This paper investigates the effects of vaccination on the dynamics of infectious disease, which is spreading in a population concurrently with awareness. The model considers contributions to the overall awareness from a global information campaign, direct contacts between unaware and aware individuals, and reported cases of infection. It is assumed that there is some time delay between individuals becoming aware and modifying their behaviour. Vaccination is administered to newborns, as well as to aware individuals, and it is further assumed that vaccine-induced immunity may wane with time. Feasibility and stability of the disease-free and endemic equilibria are studied analytically, and conditions for the Hopf bifurcation of the endemic steady state are found in terms of system parameters and the time delay. Analytical results are supported by numerical continuation of the Hopf bifurcation and numerical simulations of the model to illustrate different types of dynamical behaviour.

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.

Behavioural change models for infectious disease transmission: a systematic review (2010-2015)

We review behavioural change models (BCMs) for infectious disease transmission in humans. Following the Cochrane collaboration guidelines and the PRISMA statement, our systematic search and selection yielded 178 papers covering the period 2010-2015. We observe an increasing trend in published BCMs, frequently coupled to (re)emergence events, and propose a categorization by distinguishing how information translates into preventive actions. Behaviour is usually captured by introducing information as a dynamic parameter (76/178) or by introducing an economic objective function, either with (26/178) or without (37/178) imitation. Approaches using information thresholds (29/178) and exogenous behaviour formation (16/178) are also popular. We further classify according to disease, prevention measure, transmission model (with 81/178 population, 6/178 metapopulation and 91/178 individual-level models) and the way prevention impacts transmission. We highlight the minority (15%) of studies that use any real-life data for parametrization or validation and note that BCMs increasingly use social media data and generally incorporate multiple sources of information (16/178), multiple types of information (17/178) or both (9/178). We conclude that individual-level models are increasingly used and useful to model behaviour changes. Despite recent advancements, we remain concerned that most models are purely theoretical and lack representative data and a validation process.

Modeling The Economic Burden Of Adult Vaccine-Preventable Diseases In The United States

Vaccines save thousands of lives in the United States every year, but many adults remain unvaccinated. Low rates of vaccine uptake lead to costs to individuals and society in terms of deaths and disabilities, which are avoidable, and they create economic losses from doctor visits, hospitalizations, and lost income. To identify the magnitude of this problem, we calculated the current economic burden that is attributable to vaccine-preventable diseases among US adults. We estimated the total remaining economic burden at approximately $9 billion (plausibility range: $4.7-$15.2 billion) in a single year, 2015, from vaccine-preventable diseases related to ten vaccines recommended for adults ages nineteen and older. Unvaccinated individuals are responsible for almost 80 percent, or $7.1 billion, of the financial burden. These results not only indicate the potential economic benefit of increasing adult immunization uptake but also highlight the value of vaccines. Policies should focus on minimizing the negative externalities or spillover effects from the choice not to be vaccinated, while preserving patient autonomy.

Systematic Review of Health Economic Analyses of Measles and Rubella Immunization Interventions

Economic analyses for vaccine-preventable diseases provide important insights about the value of prevention. We reviewed the literature to identify all of the peer-reviewed, published economic analyses of interventions related to measles and rubella immunization options to assess the different types of analyses performed and characterize key insights. We searched PubMed, the Science Citation Index, and references from relevant articles for studies in English and found 67 analyses that reported primary data and quantitative estimates of benefit-cost or cost-effectiveness analyses for measles and/or rubella immunization interventions. We removed studies that we characterized as cost-minimization analyses from this sample because they generally provide insights that focused on more optimal strategies to achieve the same health outcome. The 67 analyses we included demonstrate the large economic benefits associated with preventing measles and rubella infections using vaccines and the benefit of combining measles and rubella antigens into a formulation that saves the costs associated with injecting the vaccines separately. Despite the importance of population immunity and dynamic viral transmission, most of the analyses used static models to estimate cases prevented and characterize benefits, although the use of dynamic models continues to increase. Many of the analyses focused on characterizing the most significant adverse outcomes (e.g., mortality for measles, congenital rubella syndrome for rubella) and/or only direct costs, and the most complete analyses present data from high-income countries.

Optimal Repellent Usage to Combat Dengue Fever

Dengue fever is one of the most important vector-borne diseases. It is transmitted by Aedes Stegomyia aegypti, and one of the most effective strategies to combat the disease is the reduction of exposure to bites of these mosquitoes. In this paper, we present a game-theoretical model in which individuals choose their own level of protection against mosquito bites in order to maximize their own benefits, effectively balancing the cost of protection and the risk of contracting the dengue fever. We find that even when the usage of protection is strictly voluntary, as soon as the cost of protection is about 10,000 times less than the cost of contracting dengue fever, the optimal level of protection will be within 5 % of the level needed for herd immunity.

Integrating Transgenic Vector Manipulation with Clinical Interventions to Manage Vector-Borne Diseases

Many vector-borne diseases lack effective vaccines and medications, and the limitations of traditional vector control have inspired novel approaches based on using genetic engineering to manipulate vector populations and thereby reduce transmission. Yet both the short- and long-term epidemiological effects of these transgenic strategies are highly uncertain. If neither vaccines, medications, nor transgenic strategies can by themselves suffice for managing vector-borne diseases, integrating these approaches becomes key. Here we develop a framework to evaluate how clinical interventions (i.e., vaccination and medication) can be integrated with transgenic vector manipulation strategies to prevent disease invasion and reduce disease incidence. We show that the ability of clinical interventions to accelerate disease suppression can depend on the nature of the transgenic manipulation deployed (e.g., whether vector population reduction or replacement is attempted). We find that making a specific, individual strategy highly effective may not be necessary for attaining public-health objectives, provided suitable combinations can be adopted. However, we show how combining only partially effective antimicrobial drugs or vaccination with transgenic vector manipulations that merely temporarily lower vector competence can amplify disease resurgence following transient suppression. Thus, transgenic vector manipulation that cannot be sustained can have adverse consequences—consequences which ineffective clinical interventions can at best only mitigate, and at worst temporarily exacerbate. This result, which arises from differences between the time scale on which the interventions affect disease dynamics and the time scale of host population dynamics, highlights the importance of accounting for the potential delay in the effects of deploying public health strategies on long-term disease incidence. We find that for systems at the disease-endemic equilibrium, even modest perturbations induced by weak interventions can exhibit strong, albeit transient, epidemiological effects. This, together with our finding that under some conditions combining strategies could have transient adverse epidemiological effects suggests that a relatively long time horizon may be necessary to discern the efficacy of alternative intervention strategies.

Despite decades of attempted vector control, several vector-borne diseases remain endemic. Recent high-profile studies suggest that candidate vaccines, particularly for dengue, may be less than completely effective as public health interventions. Nevertheless, the epidemiological consequences of using other novel approaches (e.g., transgenic strategies to reduce or replace vector populations) remain highly uncertain. Faced with unclear prospects of any one strategy succeeding in isolation, there is increasing interest in designing a comprehensive public health response to manage vector-borne diseases. Here we use a relatively simple model to study how combining vaccines, transgenic vector manipulation and antimicrobial medications can facilitate disease management. We explain why the epidemiological consequences for combining strategies are not expected to merely sum their effects. Contrary to the prevailing assumption that comprehensive disease management always yields public health benefits, we find integrating transgenic vector manipulation with clinical interventions can, in some cases, temporarily exacerbate the adverse consequences of any one strategy failing. These results highlight the need for system-specific modeling efforts aimed at assessing whether our conclusions apply to specific vector-borne diseases. We outline the implications for proceeding with public health responses integrating currently available products, as well as assessing their efficacy.

An evolutionary vaccination game in the modified activity driven network by considering the closeness

In this paper, we explore an evolutionary vaccination game in the modified activity driven network by considering the closeness. We set a closeness parameter p which is used to describe the way of connection between two individuals. The simulation results show that the closeness p may have an active role in weakening both the spreading of epidemic and the vaccination. Besides, when vaccination is not allowed, the final recovered density increases with the value of the ratio of the infection rate to the recovery rate λ / μ . However, when vaccination is allowed the final density of recovered individual first increases and then decreases with the value of λ / μ . Two variables are designed to identify the relation between the individuals' activities and their states. The results draw that both recovered and vaccinated frequency increase with the increase of the individuals' activities. Meanwhile, the immune fee has less impact on the individuals' vaccination than the closeness. While the λ / μ is in a certain range, with the increase of the value of λ / μ , the recovered frequency of the whole crowds reduces. Our results, therefore, reveal the fact that the best of intentions may lead to backfire.

Imitation dynamics of vaccine decision-making behaviours based on the game theory

Based on game theory, we propose an age-structured model to investigate the imitation dynamics of vaccine uptake. We first obtain the existence and local stability of equilibria. We show that Hopf bifurcation can occur. We also establish the global stability of the boundary equilibria and persistence of the disease. The theoretical results are supported by numerical simulations.

A game-theoretic approach to valuating toxoplasmosis vaccination strategies

The protozoan Toxoplasma gondii is a parasite often found in wild and domestic cats, and it is the cause of the disease toxoplasmosis. More than 60 million people in the United States carry the parasite, and the Centers for Disease Control have placed toxoplasmosis in their disease classification group Neglected Parasitic Infections as one of five parasitic diseases targeted as priorities for public health action. In recent years, there has been significant progress toward the development of a practical vaccine, so vaccination programs may soon be a viable approach to controlling the disease. Anticipating the availability of a toxoplasmosis vaccine, we are interested in determining when cat owners should vaccinate their own pets. We have created a mathematical model describing the conditions under which vaccination is advantageous. Our model can be used to predict the average vaccination level in the population. We find that there is a critical vaccine cost threshold above which no one will use the vaccine. A vaccine cost slightly below this threshold, however, results in high usage of the vaccine, and consequently in a significant reduction in population seroprevalence. Not surprisingly, we find that populations may achieve herd immunity only if the cost of vaccine is zero.

Conflicts of interest during contact investigations: a game-theoretic analysis

The goal of contact tracing is to reduce the likelihood of transmission, particularly to individuals who are at greatest risk for developing complications of infection, as well as identifying individuals who are in need of medical treatment of other interventions. In this paper, we develop a simple mathematical model of contact investigations among a small group of individuals and apply game theory to explore conflicts of interest that may arise in the context of perceived costs of disclosure. Using analytic Kolmogorov equations, we determine whether or not it is possible for individual incentives to drive noncooperation, even though cooperation would yield a better group outcome. We found that if all individuals have a cost of disclosure, then the optimal individual decision is to simply not disclose each other. With further analysis of (1) completely offsetting the costs of disclosure and (2) partially offsetting the costs of disclosure, we found that all individuals disclose all contacts, resulting in a smaller basic reproductive number and an alignment of individual and group optimality. More data are needed to understand decision making during outbreak investigations and what the real and perceived costs are.

Caregivers who refuse preventive care for their children: the relationship between immunization and topical fluoride refusal

OBJECTIVES

The aim of this study was to examine caregivers' refusal of preventive medical and dental care for children.

METHODS

Prevalence rates of topical fluoride refusal based on dental records and caregiver self-reports were estimated for children treated in 3 dental clinics in Washington State. A 60-item survey was administered to 1024 caregivers to evaluate the association between immunization and topical fluoride refusal. Modified Poisson regression models were used to estimate prevalence rate ratios (PRRs).

RESULTS

The prevalence of topical fluoride refusal was 4.9% according to dental records and 12.7% according to caregiver self-reports. The rate of immunization refusal was 27.4%. In the regression models, immunization refusal was significantly associated with topical fluoride refusal (dental record PRR = 1.61; 95% confidence interval [CI] = 1.32, 1.96; P < .001; caregiver self-report PRR = 6.20; 95% CI = 3.21, 11.98; P < .001). Caregivers younger than 35 years were significantly more likely than older caregivers to refuse both immunizations and topical fluoride (P < .05).

CONCLUSIONS

Caregiver refusal of immunizations is associated with topical fluoride refusal. Future research should identify the behavioral and social factors related to caregiver refusal of preventive care with the goal of developing multidisciplinary strategies to help caregivers make optimal preventive care decisions for children.

Disease control through voluntary vaccination decisions based on the smoothed best response

We investigate game-theory based decisions on vaccination uptake and its effects on the spread of an epidemic with nonlinear incidence rate. It is assumed that each individual's decision approximates his/her best response (called smoothed best response) in that this person chooses to take the vaccine based on its cost-benefit analysis. The basic reproduction number of the resultant epidemic model is calculated and used to characterize the existence and stability of the disease-free and endemic equilibria of the model. The effects on the spread and control of the epidemic are revealed in terms of the sensitivity of the response to changes in costs and benefits, in the “cost” of the vaccination, and in the proportion of susceptible individuals who are faced with the decision of whether or not to be vaccinated per unit time. The effects of the best response decision rule are also analyzed and compared to those of the smoothed best response. Our study shows that, when there is a perceived cost to take the vaccine, the smoothed best response is more effective in controlling the epidemic. However, when this cost is 0, the best response is the more efficient control.

FRED (a Framework for Reconstructing Epidemic Dynamics): an open-source software system for modeling infectious diseases and control strategies using census-based populations

BACKGROUND

Mathematical and computational models provide valuable tools that help public health planners to evaluate competing health interventions, especially for novel circumstances that cannot be examined through observational or controlled studies, such as pandemic influenza. The spread of diseases like influenza depends on the mixing patterns within the population, and these mixing patterns depend in part on local factors including the spatial distribution and age structure of the population, the distribution of size and composition of households, employment status and commuting patterns of adults, and the size and age structure of schools. Finally, public health planners must take into account the health behavior patterns of the population, patterns that often vary according to socioeconomic factors such as race, household income, and education levels.

RESULTS

FRED (a Framework for Reconstructing Epidemic Dynamics) is a freely available open-source agent-based modeling system based closely on models used in previously published studies of pandemic influenza. This version of FRED uses open-access census-based synthetic populations that capture the demographic and geographic heterogeneities of the population, including realistic household, school, and workplace social networks. FRED epidemic models are currently available for every state and county in the United States, and for selected international locations.

CONCLUSIONS

State and county public health planners can use FRED to explore the effects of possible influenza epidemics in specific geographic regions of interest and to help evaluate the effect of interventions such as vaccination programs and school closure policies. FRED is available under a free open source license in order to contribute to the development of better modeling tools and to encourage open discussion of modeling tools being used to evaluate public health policies. We also welcome participation by other researchers in the further development of FRED.

Provider dismissal policies and clustering of vaccine-hesitant families: an agent-based modeling approach

Many pediatric practices have adopted vaccine policies that require parents who refuse to vaccinate according to the ACIP schedule to find another health care provider. Such policies may inadvertently cluster unvaccinated patients into practices that tolerate non vaccination or alternative schedules, turning them into risky pockets of low herd immunity. The objective of this study was to assess the effect of provider zero-tolerance vaccination policies on the clustering of intentionally unvaccinated children. We developed an agent-based model of parental vaccine hesitancy, provider non-vaccination tolerance, and selection of patients into pediatric practices. We ran 84 experiments across a range of parental hesitancy and provider tolerance scenarios. When the model is initialized, all providers accommodate refusals and intentionally unvaccinated children are evenly distributed across providers. As provider tolerance decreases, hesitant children become more clustered in a smaller number of practices and eventually are not able to find a practice that will accept them. Each of these effects becomes more pronounced as the level of hesitancy in the population rises. Heterogeneity in practice tolerance to vaccine-hesitant parents has the unintended result of concentrating susceptible individuals within a small number of tolerant practices, while providing little if any compensatory protection to adherent individuals. These externalities suggest an agenda for stricter policy regulation of individual practice decisions.

Impacts of subsidy policies on vaccination decisions in contact networks

To motivate more people to participate in vaccination campaigns, various subsidy policies are often supplied by government and the health sectors. However, these external incentives may also alter the vaccination decisions of the broader public, and hence the choice of incentive needs to be carefully considered. Since human behavior and the networking-constrained interactions among individuals significantly impact the evolution of an epidemic, here we consider the voluntary vaccination on human contact networks. To this end, two categories of typical subsidy policies are considered: (1) under the free subsidy policy, the total amount of subsidy is distributed to a certain fraction of individual and who are vaccinated without personal cost, and (2) under the partial-offset subsidy policy, each vaccinated person is offset by a certain amount of subsidy. A vaccination decision model based on evolutionary game theory is established to study the effects of these different subsidy policies on disease control. Simulations suggest that, because the partial-offset subsidy policy encourages more people to take vaccination, its performance is significantly better than that of the free subsidy policy. However, an interesting phenomenon emerges in the partial-offset scenario: with limited amount of total subsidy, a moderate subsidy rate for each vaccinated individual can guarantee the group-optimal vaccination, leading to the maximal social benefits, while such an optimal phenomenon is not evident for the free subsidy scenario.

Behavioral responses to epidemics in an online experiment: using virtual diseases to study human behavior

We report the results of a study we conducted using a simple multiplayer online game that simulates the spread of an infectious disease through a population composed of the players. We use our virtual epidemics game to examine how people respond to epidemics. The analysis shows that people's behavior is responsive to the cost of self-protection, the reported prevalence of disease, and their experiences earlier in the epidemic. Specifically, decreasing the cost of self-protection increases the rate of safe behavior. Higher reported prevalence also raises the likelihood that individuals would engage in self-protection, where the magnitude of this effect depends on how much time has elapsed in the epidemic. Individuals' experiences in terms of how often an infection was acquired when they did not engage in self-protection are another factor that determines whether they will invest in preventive measures later on. All else being equal, individuals who were infected at a higher rate are more likely to engage in self-protective behavior compared to those with a lower rate of infection. Lastly, fixing everything else, people's willingness to engage in safe behavior waxes or wanes over time, depending on the severity of an epidemic: when prevalence is high, people are more likely to adopt self-protective measures as time goes by; when prevalence is low, a ‘self-protection fatigue’ effect sets in whereby individuals are less willing to engage in safe behavior over time.

Distinguishing vaccine efficacy and effectiveness

BACKGROUND

Mathematical models of disease transmission and vaccination typically assume that protective vaccine efficacy (i.e. the relative reduction in the transmission rate among vaccinated individuals) is equivalent to direct effectiveness of vaccine. This assumption has not been evaluated.

METHODS

We used dynamic epidemiological models of influenza and measles vaccines to evaluate the common measures of vaccine effectiveness in terms of both the protection of individuals and disease control within populations. We determined how vaccine-mediated reductions in attack rates translate into vaccine efficacy as well as into the common population measures of 'direct', 'indirect', 'total', and 'overall' effects of vaccination with examples of compartmental models of influenza and measles vaccination.

RESULTS

We found that the typical parameterization of vaccine efficacy using direct effectiveness of vaccine can lead to the underestimation of the impact of vaccine. Such underestimation occurs when the vaccine is assumed to offer partial protection to every vaccinated person, and becomes worse when the level of vaccine coverage is low. Nevertheless, estimates of 'total', 'indirect' and 'overall' effectiveness increase with vaccination coverage in the population. Furthermore, we show how the measures of vaccine efficacy and vaccine effectiveness can be correctly calculated.

CONCLUSIONS

Typical parameterization of vaccine efficacy in mathematical models may underestimate the actual protective effect of the vaccine, resulting in discordance between the actual effects of vaccination at the population level and predictions made by models. This work shows how models can be correctly parameterized from clinical trial data.

The influence of altruism on influenza vaccination decisions

Game theory is based on the assumption that individuals act according to self-interest and make decisions that maximize their personal payoffs. To test this fundamental assumption, we conducted a survey study in the context of influenza vaccination decisions. Contrary to the assumption of self-interest, we found that altruism plays an important role in vaccination decisions. Nevertheless, altruistic motivation has not yet been considered in epidemiological models, in predictions of vaccination decisions or in the design of vaccination policies. To determine the impact of altruism on the adherence to optimal vaccination policies and on resulting disease burden, we incorporated altruism into a game-theoretic epidemiological model of influenza vaccination. We found that altruism significantly shifted vaccination decisions away from individual self-interest and towards the community optimum, greatly reducing the total cost, morbidity and mortality for the community. Therefore, promoting altruism could be a potential strategy to improve public health outcomes.