Vaccination Game Research Articles

Social vs. individual age-dependent costs of imperfect vaccination

In diseases with long-term immunity, vaccination is known to increase the average age at infection as a result of the decrease in the pathogen circulation. This implies that a vaccination campaign can have negative effects when a disease is more costly (financial or health-related costs) for higher ages. This work considers an age-structured population transmission model with imperfect vaccination. We aim to compare the social and individual costs of vaccination, assuming that disease costs are age-dependent, while the disease’s dynamic is age-independent. A model for pathogen deterministic dynamics in a population consisting of juveniles and adults, assumed to be rational agents, is introduced. The parameter region for which vaccination has a positive social impact is fully characterized and the Nash equilibrium of the vaccination game is obtained. Finally, collective strategies designed to promote voluntary vaccination, without compromising social welfare, are discussed.

An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases

This study uses imposed control techniques and vaccination game theory to study disease dynamics with transitory or diminishing immunity. Our model uses the ABC fractional-order derivative mechanism to show the effect of non-pharmaceutical interventions such as personal protection or awareness, quarantine, and isolation to simulate the essential control strategies against an infectious disease spread in an infinite and uniformly distributed population. A comprehensive evolutionary game theory study quantified the significant influence of people’s vaccination choices, with government forces participating in vaccination programs to improve obligatory control measures to reduce epidemic spread. This model uses the intervention options described above as a control strategy to reduce disease prevalence in human societies. Again, our simulated results show that a combined control strategy works exquisitely when the disease spreads even faster. A sluggish dissemination rate slows an epidemic outbreak, but modest control techniques can reestablish a disease-free equilibrium. Preventive vaccination regulates the border between the three phases, while personal protection, quarantine, and isolation methods reduce disease transmission in existing places. Thus, successfully combining these three intervention measures reduces epidemic or pandemic size, as represented by line graphs and 3D surface diagrams. For the first time, we use a fractional-order derivate to display the phase-portrayed trajectory graph to show the model’s dynamics if immunity wanes at a specific pace, considering various vaccination cost and effectiveness settings.

Assessing the instantaneous social dilemma on social distancing attitudes and vaccine behavior in disease control

In the face of infectious disease outbreaks, the collective behavior of a society can has a profound impact on the course of the epidemic. This study investigates the instantaneous social dilemma presented by individuals' attitudes toward vaccine behavior and its influence on social distancing as a critical component in disease control strategies. The research employs a multifaceted approach, combining modeling techniques and simulation to comprehensively assess the dynamics between social distancing attitudes and vaccine uptake during disease outbreaks. With respect to modeling, we introduce a new vaccination game (VG) where, unlike conventional VG models, a 2-player and 2-strategy payoff structure is aptly embedded in the individual behavior dynamics. Individuals' willingness to adhere to social distancing measures, such as mask-wearing and physical distancing, is strongly associated with their inclination to receive vaccines. The study reveals that a positive attitude towards social distancing tends to align with a higher likelihood of vaccine acceptance, ultimately contributing to more effective disease control. As the COVID-19 pandemic has demonstrated, swift and coordinated public health measures are essential to curbing the spread of infectious diseases. This study underscores the urgency of addressing the instantaneous social dilemma posed by individuals' attitudes. By understanding the intricate relationship between these factors, policymakers, and healthcare professionals can develop tailored strategies to promote both social distancing compliance and vaccine acceptance, thereby enhancing our ability to control and mitigate the impact of disease outbreaks in the future.

Modelling the dynamic vaccination game with evolutionary feedback: exploring pairwise interactions and vaccine strategies.

A novel approach rooted in co-evolutionary game theory has been introduced to investigate how the interaction between human decision-making and the dynamics of the epidemic environment can shape vaccine acceptance during disease outbreaks. This innovative framework combines two key game concepts: the cooperation-defection game and the cost-benefit vaccination game. By doing so, it enables us to delve into the various factors that influence the success of a vaccination campaign amid an outbreak. Within this framework, individuals engage in a thorough evaluation of the risks, benefits and incentives associated with either cooperating by getting vaccinated or defecting by refusing the vaccine. Additionally, it involves a careful analysis of the costs and benefits linked to vaccine acceptance. The outcomes of this study stress the importance of two main factors: the effectiveness of the vaccine and the prevalence of a cooperative culture within society. This insight into the strategic interactions between individuals and their decisions about vaccination holds significant implications for public health policymakers. It equips to boost vaccination coverage and address vaccine hesitancy within society ultimately contributing to better public health outcomes during epidemic outbreaks.

Vaccination games and imitation dynamics with age structure combining perceived payoffs and media information

We propose an age-structured model based on game theory to investigate the dynamics of imitation in vaccination decisions. In our model, the rate at which individuals switch vaccination strategies is proportional to the perceived payoffs and media information. We analyze the existence and local stability of equilibria and demonstrate the possibility of Hopf bifurcation. Additionally, we establish the global stability of boundary equilibria and the persistence of the disease. The theoretical results are supported by numerical simulations. This model can be applied to study vaccination behavior among individuals of different ages and infectious disease stages, providing insights for the formulation of effective public health policies.

Newborn vaccination game model with potentially periodic behavior

We explore the complex dynamics of epidemics, considering the significant effects of disease transmission, newborn individuals, and mortality rate. Employing an evolutionary game theory approach, we model the vaccination aspect for newborns, incorporating potential periodic behavior. The goal is to create an engaging simulation that underscores the criticality of timely infant vaccinations. By introducing periodic elements, the game adds complexity, fostering player participation and awareness of vaccination schedules. In contrast to traditional intervention game models focused on adult vaccine behavior, our approach recognizes the unique challenges posed by newborn vaccination. We address the limitations of existing models by developing a generalized compartmental model, accommodating infection duration distribution, and accurately capturing both periodic and non-periodic disease trajectories. The results show that higher efficacy in a newborn vaccine program can potentially eradicate the disease, but higher effectiveness and cost may deter vaccination. Increased motivation cost boosts vaccination rates without impacting epidemic size, whereas lower costs stabilize vaccination rates. Lower vaccine costs call for increased government investment to counter hesitancy. However, reduced efficacy and lower motivation lead to higher Vaccine Fear Scores, discouraging participation. Our work also offers a unique perspective on the dilemma of newborn vaccination, providing solutions with closed-form expressions that may exhibit periodic or non-periodic behavior. This approach facilitates disease modelers in exploring the potential periodicity of newborn vaccination programs, aiding efforts to prevent recurrent outbreaks.

Effect of vaccine efficacy on vaccination behavior with adaptive perception

Most individuals opt for vaccination to acquire immunity protection and prevent disease transmission. However, individuals cannot obtain perfect immunity protection after vaccination, due to various factors such as the limitation of vaccine itself, storage and transportation. Failed vaccination experiences can alter individuals' perception of vaccination behavior. To analyze the influence of vaccine efficacy on vaccination behavior with adaptive perception, we propose a novel vaccination game model. The results demonstrate that for the moderate vaccination cost, the introduction of adaptive perception can promote vaccination behavior, and the promoting effect becomes more pronounced in the population with smaller perception fluctuation. Nonetheless, vaccination behavior is still constrained by a significant number of free-riders when vaccine effectiveness is high. Analyzing the distribution of strategies among individuals with different degrees, it is revealed that the reduction in vaccinated individuals influenced by free-riders predominantly occurs in individuals with low-degree. Furthermore, we examine the coupled effects of vaccination cost and vaccine efficacy on vaccination behavior, considering various levels of perception fluctuations. The results indicate the crucial role of vaccination cost in enhancing vaccination behavior, and previous findings also are consistent across scenarios with diverse vaccination cost. Our work contributes to an improved comprehension of vaccination behavior considering vaccine efficacy and perception.

First‐best health policy in vaccine markets with health and network externalities

AbstractThis paper considers an oligopolistic market for a vaccine, characterized by negative network effects, which stem from the free‐riding behavior of individuals engaged in a vaccination game. Vaccine markets often suffer from three imperfections: high concentration, network effects, and a health externality (contagion). The first conclusion of the paper is that the negative network externality is important as a market distortion, as it may lead to significant welfare losses. The second and main part of the paper develops a two‐part per‐unit subsidy scheme that a social planner could use to target both consumers and producers of vaccines. The scope of such a subsidy scheme to induce the firms to produce the first‐best output without network effects (which is the most ambitious first‐best target) is investigated. In many cases, while the first‐best is attainable, it requires negative prices for vaccines, which amounts to rewarding consumers to induce them to vaccinate.

Negative network effects and public policy in vaccine markets

This paper provides a thorough analysis of an oligopolistic market for a vaccine, characterized by negative (demand-side) network externalities, which stem from the free-riding behavior of individuals engaged in a vaccination game. We investigate industry viability in terms of a standard natural Cournot-type learning process for network industries and show that viability tends to favor monopoly or competition among few suppliers. We confirm that market performance is highly inefficient, due to the combination of three imperfections: market power, network effects and a health externality (i.e., contagion). We investigate the extent of these imperfections. Finally, we devise a two-part government subsidy scheme for producers and consumers that may restore social efficiency in such markets.

How committed individuals shape social dynamics: A survey on coordination games and social dilemma games

Committed individuals, who feature steadfast dedication to advocating strong beliefs, values, and preferences, have garnered much attention across statistical physics, social science, and computer science. This survey delves into the profound impact of committed individuals on social dynamics that emerge from coordination games and social dilemma games. Through separate examinations of their influence on coordination, including social conventions and color coordination games, and social dilemma games, including one-shot settings, repeated settings, and vaccination games, this survey reveals the significant role committed individuals play in shaping social dynamics. Their contributions range from accelerating or overturning social conventions to addressing cooperation dilemmas and expediting solutions for color coordination and vaccination issues. Furthermore, the survey outlines three promising directions for future research: conducting human behavior experiments for empirical validation, leveraging advanced large language models as proxies for committed individuals in complex scenarios, and addressing the potential negative impacts of committed individuals.

Stochastic Vaccination Game Among Influencers, Leader and Public

Stochastic Vaccination Game Among Influencers, Leader and Public

Analyzing the Costs and Benefits of Utilizing a Mixed-Strategy Approach in Infectious Disease Control under a Voluntary Vaccination Policy.

Infectious diseases pose significant public health risks, necessitating effective control strategies. One such strategy is implementing a voluntary vaccination policy, which grants individuals the autonomy to make their own decisions regarding vaccination. However, exploring different approaches to optimize disease control outcomes is imperative, and involves assessing their associated costs and benefits. This study analyzes the advantages and disadvantages of employing a mixed-strategy approach under a voluntary vaccination policy in infectious disease control. We examine the potential benefits of such an approach by utilizing a vaccination game model that incorporates cost and benefit factors, where lower costs and higher benefits lead to reduced infection rates. Here, we introduce a mixed-strategy framework that combines individual-based risk assessment (IB-RA) and society-based risk assessment (SB-RA) strategies. A novel dynamical equation is proposed that captures the decision-making process of individuals as they choose their strategy based on personal or communal considerations. In addition, we explore the implications of the mixed-strategy approach within the context of social dilemmas. We examine deviations from expected behavior and the concept of social efficiency deficit (SED) by allowing for the evolution of vaccine strategy preferences alongside risk perception. By comprehensively evaluating the financial implications and societal advantages associated with the mixed-strategy approach, decision-makers can allocate resources and implement measures to combat infectious diseases within the framework of a voluntary vaccination policy.

Behavioral vaccination policies and game-environment feedback in epidemic dynamics

Many policymakers have adopted voluntary vaccination policies to alleviate the consequences of contagious diseases. Such policies have several well-established feathers, i.e. they are seasonal, depending on an individual’s decision, adaptive, and control epidemic activity. Here, we study ideas from behavioral epidemiology embedded with a vaccination game and pairwise two-player two-strategy game to represent the environmental feedback in an SVIR model by using a composite information index including disease incidence, vaccine factors and cooperative behavior on a global time scale (repeated season). In its turn, the information index’s game dynamics to participate in the vaccine program (cooperation) is supposed to reflect the feedback-evolving dynamics of competitive cognitions and the environment. The assuming model is described by two different evolutionary game systems connected by an unknown external public opinion environment feedback. The embedded model is described by an inherited system showing a behavioral aspect, i.e. pairwise game indicates an individual’s cooperative behavior, and a vaccine game refers to vaccine-cost influence. This is a novel attempt to stabilize the two different decision processes to pool them into a single index. Extensive simulations suggest a rich spectrum of achievable results, including epidemic control, human behavior, social dilemma, and policy suggestions.

A geometric analysis of the impact of large but finite switching rates on vaccination evolutionary games

In contemporary society, social networks accelerate decision dynamics causing a rapid switch of opinions in a number of fields, including the prevention of infectious diseases by means of vaccines. This means that opinion dynamics can nowadays be much faster than the spread of epidemics. Hence, we propose a Susceptible–Infectious–Removed epidemic model coupled with an evolutionary vaccination game embedding the public health system efforts to increase vaccine uptake. This results in a global system “epidemic model + evolutionary game”. The epidemiological novelty of this work is that we assume that the switching to the strategy “pro vaccine” depends on the incidence of the disease. As a consequence of the above-mentioned accelerated decisions, the dynamics of the system acts on two different scales: a fast scale for the vaccine decisions and a slower scale for the spread of the disease. Another, and more methodological, element of novelty is that we apply Geometrical Singular Perturbation Theory (GSPT) to such a two-scale model and we then compare the geometric analysis with the Quasi-Steady-State Approximation (QSSA) approach, showing a criticality in the latter. Later, we apply the GSPT approach to the disease prevalence-based model already studied in (Della Marca and d’Onofrio, Comm Nonl Sci Num Sim, 2021) via the QSSA approach by considering medium–large values of the strategy switching parameter.

Subsidy policy with punishment mechanism can promote voluntary vaccination behaviors in structured populations

Subsidy policies have been a common way for governments and health organizations to encourage individuals’ voluntary vaccination behaviors. However, subsidy policies are often used in combination with punishment policies in reality. So far, few researchers have studied the combination of vaccination subsidy policies and punishment policies. In this study, a new subsidy policy with the punishment mechanism (P-TAR) is first introduced in the vaccination game to explore its impact on voluntary vaccination behaviors. P-TAR selects to subsidize punishers of the last season based on the degree, which is similar to targeted subsidy policy (S-TAR). We first adjust fines and punishment costs to explore how the punishment mechanism of P-TAR influences vaccination coverage and epidemic dynamics. The results show that vaccination coverage can be significantly improved when the fine is high and the punishment cost is low. By comparing P-TAR with S-TAR, we find that P-TAR can more effectively increase the number of vaccinated individuals to control the epidemic size. However, the P-TAR has a higher social cost than S-TAR. Through micro-analyzing the evolution of vaccination behaviors, the P-TAR effectively improves the voluntary vaccination behaviors of non-hub nodes, which is the main reason for P-TAR has more vaccinated individuals than S-TAR. To analyze the model robustness, experiments are conducted with larger network sizes. In addition, we compare the results of unvaccinated individuals who are sequentially punished by their surrounding punishers, as well as those who are punished only once. Finally, we perform the sensitivity analysis on the effectiveness of imperfect vaccine. Current results conclude that implementing strict policies usually incurs significant social costs, while effectively preventing epidemic spreading. We anticipate that this study can offer policymakers valuable insights into the balance between social costs and benefits when formulating vaccination policies.

Impact of human cooperation on vaccination behaviors

This paper studies a dynamic vaccination game model embedded with vaccine cost-effectiveness and dyadic game during an epidemic, assuming the appearance of cooperation among individuals from an evolutionary perspective. The infection dynamics of the individuals' states follow a modified S/VIS (susceptible/vaccinated-infected-susceptible) dynamics. Initially, we assume that the individuals are unsure about their infection status. Thus, they make decisions regarding their options based on their neighbors' perceptions, the prevalence of the disease, and the characteristics of the available vaccines. We then consider the strategy updating process IBRA (individuals-based risk assessment) concerning an individual's committing vaccination based on a neighbor's decision. In the perspective of social dilemma, it presents the idea of social efficiency deficit to find the gap between social optimum and Nash equilibrium point based on dilemma strength by considering vaccine decision. The cost and cooperative behavior depend on disease severity, neighbor's attitude, and vaccine properties to obtain a reduced-order optimal solution to control infectious diseases. Vaccine factors (efficiency, cost, and benefit) are crucial in changing human vaccine decisions and cooperative behavior. It turns out that, even in the prisoner's dilemma case, where all defection attitude occurs, vaccine uptake (cooperation) increases. Finally, extensive numerical studies were presented that illustrate interesting phenomena and investigate the ultimate extent of the epidemic, vaccination coverage, average social benefits, and the social efficiency deficit concerning optimal strategies and the dynamic vaccine attitudes of individuals.PACS numbers.Theory and modeling; computer simulation, 87.15. Aa; Dynamics of evolution, 87.23. Kg.

Game Theory of Universal Health Coverage for Sustainable Development

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Social dilemma analysis on vaccination game accounting for the effect of immunity waning

A new SEIRS-based ODE (Ordinary Differential Equation) model is built, where asymptomatic and symptomatic infectious compartments, hospitalized state and immune state are additionally introduced, which is dovetailed with a behavior model that defines the vaccination rate as time-variable. We also apply Social Efficiency Deficit; SED, to quantitatively identify whether or not social dilemma taking place behind the model dynamics. Numerical results prove that, depending on the fraction of asymptomatic infected individuals and the discount ratio of infected force for asymptomatic state compared with that for symptomatic one, whether or not social dilemma appearing is different, which is also substantially affected by the vaccination cost and the immunity waning rate. The behavior model tends to incur a slight social dilemma brought by wasting vaccination even in the region of disease free, identified by R0<1. Meanwhile, a relatively strong social dilemma is indicated in the parameter region where the behavior model shows less amount of vaccinated population while the social optimal state needs much more vaccinated for complete remission of disease.

Vaccination games and imitation dynamics with memory

In this paper, we model dynamics of pediatric vaccination as an imitation game, in which the rate of switching of vaccination strategies is proportional to perceived payoff gain that consists of the difference between perceived risk of infection and perceived risk of vaccine side effects. To account for the fact that vaccine side effects may affect people's perceptions of vaccine safety for some period of time, we use a delay distribution to represent how memory of past side effects influences current perception of risk. We find disease-free, pure vaccinator, and endemic equilibria and obtain conditions for their stability in terms of system parameters and characteristics of a delay distribution. Numerical bifurcation analysis illustrates how stability of the endemic steady state varies with the imitation rate and the mean time delay, and this shows that it is not just the mean duration of memory of past side effects, but also the actual distribution that determines whether disease will be maintained in the population at some steady level, or if sustained periodic oscillations around this steady state will be observed. Numerical simulations illustrate a comparison of the dynamics for different mean delays and different distributions, and they show that even when periodic solutions are observed, there are differences in their amplitude and period for different distributions. We also investigate the effect of constant public health information campaigns on vaccination dynamics. The analysis suggests that the introduction of such campaigns acts as a stabilizing factor for endemic equilibrium, allowing it to remain stable for larger values of mean time delays.

Vaccination dilemma in the thermodynamic limit.

The vaccination game is a social dilemma that refers to the conundrum individuals face (to get immunized or not) when the population is exposed to an infectious disease. The model has recently gained much traction due to the COVID-19 pandemic since the public perception of vaccines plays a significant role in disease dynamics. This paper studies the vaccination game in the thermodynamic limit with an analytical method derived from the 1D Ising model called Nash equilibrium mapping. The individual dilemma regarding vaccination comes from an internal conflict wherein one tries to balance the perceived advantages of immunizing with the apparent risks associated with vaccination, which they hear through different news media. We compare the results of Nash equilibrium (NE) mapping from other 1D Ising-based models, namely, Darwinian evolution (DE) and agent-based simulation. This study aims to analyze the behavior of an infinite population regarding what fraction of people choose to vaccinate or not vaccinate. While Nash equilibrium mapping and agent-based simulation agree mostly, DE strays far from the two models. DE fails to predict the equilibrium behavior of players in the population reasonably. We apply the results of our study to analyze the AstraZeneca (AZ) COVID-19 vaccine risk vs disease deaths debate, both via NE mapping and the agent-based method. Both predict nearly 100% AZ vaccine coverage for people aged above 40, notwithstanding the risk. At the same time, younger people show a slight reluctance. We predict that while government intervention via vaccination mandates and/or advertisement campaigns are unnecessary for the older population, for the younger population (ages: 20-39), some encouragement from the government via media campaigns and/or vaccine mandates may be necessary.