Vaccination Game Research Articles

Vaccinating behaviour guided by imitation and aspiration

Vaccinating decisions can be influenced by imitation as well as self-evaluation or aspiration. This work analyses vaccinating behaviours by coupling both imitation and aspiration update rules, adopting an existing set-up of the mean-field vaccination game. We incorporate the imitation mechanism with several variants of the aspiration protocol, encompassing constant and adaptive aspirations. Equations of the combined dynamics have been derived by grouping the population according to (i) vaccinating strategies and (ii) healthy and infected status within each strategy. If aspiration levels are fixed but differentiated by vaccinating strategies, then vaccinators aspiring less than non-vaccinators are found to ameliorate the vaccination coverage, thereby yielding a less infectious state. The adaptive aspirations maintain a positive correlation with the vaccine efficacy while keeping the opposite relation with vaccination cost. When vaccinating strategies, aspirations and update rules are allowed to evolve synchronously, then either the imitation or aspiration process takes over the entire population. If aspiration rules prevail, then vaccinees and non-vaccinees coexist equally (according to (i)) or vaccine uptake follows a non-monotonic trend with the efficacy (according to (ii)). The imitative rule performs better when vaccination is less expensive or cheap, while aspiration updating safeguards the tenacity of vaccinees despite vaccination being expensive.

Herd immunity and a vaccination game: An experimental study.

Would the affected communities voluntarily obtain herd immunity if a cure for COVID-19 was available? This paper experimentally investigates people’s vaccination choices in the context of a nonlinear public good game. A “vaccination game” is defined in which costly commitments (vaccination) are required of a fraction of the population to reach the critical level needed for herd immunity, without which defectors are punished by the natural contagion of epidemics. Our experimental implementation of a vaccination game in a controlled laboratory setting reveals that endogenous epidemic punishment is a credible threat, resulting in voluntary vaccination to obtain herd immunity, for which the orthodox principle of positive externalities fails to account. The concave nature of the infection probability plays a key role in facilitating the elimination of an epidemic.

Based on mathematical epidemiology and evolutionary game theory, which is more effective: quarantine or isolation policy?

Outbreaks of repeated pandemics and heavy epidemics are daunting threats to human life. This study aims at investigating the dynamics of disease conferring temporary or waning immunity with several forced-control policies aided by vaccination game theory. Considering an infinite and well-mixed homogenous population, our proposed model further illustrates the significance of introducing two well-known forced control techniques, namely, quarantine and isolation, in order to model the dynamics of an infectious disease that spreads within a human population where pre-emptive vaccination has partially been taken before the epidemic season begins. Moreover, we carefully examine the combined effects of these two types (pre-emptive and forced) of protecting measures using the SEIR-type epidemic model. An in-depth investigation based on evolutionary game theory numerically quantifies the weighing impact of individuals’ vaccinating decisions to improve the efficacy of forced control policies leading up to the relaxation of the epidemic spreading severity. A deterministic SVEIR model, including vaccinated (V) and exposed (E) states, is proposed having no spatial structure while implementing these intervention techniques. This study uses a mixed control strategy relying on quarantine and isolation policies to quantify the optimum requirement of vaccines for eradicating disease prevalence completely from human societies. Furthermore, our theoretical study justifies the fact that adopting forced control policies significantly reduces the required level of vaccination to suppress emerging disease prevalence, and it also confirms that the joint policy works even better when the epidemic outbreak takes place at a higher transmission rate. Research reveals that the isolation policy is a better disease attenuation tool than the quarantine policy, especially in endemic regions where the disease progression rate is relatively higher. However, a meager progression rate gradually weakens the speed of an epidemic outbreak and, therefore, applying a moderate level of control policies is sufficient to restore the disease-free state. Essentially, positive measures (pre-emptive vaccination) regulate the position of the critical line between two phases, whereas exposed provisions (quarantine or isolation) are rather dedicated to mitigating the disease spreading in endemic regions. Thus, an optimal interplay between these two types of intervention techniques works remarkably well in attenuating the epidemic size. Despite having advanced on the development of new vaccines and control strategies to mitigate epidemics, many diseases like measles, tuberculosis, Ebola, and flu are still persistent. Here, we present a dynamic analysis of the SVEIR model using mean-field theory to develop a simple but efficient strategy for epidemic control based on the simultaneous application of the quarantine and isolation policies.Highlights• This model incorporates the elements of mathematical epidemiology and a vaccination game into a single framework.• A dynamical analysis of the SEIR/V epidemic model equipped with quarantine and isolation policies is introduced.• The proposed game-theoretic framework rigorously addresses real situations when control policies are adopted simultaneously as well as separately.• Adopting control policies can significantly reduce the required level of vaccination to suppress disease prevalence.• A joint policy seems impressive when an epidemic outbreak takes place at a higher transmission rate.• For a smaller basic reproduction number, the quarantine policy outperforms the isolation policy.

A mean-field vaccination game scheme to analyze the effect of a single vaccination strategy on a two-strain epidemic spreading

We propose a mean-field vaccination game framework that combines two distinct processes: the simultaneous spreading of two strains of an influenza-like disease, and the adoption of vaccination based on evolutionary game theory presuming an infinite and well-mixed population. The vaccine is presumed to be imperfect such that it shows better efficacy against the original (resident) strain rather than the new one (mutant). The vaccination-decision takes place at the beginning of an epidemic season and depends upon the vaccine-effectiveness along with the cost. Additionally, we explore a situation if the original strain continuously converts to a new strain through the process of mutation. With the aid of numerical experiments, we explore the impact of vaccinating behavior on a specific strain prevalence. Our results suggest that the emergence of vaccinators can create the possibility of infection-prevalence of the new strain if the vaccine cannot bestow a considerable level of efficiency against that strain. On the other hand, the resident strain can continue to dominate under large-scale vaccine avoidance. Moreover, in the case of continuous mutation, the vaccine efficacy against the new strain plays a pivotal role to control the disease prevalence. We successfully obtain phase diagrams, displaying the infected fraction with each strain, final epidemic size, vaccination coverage, and average social payoff considering two-different strategy-update rules and provide a comprehensive discussion to get an encompassing idea, justifying how the vaccinating behavior can affect the spread of a disease having two strains.Highlights–We build a mean-field vaccination game scheme to analyze the effect of an imperfect vaccine on a two-strain epidemic spreading taking into account individuals’ vaccination behavior.–En masse vaccine avoidance can enhance the possibility of the original strain prevalence.–Propensity for vaccination can create the possibility of infection by the new strain if the vaccine is unable to provide a considerable level of efficiency against that strain.

Perception Effect in Evolutionary Vaccination Game Under Prospect-Theoretic Approach

Vaccination is one of the most effective strategies against epidemics. Traditionally, the evolutionary game theory focuses on individual behaviors, rather than psychological cognition behind which reflects individual risk attitude. How does individual perception impact the collective decision and performance of vaccination? To explore this question, we propose an evolutionary vaccination game model by integrating the prospect theory (PT), which accounts for individual subjective perception under uncertainty. In this article, the uncertainty stems from the interactions of individuals in the potential infection process. After analyzing the evolutionary vaccination dynamics, we compare the vaccination equilibrium under the PT and the expected utility theory (EUT) and highlight the role of perceptions on promoting vaccination. In addition, we find that the performance of different perceptions captured by the weighting effect (WE) and the framing effect in epidemic control depends on the vaccination cost. Specifically, both the fraction of infected individuals and the social cost decrease with the decrease of the rationality coefficient under the WE when the vaccination cost is relatively small. The dependence reveals that risk-averse and loss aversion dominate individual vaccination behavior. The numerical simulations verify the effect of perception and the effectiveness of vaccinating the network epidemics.

Realistic decision-making process with memory and adaptability in evolutionary vaccination game

Abstract Of particular importance for controlling infectious diseases by voluntary vaccination is how to understand individuals’ strategic vaccination behavior in social networks. Previous studies have always assumed an imitating and learning process by the Fermi’s rule, however, individuals’ stochastic behavior of whether to vaccinate is influenced by their intentions instead of simply imitating others. In this paper, a new strategy updating rule is proposed, demonstrating a more realistic vaccination decision-making process with memory effect and adaptability. Individuals determine whether vaccination is significant by comparing the vaccination cost and the average cost of their unvaccinated neighbors, and accordingly change their intentions to vaccinate in the next season, during which the memory effect and adaptability are taken into account. We find that the new updating rule has an extraordinary impact on the vaccination behavior of individuals, and, as a result, on the final epidemic size. It is especially noteworthy that, comparing with the traditional model, the vaccination coverage is improved and the infection size is reduced. Our results highlight that it is necessary to consider memory effect and adaptability in controlling the infectious spreading.

The impact of information spreading on epidemic vaccination game dynamics in a heterogeneous complex network- A theoretical approach

Abstract A modified susceptible-vaccinated-infected-recovered (SIR/V) with unaware-aware (UA) epidemic model in heterogeneous networks is presented to study the effect of information spreading in the spatial structure of the vaccination game on epidemic dynamics. Two layers SIR/V epidemic model is considered to elucidate information spreading, where the fraction of susceptible, vaccinated and infected individuals are parted as unaware and aware state as each susceptible and vaccinated persons are allied with their infected neighbors by a spatial structure, say, an underlying network. The context deduces epidemic vaccination game with awareness influence dynamics in one single season followed by a strategy update process that refer an individual to take imperfect vaccination or not. We considered two different strategy updating rules: individual based risk assessment (IB-RA) and strategy-based risk assessment (SB-RA) to explore how different underlying network topologies, say, random graph and scale free networks, subsequently giving impact on the final epidemic size, vaccination coverage and average social payoff through the effect of information spreading on epidemic. Thus, it can be seen that, awareness can enhance the epidemic threshold effectiveness and lessen the spreading of infection in a scale free network other than random graph and homogeneous network.

Modelling and analysing the coexistence of dual dilemmas in the proactive vaccination game and retroactive treatment game in epidemic viral dynamics

The dynamics of a spreadable disease are largely governed by four factors: proactive vaccination, retroactive treatment, individual decisions, and the prescribing behaviour of physicians. Under the imposed vaccination policy and antiviral treatment in society, complex factors (costs and expected effects of the vaccines and treatments, and fear of being infected) trigger an emulous situation in which individuals avoid infection by the pre-emptive or ex post provision. Aside from the established voluntary vaccination game, we propose a treatment game model associated with the resistance evolution of antiviral/antibiotic overuse. Moreover, the imperfectness of vaccinations has inevitably led to anti-vaccine behaviour, necessitating a proactive treatment policy. However, under the excessively heavy implementation of treatments such as antiviral medicine, resistant strains emerge. The model explicitly exhibits a dual social dilemma situation, in which the treatment behaviour changes on a local time scale, and the vaccination uptake later evolves on a global time scale. The impact of resistance evolution and the coexistence of dual dilemmas are investigated by the control reproduction number and the social efficiency deficit, respectively. Our investigation might elucidate the substantial impacts of both vaccination and treatment in the framework of epidemic dynamics, and hence suggest the appropriate use of antiviral treatment.

Interplay between cost and effectiveness in influenza vaccine uptake: a vaccination game approach.

Pre-emptive vaccination is regarded as one of the most protective measures to control influenza outbreak. There are mainly two types of influenza viruses—influenza A and B with several subtypes—that are commonly found to circulate among humans. The traditional trivalent (TIV) flu vaccine targets two strains of influenza A and one strain of influenza B. The quadrivalent (QIV) vaccine targets one extra B virus strain that ensures better protection against influenza; however, the use of QIV vaccine can be costly, hence impose an extra financial burden to society. This scenario might create a dilemma in choosing vaccine types at the individual level. This article endeavours to explain such a dilemma through the framework of a vaccination game, where individuals can opt for one of the three options: choose either of QIV or TIV vaccine or none. Our approach presumes a mean-field framework of a vaccination game in an infinite and well-mixed population, entangling the disease spreading process of influenza with the coevolution of two types of vaccination decision-making processes taking place before an epidemic season. We conduct a series of numerical simulations as an attempt to illustrate different scenarios. The framework has been validated by the so-called multi-agent simulation (MAS) approach.

Individual preferences for voluntary vs. mandatory vaccination policies: an experimental analysis.

More and more countries are discussing the introduction of mandatory vaccination policies. Yet, little is known about individuals' actual preferences for voluntary vs. mandatory vaccination policies, and the psychological processes underlying such preferences. Objective of the present research was to investigate the development of individual preferences for voluntary and mandatory vaccination policies. We conducted a controlled laboratory study (N = 168) using a repeated interactive vaccination game with decision-contingent monetary incentives. In each round, participants decided in favour of either a voluntary or a mandatory vaccination policy, followed by the vaccination decision (voluntary policy) or vaccination (mandatory policy) which both resulted in actual (financial) consequences. We observe large heterogeneity in participants' preferences for the voluntary vs. mandatory policy. Under voluntary vaccination, the preference for the mandatory policy increased with decreasing vaccination rates (and increasing risk of infection). In contrast, experiencing vaccine-adverse events under mandatory vaccination increased the preference for the voluntary policy. The latter effect was larger for individuals with a negative (vs. positive) attitude toward vaccination. Overall, as individuals gathered experiences under both the voluntary and the mandatory policy, the preference for voluntary vaccination policy increased over time. Individuals are more willing to accept mandatory vaccination policies when vaccination rates are low. In the long run, the occurrence of vaccine-adverse events may spark opposition to mandatory vaccination.

A Rational Explanation of Limited FMD Vaccine Uptake in Endemic Regions.

Vaccination for foot-and-mouth (FMD) disease remains low in parts of Africa despite the existence of vaccines. In East Africa, the presence of multiple virus serotypes and sub-types makes matching a vaccine with the circulating virus type in the field, or providing a high potency vaccine, a challenge. In this paper we use game theory to show that the resulting vaccine uncertainty associated with these vaccination conditions in an endemic setting help explain the low vaccine uptake. We evaluate vaccination for FMD in the context of East Africa due to FMD being endemic in the region, the diversity of FMD virus types, and barriers to implementing other disease control measures, such as controlled movements. We incorporate these conditions into a vaccination game setting and compare the payoffs to those of a traditional vaccination game for seasonal influenza and commercial livestock vaccination in a developed country context. In showing that vaccination provides households with a lower payoff than not vaccinating, our simple game theoretical explanation supports existing evidence calling for improved vaccine quality and efforts to enhance surveillance to provide early information on disease status.

Cost effectiveness and policy announcement: The case of measles mandatory vaccination

In a vaccination game, individuals respond to an epidemic by engaging in preventive behaviors that, in turn, influence the course of the epidemic. Such feedback loops need to be considered in the cost effectiveness evaluations of public health policies. We elaborate on the example of mandatory measles vaccination and the role of its anticipation. Our framework is a SIR compartmental model with fully rational forward looking agents who can therefore anticipate on the effects of the mandatory vaccination policy. Before vaccination becomes mandatory, parents decide altruistically and freely whether to vaccinate their children. We model eager and reluctant vaccinationist parents. We provide numerical evidence suggesting that individual anticipatory behavior may lead to a transient increase in measles prevalence before steady state eradication. This would cause non negligible welfare transfers between generations. Ironically, in our scenario, reluctant vaccinationists are among those who benefit the most from mandatory vaccination.

Suppressing Epidemic Spreading by Imitating Hub Nodes’ Strategy

In this brief, we incorporate the impact of preferential imitation rule into a vaccination game based epidemic spreading model on social networks, where each individual chooses one of its neighbors as an imitation reference with a probability proportional to the neighbor’s degree. Our results indicate that the vaccination coverage can be remarkably increased if hub nodes are preferentially imitated, leading to the dramatic reduction of the epidemic size. We explain this by suggesting that the vaccination willingness of hub nodes is very high when voluntary vaccination mechanism is assumed, who can attract more individuals to take vaccination if they are preferentially imitated. Moreover, a mean-field theoretical approach is developed to further verify our findings. This brief suggests that the human behavioral response is an important factor for spreading dynamics.

BJN Awards 2019: innovation runner up: creating a staff flu vaccination game.

The Flu Bee Game earned Joan Pons Laplana a runner-up place in the innovation category, as Andy Yeoman of Focus Games Ltd explains.

Dynamic vaccination game in a heterogeneous mixing population

Opposition to vaccination has long been a non-negligible public health phenomenon resulted from people’s varied perceptions toward vaccination (e.g., vaccine-phobia). This paper investigates the voluntary vaccination behavior of a heterogeneous population during an epidemic outbreak, where each individual makes its own vaccination decision to minimize its expected disutility from both vaccine-phobia and the risk of infection. Such a problem is known as a vaccination game, as people’s vaccination decisions not only affect their own disutilities but those of all others through probabilistic disease transmissions. To study the vaccination game, the susceptible–infected–removed disease propagation process is generalized into a new epidemic dynamics model to allow dynamic vaccination and immunity activation in a heterogeneous mixing population. An efficient computation method is proposed to evaluate the final state of the dynamic epidemic system. Then, a classic game-theoretical equilibrium model is built upon these results to examine the impacts of people’s vaccination behavior on the overall risk of epidemic outbreak. A hypothetical case study is used to validate the dynamics model and the derived results, and extensive numerical experiments are conducted to identify the key factors that affect people’s vaccination decisions and the risk of an outbreak. Moreover, three alternative vaccination schemes are also studied to examine the effects of early and non-differential vaccination treatments, respectively.

A game theoretic approach to discuss the positive secondary effect of vaccination scheme in an infinite and well-mixed population

Abstract Pre-emptive vaccination policy used in controlling the rapid spreading of infectious diseases is considered as one of the most challenging issues imposed to mankind, causing enormous death tolls over the years. This paper dedicatedly studies the dilemma effect coming from the failure of getting perfect immunity to those individuals who committed vaccination earlier. Therefore, we propose a new theoretical model that slows down the infection spreading and also facilitates quicker recovery time than what the previous model does even if a vaccinator fails to obtain perfect immunity. We name this effect as the “positive secondary effect” of vaccination as it gives a second chance to the vaccinators which in return subdues the rapid spreading that helps in producing better social average payoff as well as keeping the final epidemic size smaller. Moreover, to address the positive secondary effect more precisely, we introduce two different parameters; namely, relaxation parameter (η) and foster parameter (δ) in two different directions to quantify the individual effects resulting from each of the parameter space as well as their superposition effect. An in-depth discussion focuses on the influential role played by our proposed model via discounting and faster recovery effects while a second chance is given to the vaccinators. In addition, we also examine the situation when discounting effect brought by η outperforms very much than its faster recovery controlled by δ as well as the superposition effects. Unlike all previous studies dealing with vaccination game, we pay much attention to investigating the secondary effect of imperfect vaccination policy. Our proposed theoretical scheme completely reproduces the decision-making process of choosing an imperfect provision based on evolutionary game theory entailed with the widely used SIR (Susceptible–Infected–Recovered) epidemic model. Without considering any spatial structure and perfect vaccination policy, our model presumes the population being infinite and well-mixed to represent the infection spreading dynamics mathematically. This study is conducted throughout using the so-called theoretical approach. Besides that, three different updating rules based on evolutionary game theory have also been considered to investigate all possible situations. Later on, we draw 2D full phase diagrams showing the final epidemic size, vaccination coverage, and average social payoff quantitatively. Finally, our theoretical result is compared with the counterpart result obtained from the multi-agent simulation (MAS) approach and a good agreement is found, hence the appropriateness of the proposed model is fully justified.

Vaccination strategies in a two-layer SIR/V–UA epidemic model with costly information and buzz effect

The promptness with which individuals respond to information has an important effect on the spread of epidemics. To study this effect, we establish a two-layer SIR/V epidemic model that incorporates the effects of information buzz and information costs in the framework of a vaccination game. Previous studies on this issue have generally assumed that only unaware people can become aware, and the relative vaccination cost is used to update their strategies for avoiding infection. Firstly, we introduce the idea that aware people can also become unaware because of a wicked rumor about a beneficial practice. Secondly, the relative cost of information is modeled for individual update strategies in a novel way of framing a game by introducing a two-strategy and 2 (information state A/UA) by 2(healthy/infected) state game, referred to as a two-under-two game. In this framework, susceptible, infected, and vaccinated individuals are divided into two states as unaware and aware, and recovered individuals are assumed to be aware, for an unbounded and well-mixed population. Information about wearing masks or taking other protection against diseases spreads locally for a season, and this information has a significant tendency to reduce the extent of contagious disease that persists through each generation of the model. Mathematical analysis shows that funds spent on awareness can reduce the vaccination cost and improve the epidemic threshold under certain conditions.

Dynamical behaviors for vaccination can suppress infectious disease – A game theoretical approach

Abstract To avoid the infection, the epidemic outburst plays a significant role that encourages people to take vaccination and induce behavioral changes. The interplay between disease incidence, vaccine uptake and the behavior of individuals are taking place on the local time scale. Here, we analyze the individual's behavior in disease-vaccination interaction model based on the evolutionary game approach that captures the idea of vaccination decisions on disease prevalence that also include social learning. The effect of herd immunity is partly important when the individuals are deciding whether to take the vaccine or not. The possibility that an individual taking a vaccination or becoming infected depends upon how many other people are vaccinated. To apprehend this interplay, four strategy updating rules: individual based risk assessment (IB-RA), society based risk assessment (SB-RA), direct commitment (DC) and modified replicator dynamics (MRD) are contemplated for game theoretical approach by how one individual can learn from society or neighbors. The theory and findings of this paper provide a new perspective for vaccination taking policy in daily basis that provision of prompt learning with the collective information reliefs to reduce infection, which gives a new ‘vaccination game’ from other previous models.

Evolutionary vaccination game approach in metapopulation migration model with information spreading on different graphs

The two layer SIR/V-UA epidemic diffusion model is incorporated in metapopulation migration model for random walkers to study the impact of awareness (rumor) for evolutionary vaccination game approach. In metapopulation, each node denoted a sub-population where the individuals migrate from one node to another by random walk following different graphs; star, cycle, wheel and complete. The framework of epidemic migration model in vaccination game with information spreading effect is observed in one single season as well as generation by some strategy update rules for an individual either taking vaccination or not. Furthermore, individuals in each node are divided into seven situations as; unaware susceptible, aware susceptible, unaware vaccinated, aware vaccinated, unaware infected, aware infected and recovered in a single season. Two strategy updating rules: individual based risk assessment (IB-RA) and strategy based risk assessment (SB-RA) are discussed for game theoretical approach for four new states; healthy vaccinated, infected vaccinated, successfully free rider and failed free rider at the end of each season to explore how different graphs of an underlying social network giving impact on the final epidemic size through the effect of information spreading in the complex population network with various number of nodes. Accordingly, the information spreading with migration in metapopulation model can enhance the epidemic threshold effectiveness and help to overcome on controlling disease diffusion.

Effect of information spreading to suppress the disease contagion on the epidemic vaccination game

The information awareness about contagious diseases have an influential effect on an individual's decision to suppress the diffusion of infections. In this work, a new mathematical framework for a vaccination game combined with susceptible-infected-recovered (SIR) and unaware-aware (UA) situation is considered. Altering wearing mask or taking protection against diseases, we consider the information spreading effect that might be represented the situation of self-protection. The information spreading is supposed only for local situation for a season, but has a very significant effect to reduce the infection through a generation. Within this concept, unaware and aware states are taken for susceptible, infected and vaccinated individuals for an infinite and well mixed population. Moreover, three different strategy updating rules concerning whether an individual committing or not vaccination: individual based, strategy based and direct selection are studied to show the comparison by depicting as full phase diagram. Finally, it can be seen that information spreading can subdue the spreading of epidemic within a population.