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Fractions of the vaccinated and the effective vaccinated for a disease with a moderate infectiveness. The upper panel shows the stationary frequency of the vaccinated with respective to the effectiveness. No one takes vaccination until it is sufficiently efficient, . Then the vaccine uptake level increases with the effectiveness. When the effectiveness exceeds a threshold, , however, the vaccination level decreases with the effectiveness. The lower panel shows the stationary abundance of the effectively vaccinated individuals with respect to the effectiveness. It is shown the efficient vaccinated individual increases with the effectiveness all the time. Thus the behavior of vaccination and the impact of the vaccination against epidemic are not in agreement: for high effectiveness, even though vaccination rate is decreasing, the number of effectively vaccinated individual increases as the effectiveness increases. Here , satisfying .
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Achieving widespread population immunity by voluntary vaccination poses a major challenge for public health administration and practice. The situation is complicated even more by imperfect vaccines. How the vaccine efficacy affects individuals' vaccination behavior has yet to be fully answered. To address this issue, we combine a simple yet effecti...
Citations
... However, vaccines often fail to provide perfect immune protection for recipients due to factors such as production, storage, transportation and utilization. Consequently, the impact of vaccine effectiveness on vaccination behavior has been a topic of interest for many scholars [37][38][39][40], and vaccination effectiveness were mainly modeled as the effectiveness of vaccination [37], the effectiveness of immune protection [40] and the reversion of the vaccinated individual to susceptible [41]. For an example, Huang et al. developed a vaccination game model with myopic update rule and the imperfect vaccination [42]. ...
... In Section 3.1, we can find that the vaccination rates of populations with different values of decrease with the increase of vaccine efficacy after various thresholds of . It is worth mentioning that the same phenomenon has been observed in previous studies of vaccination behavior [37,[52][53][54]. Specially, Wu et al. found that although increased vaccine effectiveness reduces the vaccination rate due to the existence of free riders, the epidemic can be more effectively curbed [37]. ...
... It is worth mentioning that the same phenomenon has been observed in previous studies of vaccination behavior [37,[52][53][54]. Specially, Wu et al. found that although increased vaccine effectiveness reduces the vaccination rate due to the existence of free riders, the epidemic can be more effectively curbed [37]. To analyze the reasons for this phenomenon of our model, Fig. 6 describes the time courses of the different states' rate for different values of and vaccine efficacy. ...
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.
... Numerous studies have demonstrated the superior effectiveness of vaccination provision compared to other provisions taken [16,17]. While a vaccine does not provide perfect immunity, it does lower the infection rate and reduces the severity of disease [18][19][20]. Despite being considered the best tool to maintain the immune system, the vaccination dilemma arises [21][22][23][24]. ...
... As vaccination performance improves, there is a rapid increase in vaccine uptake in a self-interested population. Wu et al. [15] demonstrated that raising vaccination effectiveness consistently raises the proportion of people who receive the vaccination efficiently, reducing the epidemic size. The impact of an epidemic can be better controlled even while improvements to vaccine effectiveness cause a decline in vaccine adoption because of free-riding effects. ...
This study aims to evaluate mankind's vaccination behavior for two alternative vaccines through the incorporation of imitation and aspiration dynamics in an existing setup of the mean-field approximation. Individuals may be immunized in advance of an outbreak to prevent infection. However, due to the immunization's imperfections, expense, or people's reluctance to get immunized, a number of individuals might opt to be immunized later. Our model can simulate two scenarios of social conundrums, one caused by early vaccination and operating on a global time scale. The other is driven by delayed vaccination and working on a local time scale. The epidemic scenario gets worse as the strategy updating interval gets longer. This work provides a comparative analysis between the dynamics of imitation and aspiration. We integrate the imitation dynamics with various cost and efficacy variations of these vaccines. Then, we demonstrate the impact of symmetric and asymmetric level of expectations for both vaccines on aspiration dynamics. The symmetric expectations for both vaccines continue to have a negative relationship with their cost and a positive association with the efficacy of the vaccines. If one of the vaccines is more expensive, the consumer may opt for another. However, fewer aspiration for the early vaccine can improve the total vaccine coverage and hence help to limit epidemic disease in the case of an asymmetric degree of aspiration for the early-delayed vaccination model.
... In this case, many others in the community can also be benefited, so they have less incentive to be vaccinated. This scenario naturally leads to the "free-riding" problem commonly observed in public goods studies [6][7][8]. ...
Pre-emptive vaccination has been proven to be the most effective measure to control influenza outbreaks. However, when vaccination behavior is voluntary, individuals may face the vaccination dilemma owing to the two sides of vaccines. In view of this, many researchers began to use evolutionary game theory to model the vaccination decisions of individuals. Many existing models assume that individuals in networks use the Fermi function based strategy to update their vaccination decisions. As we know, human beings have strong learning capability and they may continuously search for the optimal strategy based on the surrounding environments. Hence, it is reasonable to use the reinforcement learning (RL) strategy to reflect the vaccination decisions of individuals. To this end, we here explore a mixed updating strategy for the vaccination decisions, specifically, some individuals called intelligent agents update their vaccination decisions based on the RL strategy, and the other individuals called regular agents update their decisions based on the Fermi function. We then investigate the impact of RL strategy on the vaccination behavior and the epidemic dynamics. Through extensive experiments, we find that the RL strategy plays a double-edged sword role: when the vaccination cost is not so high, more individuals are willing to choose vaccination if more individuals adopt the RL strategy, leading to the significant suppression of epidemics. On the contrary, when the vaccination cost is extremely high, the vaccination coverage is dramatically reduced, inducing the outbreak of the epidemic. We also analyze the underlying reasons for the double-edged sword role of the RL strategy.
... However, decisions made by individuals, within a given epidemiological context, have been typically described using mixed models, merging a game-theoretic model and an epidemic model [40,51,52]. Several topics have been addressed thus far: voluntary vaccination [42,50,[53][54][55][56][57][58][59][60][61][62][63][64], adoption of pre-exposure prophylaxis [65], social distancing [66][67][68] and self-isolation [69]. In fact, Hellmann and Thiele [69] modeled home testing as an aid in the decision making about whether or not to self-isolate. ...
The World Health Organization recommends test-and-treat interventions to curb and even eliminate epidemics of HIV, viral hepatitis, and sexually transmitted infections (e.g., chlamydia, gonorrhea, syphilis and trichomoniasis). Epidemic models show these goals are achievable, provided the participation of individuals in test-and-treat interventions is sufficiently high. We combine epidemic models and game theoretic models to describe individual’s decisions to get tested for infectious diseases within certain epidemiological contexts, and, implicitly, their voluntary participation to test-and-treat interventions. We develop three hybrid models, to discuss interventions against HIV, HCV, and sexually transmitted infections, and the potential behavioral response from the target population. Our findings are similar across diseases. Particularly, individuals use three distinct behavioral patterns relative to testing, based on their perceived costs for testing, besides the payoff for discovering their disease status. Firstly, if the cost of testing is too high, then individuals refrain from voluntary testing and get tested only if they are symptomatic. Secondly, if the cost is moderate, some individuals will test voluntarily, starting treatment if needed. Hence, the spread of the disease declines and the disease epidemiology is mitigated. Thirdly, the most beneficial testing behavior takes place as individuals perceive a per-test payoff that surpasses a certain threshold, every time they get tested. Consequently, individuals achieve high voluntary testing rates, which may result in the elimination of the epidemic, albeit on temporary basis. Trials and studies have attained different levels of participation and testing rates. To increase testing rates, they should provide each eligible individual with a payoff, above a given threshold, each time the individual tests voluntarily.
... The vaccination behavior of individual is more of a voluntary behavior. For instance, non-fatal and vaccine-preventable diseases such Therefore, many researchers have explored the evolutionary dynamics of voluntary vaccination [12][13][14][15][16]. Fu et al. [17] published a pioneering work that used evolutionary game theory to study individual vaccination behavior in different networks. ...
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 STAR , 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 STAR. 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 STAR. To analyze the model robust-ness, 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.
... We also assume that the vaccine works perfectly. This is an idealisation, since vaccines in practice can work imperfectly and it is known that the effectiveness of a vaccine can have an effect on whether individuals decide to get vaccinated or not [9,37,[43][44][45][46][47], thereby increasing the social dilemma's strength. However, the inclusion of vaccine effectiveness would drastically complicate this study and thus lies outside the scope of this work. ...
During epidemics people may reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision-making depends on information about vaccination timing in a differential game in which individual decision-making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We predict stronger social distancing the earlier the vaccination is expected and also the more sharply peaked its probability distribution. In particular, equilibrium social distancing only meaningfully deviates from the no-vaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting.
... Additionally, there are two payoffs: sucker (S) when one player cooperates and the other defects, and temptation (T) when one player defects while the other cooperates [15,16]. The concept of universal dilemma strength (SD) [17][18][19][20][21] considers two parameters: ′ and ′ , that determine the level of social viscosity required or the degree to which anonymity should be reduced to mitigate social dilemmas across different game classes. These game classes include the Prisoner's Dilemma (PD), Chicken (CH) game, Stag Hunt (SH), and Trivial game (TR), each characterized by distinct behavioral dynamics by, ′ > 0 & ′ > 0, ′ > 0 & ′ < 0 , ′ < 0 & ′ > 0 , and ′ < 0 & ′ < 0. To implement the dynamic mutation effect in the dyadic game, we consider a volatile mutation process on the repeated seasons instead of relying on the constant mutation rate. ...
The typical framework of replicator dynamics in evolutionary game theory assumes that all mutations are equally likely, meaning that the mutation of an evolving inhabitant only contributes constantly. However, in natural systems in biological and social sciences, mutations can arise due to their repetitive regeneration. The phenomenon of changing strategies (updating), typically prolonged sequences repeated many times, is defined as a volatile mutation that has been overlooked in evolutionary game theory. Implementing a repeated time framework introduces a dynamic mutation aspect incorporated with the pairwise Fermi rule. Network structure, ubiquitous in many natural and artificial systems, has significantly affected the dynamics and outcomes of evolutionary games. We examine the evolution of the pairwise game in terms of dilemma strength. It is revealed that mutation intensity can influence evolutionary dynamics. We also demonstrated that the obtained outcomes run by the deterministic and multi-agent simulation (MAS) process present similar stability regions for both linear and non-linear dynamics, even in various game classes. In particular, the most stimulating effect is detected for the relationship between the fraction of cooperation and the fraction of the mutated individuals, as inclination tends to provide an increasing tendency and supporting defection in the opposite case. In conclusion, we identified a form of volatile mutation as a form of noise that, under certain situations, could be used to enhance cooperation in social systems and design strategies for promoting cooperation in networked environments. 2
... Many works were published, including when strategychanging behavior depends on repeated seasons [10,11] or a single season [12,13], and when strategy relies on various updating strategies: IB-RA (individual-based risk assessment), SB-RA (societybased risk assessment), and DC (direct commitment) [10,14]. Several works have been investigated to explore the epidemic control framework on vaccination in which individuals interact with neighborhoods [15][16][17][18]. However, the vaccinating behavior of participants relies not only on the vaccine factors (cost-effectiveness), infection risk, vaccine hesitancy, and self-interest but also on the individual's or their neighbor's cooperative behavior [19]. ...
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.
... On the other hand, voluntary vaccination is a generally effective measure for controlling the epidemic in most countries. In this setting, a social dilemma exists between personal benefits and public health: non-vaccinators take a free ride by means of herd immunity caused by sufficient vaccine recipients that pay for vaccination [19][20][21][22] . Game theory is a classic theory for quantifying individual behavioral decisions, providing a natural framework to study how individuals choose different vaccination strategies to maximize benefits [ 23 , 24 ]. ...
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.
