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.

Enhancing vaccination strategies for epidemic control through effective lockdown measures.

Evolutionary epidemiology models have substantially impacted the study of various infections and prevention methods in the biology field. These models are called Susceptible, Lockdown, Vaccinated, Infected, and Recovered (SLVIR) epidemic dynamics. We explore how human behavior, particularly in the context of disease transmission, is influenced by two intervention strategies: vaccination and lockdown, both of which are grounded in the principles of evolutionary game theory (EGT). This comprehensive study using evolutionary game theory delves into the dynamics of epidemics, explicitly focusing on the transition rate from susceptibility to immunity and susceptibility to lockdown measures. Our research involves a thorough analysis of the structural aspects of the SLVIR epidemic model, which delineates disease-free equilibria to ensure stability in the system. Our investigation supports the notion that implementing lockdown measures effectively reduces the required level of vaccinations to curtail the prevalence of new infections. Furthermore, it highlights that combining both strategies is particularly potent when an epidemic spreads rapidly. In regions where the disease spreads comparatively more, our research demonstrates that lockdown measures are more effective in reducing the spread of the disease than relying solely on vaccines. Through significant numerical simulations, our research illustrates that integrating lockdown measures and efficient vaccination strategies can indirectly lower the risk of infection within the population, provided they are both dependable and affordable. The outcomes reveal a nuanced and beneficial scenario where we examine the interplay between the evolution of vaccination strategies and lockdown measures, assessing their coexistence through indicators of average social payoff.

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.

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.

Investigation of vaccination game approach in spreading covid-19 epidemic model with considering the birth and death rates.

In this study, an epidemic model for spreading COVID-19 is presented. This model considers the birth and death rates in the dynamics of spreading COVID-19. The birth and death rates are assumed to be the same, so the population remains constant. The dynamics of the model are explained in two phases. The first is the epidemic phase, which spreads during a season based on the proposed SIR/V model and reaches a stable state at the end of the season. The other one is the "vaccination campaign", which takes place between two seasons based on the rules of the vaccination game. In this stage, each individual in the population decides whether to be vaccinated or not. Investigating the dynamics of the studied model during a single epidemic season without consideration of the vaccination game shows waves in the model as experimental knowledge. In addition, the impact of the parameters is studied via the rules of the vaccination game using three update strategies. The result shows that the pandemic speeding can be changed by varying parameters such as efficiency and cost of vaccination, defense against contagious, and birth and death rates. The final epidemic size decreases when the vaccination coverage increases and the average social payoff is modified.

Proposal of an apposite strategy-updating rule for the vaccination game where hubs refer to hubs and lower-degree agents refer to lower-degree agents.

In the vaccination game, the spread of disease and the human decision-making to obtain pre-emptive vaccinations are coordinately united in successive seasons. This is backed both by epidemiological models, such as SIR, and by evolutionary game theory, assuming a given strategy-updating rule. Several rules have been proposed by the community and rely on either the imitation concept or the switching-action concept. The latter directly stipulates whether or not an agent commits to a course of action based on a rule, such as the aspiration concept. In contrast, the former borrowed its fundamental idea from the spatial version of a two-player, two-strategy (2 × 2) game, such as the spatial prisoner's dilemma (SPD). The pairwise Fermi (PW-Fermi) strategy has been heavily employed as the most representative idea. The present study modifies PW-Fermi, which consists of two processes: one for selecting a pairwise opponent to imitate and the other giving the probability of copying from the opponent. Instead of a random selection, our proposed model applies a stochastically skewed selection in which a neighbor who has a similar degree to the focal player is preferentially selected. This specific rule allows us to establish a quite efficient society, in which hub agents spontaneously obtain vaccination, but lower-degree agents do not. To this end, a small number of higher-degree agents, who are exposed to higher infection risk, are urged to be vaccinated, whereas many other agents enjoy free-riding. This produces a relatively small vaccination cost as a social sum and also effectively suppresses the spread of disease, resulting in a small disease cost for society as a whole.

Free ticket, discount ticket or intermediate of the best of two worlds - Which subsidy policy is socially optimal to suppress the disease spreading?

With the aid of the evolutionary vaccination game on a scale-free network, we design a new subsidy policy, named degree dependent subsidy, where cooperative agents get incentives according to their connectivity or degree. That is, agents, having a greater degree, receive a higher incentive, and vice versa. Here we presume that vaccinators are cooperative agents. The new scheme can be said to an intermediate policy between two previously studies policies, namely free ticket and flat discount policies. The former policy distributes free tickets to cooperative hub agents as a priority, whereas the latter dispenses a fixed discount to every cooperator. We compare the efficiency of each policy in terms of having a less infectious state with a minimum social cost. While investigating the performance of the three policies in terms of average social payoff-which takes into account the cost of vaccination as well as infection-the free ticket scheme is found to be the most appealing policies among the three when the budget for subsidy is quite low. The degree dependent subsidy policy outperforms others for a moderate budget size, while the flat discount policy requires a higher budget to effectively suppress the disease. We further estimate threshold levels of the subsidy budget for each policy beyond which subsidizing results in excessive use of vaccination. As a whole, concerning vaccination coverage and final epidemic size, the degree-dependent subsidy scheme outperforms the flat discount scheme, but is dominated by the free ticket policy.

Pair approximation model for the vaccination game: predicting the dynamic process of epidemic spread and individual actions against contagion.

We successfully establish a theoretical framework of pairwise approximation for the vaccination game in which both the dynamic process of epidemic spread and individual actions in helping prevent social behaviours are quantitatively evaluated. In contrast with mean-field approximation, our model captures higher-order effects from neighbours by using an underlying network that shows how the disease spreads and how individual decisions evolve over time. This model considers not only imperfect vaccination but also intermediate protective measures other than vaccines. Our analytical predictions are validated by multi-agent simulation results that estimate random regular graphs at varying degrees.

Analysis of individual strategies for artificial and natural immunity with imperfectness and durability of protection.

As protection against infectious disease, immunity is conferred by one of two main defense mechanisms, namely (i) resistance generated by previous infection (known as natural immunity) or (ii) by being vaccinated (known as artificial immunity). To analyze, a modified SVIRS epidemic model is established that integrates the effects of the durability of protection and imperfectness in the framework of the human decision-making process as a vaccination game. It is supposed that immunized people become susceptible again when their immunity expires, which depends on the duration of immunity. The current theory for most voluntary vaccination games assumes that seasonal diseases such as influenza are controlled by a temporal vaccine, the immunity of which lasts for only one season. Also, a novel perspective is established involving an individual's immune system combined with self-interest to take the vaccine and natural immunity obtained from infection by coupling a disease-spreading model with an evolutionary game approach over a long period. Numerical simulations show that the longer attenuation helps significantly to control the spread of disease. Also discovered is the entire mechanism of active and passive immunities, in the sense of how they coexist with natural and artificial immunity. Thus, the prospect of finding the optimal strategy for eradicating a disease could help in the design of effective vaccination campaigns and policies.

Cost-efficiency analysis of voluntary vaccination against n-serovar diseases using antibody-dependent enhancement: A game approach.

Records of epidemics acknowledge immunological multi-serotype illnesses as an important aspect of the occurrence and control of contagious diseases. These patterns occur due to antibody-dependent-enhancement (ADE) among serotype diseases, which leads to infection of secondary infectious classes. One example of this is dengue hemorrhagic fever and dengue shock syndrome, which comprises the following four serotypes: DEN-1, DEN-2, DEN-3, and DEN-4. The evolutionary vaccination game approach is able to shed light on this long-standing issue in a bid to evaluate the success of various control programs. Although immunization is regarded as one of the most accepted approaches for minimizing the risk of infection, cost and efficiency are important factors that must also be considered. To analyze the n-serovar aspect alongside ADE consequence in voluntary vaccination, this study establishes a new mathematical epidemiological model that is dovetailed with evolutionary game theory, an approach through which we explored two vaccine programs: primary and secondary. Our findings illuminate that the 'cost-efficiency' effect for vaccination decision exhibits an impact on controlling n-serovar infectious diseases and should be designed in such a manner as to avoid adverse effects. Furthermore, our numerical result justifies the fact that adopting ADE significantly boosted emerging disease incidence, it also suggest that the joint vaccine policy works even better when the complex cyclical epidemic outbreak takes place among multi serotypes interactions. Research also exposes that the primary vaccine is a better controlling tool than the secondary; however, introducing a highly-efficiency secondary vaccine against secondary infection plays a key role to control the disease prevalence.

Is subsidizing vaccination with hub agent priority policy really meaningful to suppress disease spreading?

A Multi Agent Simulation (MAS) model that joins evolutionary game theory with epidemiological dynamics is established. Various subsidy policies that encourage vaccination are evaluated quantitatively with the model. The underlying social network topology is based on a scale-free network. Individual subsidies for vaccinations can be directed to hub agents with priority, to efficiently suppress the overall social cost of a vaccination program. These hub agents are more likely to spread both knowledge about vaccination and the disease in question. Our comprehensive simulations showed that this intuitively appealing strategy cannot be effective if the vaccination cost is low and the vaccination budget is small. Thus, we find that the hub agent priority strategy is not always effective.

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.

Open-minded imitation can achieve near-optimal vaccination coverage.

Game-theoretic studies of voluntary vaccination predict that a socially unstructured population that is guided exclusively by individual rational self-interest always reaches a Nash equilibrium with vaccination coverage that is below the societal optimum. Human decision-making involves additional mechanisms, such as imitation of the successful strategies of others. However, previous research has found that imitation leads to vaccination coverage that is even below the Nash equilibrium. In this work, we note that these conclusions rely on the widely accepted use of Fermi functions for modeling the probabilities of switching to another strategy. We consider here a more general functional form of the switching probabilities. It involves one additional parameter [Formula: see text]. This parameter can be loosely interpreted as a degree of open-mindedness. The resulting dynamics are consistent with the ones that would be generated by functions that give best fits for empirical data in a widely cited psychological experiment. We show that sufficiently high levels of open-mindedness, as conceptualized by our parameter [Formula: see text], will drive equilibrium vaccination coverage levels above the Nash equilibrium, and in fact arbitrarily close to the societal optimum. These results were obtained both through mathematical analysis and numerical simulations.

To vaccinate or not to vaccinate: A comprehensive study of vaccination-subsidizing policies with multi-agent simulations and mean-field modeling.

We combined the elements of evolutionary game theory and mathematical epidemiology to comprehensively evaluate the performance of vaccination-subsidizing policies in the face of a seasonal epidemic. We conducted multi-agent simulations to, among others, find out how the topology of the underlying social networks affects the results. We also devised a mean-field approximation to confirm the simulation results and to better understand the influences of an imperfect vaccine. The main measure of a subsidy' performance was the total social payoff as a sum of vaccination costs, infection costs, and tax burdens due to the subsidy. We find two types of situations in which vaccination-subsidizing policies act counterproductively. The first type arises when the subsidy attempts to increase vaccination among past non-vaccinators, which inadvertently creates a negative incentive for voluntary vaccinators to abstain from vaccination in hope of getting subsidized. The second type is a consequence of overspending at which point the marginal cost of further increasing vaccination coverage is higher than the corresponding marginal cost of infections avoided by this increased coverage. The topology of the underlying social networks considerably worsens the subsidy's performance if connections become random and heterogeneous, as is often the case in human social networks. An imperfect vaccine also worsens the subsidy's performance, thus narrowing or completely closing the window for vaccination-subsidizing policies to beat the no-subsidy policy. These results imply that subsidies should be aimed at voluntary vaccinators while avoiding overspending. Once this is achieved, it makes little difference whether the subsidy fully or partly offsets the vaccination cost.

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.

Adoption costs of new vaccines - A Stackelberg dynamic game with risk-perception transition states.

Vaccination has become an integral part of public health, since an increase in overall vaccination in a given population contributes to a decline in infectious diseases and mortality. Vaccination also contributes to a lower rate of infection even for nonvaccinators due to herd immunity ((Brisson and Edmunds, 2002)). In this work we model human decision-making (with respect to a vaccination program in a single-payer health care provider country) using a leader-follower game framework. We then extend our model to a discrete dynamic game, where time passing is modelled by risk perception changes among population groups considering whether or not to vaccinate. The risk perception changes are encapsulated by probability transition matrices. We assume that the single-payer provider has a given fixed budget which would not be sufficient to cover 100% of a new vaccine for the entire population. To increase the potential coverage, we propose the introduction of a partial vaccine adoption policy, whereby an individual would pay a portion of the vaccine price and the single payer would support the rest for the entire population. We show how this policy, together with changes in risk perceptions regarding vaccination, impact the strategic decisions of individuals in each group, the policy cost under budgetary constraints and, ultimately, how it impacts the overall uptake of the vaccine in the entire population.

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.