Imitation dynamics of vaccination behaviour on social networks

Social Dilemma Analysis of the Spread of Infectious Disease

Understanding and controlling the spread of infectious disease is a pressing issue for our society. Contemporary globally connected civilization is more at risk from various modern infectious diseases than classical ones such as pests, cholera, and tuberculosis. Over the last few years, pandemic outbreaks of highly virulent influenza, possibly related to avian flu, severe acute respiratory syndrome (SARS), and middle-eastern respiratory syndrome coronavirus (MARSE) have been a threat. Beyond this, the intentional spread of infectious disease, e.g., “bioterrorism”, has come to be recognized as being just as dangerous as nuclear weapons. An infectious disease spreads on human social networks. Each individual can protect himself through several measures. Pre-emptive vaccination is thought to be most effective, although it incurs a partial cost to each individual. This brings about a social dilemma, because an individual may be able to rely on so-called “herd immunity” to avoid his own infection without himself being vaccinated. Also, besides vaccination, there may be several practical ways to protect against contagion, such as wearing a mask, keeping away from crowds, and self-isolation by leaving the home less often, which may be less costly and less effective than vaccination. In any case, there is a human-decision-making process regarding what steps should be taken, while the dynamics of infectious-disease spread can themselves be evaluated as a diffusion problem that has been well-studied in physics for many years. Thus, based on the concept of human–environment–social interaction, a basic-physics model for this diffusion problem that considers evolutionary game theory (EGT) may lead us to obtain some meaningful solutions that can be proposed to our society. Following the previous chapter explaining how EGT can be applied to traffic-flow analysis, this chapter describes this practical problem.

Voluntary vaccination dilemma with evolving psychological perceptions

Voluntary vaccination is a universal control protocol for infectious diseases. Yet there exists a social dilemma between individual benefits and public health: non-vaccinators free ride via the herd immunity from adequate vaccinators who bear vaccination cost. This is due to the interplay between disease prevalence and individual vaccinating behavior. To complicate matters further, individual vaccinating behavior depends on the perceived vaccination cost rather than the actual one. The perception of vaccination cost is an individual trait, which varies from person to person, and evolves in response to the disease prevalence and vaccination coverage. To explore how evolving perception shapes individual vaccinating behavior and thus the vaccination dynamics, we provide a model combining epidemic dynamics with evolutionary game theory which captures the voluntary vaccination dilemma. In particular, individuals adjust their perception based on the inertia effect in psychology and then update their vaccinating behavior through imitating the behavior of a more successful peer. We find that i) vaccination is acceptable when the expected vaccination cost considering perception and actual vaccination cost is less than the maximum of the expected non-vaccination cost; ii) the evolution of perception is a "double-edged sword" for vaccination dynamics: it can improve vaccination coverage when most individuals perceive exaggerated vaccination cost, and it inhibits vaccination coverage in the other cases.

Considering behaviour to ensure the success of a disease control strategy

The success or failure of a disease control strategy can be significantly affected by the behaviour of individual agents involved, influencing the effectiveness of disease control, its cost and sustainability. This behaviour has rarely been considered in agricultural systems, where there is significant opportunity for impact. Efforts to increase the adoption of control while decreasing oscillations in adoption and yield, particularly through the administration of subsidies, could increase the effectiveness of interventions. We study individual behaviour for the deployment of clean seed systems to control cassava brown streak disease in East Africa, noting that high disease pressure is important to stimulate grower demand of the control strategy. We show that it is not necessary to invest heavily in formal promotional or educational campaigns, as word-of-mouth is often sufficient to endorse the system. At the same time, for improved planting material to have an impact on increasing yields, it needs to be of a sufficient standard to restrict epidemic spread significantly. Finally, even a simple subsidy of clean planting material may be effective in disease control, as well as reducing oscillations in adoption, as long as it reaches a range of different users every season.

Exploring Voluntary Vaccinating Behaviors using Evolutionary N-person Threshold Games

Understanding individuals' voluntary vaccinating behaviors plays essential roles in making vaccination policies for many vaccinepreventable diseases. Usually, individuals decide whether to vaccinate through evaluating the relative cost of vaccination and infection according to their own interests. Mounting evidence shows that the best vaccine coverage level for the population as a whole can hardly be achieved due to the effects of herd immunity. In this paper, taking into consideration the herd immunity threshold, we present an evolutionary N-person threshold game, where individuals can dynamically adjust their vaccinating strategies and their payoffs depend nonlinearly on whether or not the herd immunity threshold is reached. First, in well-mixed populations, we analyze the relationships at equilibrium among the fraction of vaccinated individuals, the population size, the basic reproduction number and the relative cost of vaccination and infection. Then, we carry out simulations on four types of complex networks to explore the evolutionary dynamics of the N-person threshold game in structured populations. Specifically, we investigate the effects of disease severity and population structure on the vaccine coverage for different relative costs of vaccination and infection. The results and findings can offer new insight into designing incentive-based vaccination policies for disease intervention and control.

Prevention of treatable infectious diseases: A game-theoretic approach

We model outcomes of voluntary prevention using an imperfect vaccine, which confers protection only to a fraction of vaccinees for a limited duration. Our mathematical model combines a single-player game for the individual-level decision to get vaccinated, and a compartmental model for the epidemic dynamics. Mathematical analysis yields a characterization for the effective vaccination coverage, as a function of the relative cost of prevention versus treatment; note that cost may involve monetary as well as non-monetary aspects. Three behaviors are possible. First, the relative cost may be too high, so individuals do not get vaccinated. Second, the relative cost may be moderate, such that some individuals get vaccinated and voluntary vaccination alleviates the epidemic. In this case, the vaccination coverage grows steadily with decreasing relative cost of vaccination versus treatment. Unlike previous studies, we find a third case where relative cost is sufficiently low so epidemics may be averted through the use of prevention, even for an imperfect vaccine. However, we also found that disease elimination is only temporary-as no equilibrium exists for the individual strategy in this third case-and, with increasing perceived cost of vaccination versus treatment, the situation may be reversed toward the epidemic edge, where the effective reproductive number is 1. Thus, maintaining relative cost sufficiently low will be the main challenge to maintain disease elimination. Furthermore, our model offers insight on vaccine parameters, which are otherwise difficult to estimate. We apply our findings to the epidemiology of measles.

Voluntary Vaccination through Self-organizing Behaviors on Locally-mixed Social Networks

Voluntary vaccination reflects how individuals weigh the risk of infection and the cost of vaccination against the spread of vaccine-preventable diseases, such as smallpox and measles. In a homogeneously mixing population, the infection risk of an individual depends largely on the proportion of vaccinated individuals due to the effects of herd immunity. While in a structured population, the infection risk can also be affected by the structure of individuals' social network. In this paper, we focus on studying individuals' self-organizing behaviors under the circumstance of voluntary vaccination in different types of social networks. Specifically, we assume that each individual together with his/her neighbors forms a local well-mixed environment, where individuals meet equally often as long as they have a common neighbor. We carry out simulations on four types of locally-mixed social networks to investigate the network effects on voluntary vaccination. Furthermore, we also evaluate individuals' vaccinating decisions through interacting with their "neighbors of neighbors". The results and findings of this paper provide a new perspective for vaccination policy-making by taking into consideration human responses in complex social networks.

Dueling biological and social contagions

Numerous models explore how a wide variety of biological and social phenomena spread in social networks. However, these models implicitly assume that the spread of one phenomenon is not affected by the spread of another. Here, we develop a model of “dueling contagions”, with a particular illustration of a situation where one is biological (influenza) and the other is social (flu vaccination). We apply the model to unique time series data collected during the 2009 H1N1 epidemic that includes information about vaccination, flu, and face-to-face social networks. The results show that well-connected individuals are more likely to get vaccinated, as are people who are exposed to friends who get vaccinated or are exposed to friends who get the flu. Our dueling contagion model suggests that other epidemiological models may be dramatically underestimating the R₀ of contagions. It also suggests that the rate of vaccination contagion may be even more important than the biological contagion in determining the course of the disease. These results suggest that real world and online platforms that make it easier to see when friends have been vaccinated (personalized vaccination campaigns) and when they get the flu (personalized flu warnings) could have a large impact on reducing the severity of epidemics. They also suggest possible benefits from understanding the coevolution of many kinds of dueling contagions.

Effects of awareness diffusion and self-initiated awareness behavior on epidemic spreading - An approach based on multiplex networks

In this paper, we study the interplay between the epidemic spreading and the diffusion of awareness in multiplex networks. In the model, an infectious disease can spread in one network representing the paths of epidemic spreading (contact network), leading to the diffusion of awareness in the other network (information network), and then the diffusion of awareness will cause individuals to take social distances, which in turn affects the epidemic spreading. As for the diffusion of awareness, we assume that, on the one hand, individuals can be informed by other aware neighbors in information network, on the other hand, the susceptible individuals can be self-awareness induced by the infected neighbors in the contact networks (local information) or mass media (global information). Through Markov chain approach and numerical computations, we find that the density of infected individuals and the epidemic threshold can be affected by the structures of the two networks and the effective transmission rate of the awareness. However, we prove that though the introduction of the self-awareness can lower the density of infection, which cannot increase the epidemic threshold no matter of the local information or global information. Our finding is remarkably different to many previous results on single-layer network: local information based behavioral response can alter the epidemic threshold. Furthermore, our results indicate that the nodes with more neighbors (hub nodes) in information networks are easier to be informed, as a result, their risk of infection in contact networks can be effectively reduced.

On the Role of Imitation on Adolescence Methamphetamine Abuse Dynamics

Adolescence methamphetamine use is an issue of considerable concern due to its correlation with later delinquency, divorce, unemployment and health problems. Understanding how adolescents initiate methamphetamine abuse is important in developing effective prevention programs. We formulate a mathematical model for the spread of methamphetamine abuse using nonlinear ordinary differential equations. It is assumed that susceptibles are recruited into methamphetamine use through imitation. An epidemic threshold value, [Formula: see text], termed the abuse reproduction number, is proposed and defined herein in the drug-using context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that methamphetamine problems may persist in the population even if [Formula: see text] is less than one. Sensitivity analysis of [Formula: see text] was performed to determine the relative importance of different parameters in methamphetamine abuse initiation. The model is then fitted to data on methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse in the treatment centres of Cape Town and parameter values that give the best fit are chosen. Results show that the proportion of methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse will continue to decrease in Cape Town of South Africa. The results suggest that intervention programs targeted at reducing adolescence methamphetamine abuse, are positively impacting methamphetamine abuse.

“Beauty contest” indicator of cognitive ability and free riding strategies. Results from a scenario experiment about pandemic flu immunization

High immunization coverage rates are desirable in order to reduce total morbidity and mortality rates, but it may also provide an incentive for herd immunity free riding strategies. The aim of this paper was to investigate the link between cognitive ability and vaccination intention in a hypothetical scenario experiment about Avian Flu immunization. A between-subject scenario experiment was utilized to examine the willingness to undergo vaccination when the vaccination coverage was proclaimed to be 36, 62 and 88%. Respondents were later assigned to a “Beauty contest” experiment, an experimental game commonly used to investigate individual's cognitive ability. Results show that there was a significant negative effect of the proclaimed vaccination uptake among others on the vaccination intention. However, there were no significant association between the “Beauty contest” indicator of cognitive ability and the use of herd immunity free riding strategies.

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Infectious diseases are a threat to human health and a hindrance to societal development. Consequently, the spread of diseases in both time and space has been widely studied, revealing the different types of spatial patterns. Transitions between patterns are an emergent property in spatial epidemics that can serve as a potential trend indicator of disease spread. Despite the usefulness of such an indicator, attempts to systematize the topic of pattern transitions have been few and far between. We present a mini-review on pattern transitions in spatial epidemics, describing the types of transitions and their underlying mechanisms. We show that pattern transitions relate to the complexity of spatial epidemics by, for example, being accompanied with phenomena such as coherence resonance and cyclic evolution. The results presented herein provide valuable insights into disease prevention and control, and may even be applicable outside epidemiology, including other branches of medical science, ecology, quantitative finance, and elsewhere.

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

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

National Survey Indicates that Individual Vaccination Decisions Respond Positively to Community Vaccination Rates

Some models of vaccination behavior imply that an individual's willingness to vaccinate could be negatively correlated with the vaccination rate in her community. The rationale is that a higher community vaccination rate reduces the risk of contracting the vaccine-preventable disease and thus reduces the individual's incentive to vaccinate. At the same time, as for many health-related behaviors, individuals may want to conform to the vaccination behavior of peers, counteracting a reduced incentive to vaccinate due to herd immunity. Currently there is limited empirical evidence on how individual vaccination decisions respond to the vaccination decisions of peers. In the fall of 2014, we used a rapid survey technology to ask a large sample of U.S. adults about their willingness to use a vaccine for Ebola. Respondents expressed a greater inclination to use the vaccine in a hypothetical scenario with a high community vaccination rate. In particular, an increase in the community vaccination rate from 10% to 90% had the same impact on reported utilization as a nearly 50% reduction in out-of-pocket cost. These findings are consistent with a tendency to conform with vaccination among peers, and suggest that policies promoting vaccination could be more effective than has been recognized.

Reputation-Based Investment Helps to Optimize Group Behaviors in Spatial Lattice Networks

Encouraging cooperation among selfish individuals is crucial in many real-world systems, where individuals’ collective behaviors can be analyzed using evolutionary public goods game. Along this line, extensive studies have shown that reputation is an effective mechanism to investigate the evolution of cooperation. In most existing studies, participating individuals in a public goods game are assumed to contribute unconditionally into the public pool, or they can choose partners based on a common reputation standard (e.g., preferences or characters). However, to assign one reputation standard for all individuals is impractical in many real-world deployment. In this paper, we introduce a reputation tolerance mechanism that allows an individual to select its potential partners and decide whether or not to contribute an investment to the public pool based on its tolerance to other individuals’ reputation. Specifically, an individual takes part in a public goods game only if the number of participants with higher reputation exceeds the value of its tolerance. Moreover, in this paper, an individual’s reputation can increase or decrease in a bounded interval based on its historical behaviors. We explore the principle that how the reputation tolerance and conditional investment mechanisms can affect the evolution of cooperation in spatial lattice networks. Our simulation results demonstrate that a larger tolerance value can achieve an environment that promote the cooperation of participants.

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

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

The Effect of Farmers' Decisions on Pest Control with Bt Crops: A Billion Dollar Game of Strategy

A farmer's decision on whether to control a pest is usually based on the perceived threat of the pest locally and the guidance of commercial advisors. Therefore, farmers in a region are often influenced by similar circumstances, and this can create a coordinated response for pest control that is effective at a landscape scale. This coordinated response is not intentional, but is an emergent property of the system. We propose a framework for understanding the intrinsic feedback mechanisms between the actions of humans and the dynamics of pest populations and demonstrate this framework using the European corn borer, a serious pest in maize crops. We link a model of the European corn borer and a parasite in a landscape with a model that simulates the decisions of individual farmers on what type of maize to grow. Farmers chose whether to grow Bt-maize, which is toxic to the corn borer, or conventional maize for which the seed is cheaper. The problem is akin to the snow-drift problem in game theory; that is to say, if enough farmers choose to grow Bt maize then because the pest is suppressed an individual may benefit from growing conventional maize. We show that the communication network between farmers' and their perceptions of profit and loss affects landscape scale patterns in pest dynamics. We found that although adoption of Bt maize often brings increased financial returns, these rewards oscillate in response to the prevalence of pests.

Coupled disease-behavior dynamics on complex networks: A review

It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease-behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease-behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years.

Beyond Rational Decision-Making: Modelling the Influence of Cognitive Biases on the Dynamics of Vaccination Coverage

BACKGROUND

Theoretical studies predict that it is not possible to eradicate a disease under voluntary vaccination because of the emergence of non-vaccinating "free-riders" when vaccination coverage increases. A central tenet of this approach is that human behaviour follows an economic model of rational choice. Yet, empirical studies reveal that vaccination decisions do not necessarily maximize individual self-interest. Here we investigate the dynamics of vaccination coverage using an approach that dispenses with payoff maximization and assumes that risk perception results from the interaction between epidemiology and cognitive biases.

METHODS

We consider a behaviour-incidence model in which individuals perceive actual epidemiological risks as a function of their opinion of vaccination. As a result of confirmation bias, sceptical individuals (negative opinion) overestimate infection cost while pro-vaccines individuals (positive opinion) overestimate vaccination cost. We considered a feedback between individuals and their environment as individuals could change their opinion, and thus the way they perceive risks, as a function of both the epidemiology and the most common opinion in the population.

RESULTS

For all parameter values investigated, the infection is never eradicated under voluntary vaccination. For moderately contagious diseases, oscillations in vaccination coverage emerge because individuals process epidemiological information differently depending on their opinion. Conformism does not generate oscillations but slows down the cultural response to epidemiological change.

CONCLUSION

Failure to eradicate vaccine preventable disease emerges from the model because of cognitive biases that maintain heterogeneity in how people perceive risks. Thus, assumptions of economic rationality and payoff maximization are not mandatory for predicting commonly observed dynamics of vaccination coverage. This model shows that alternative notions of rationality, such as that of ecological rationality whereby individuals use simple cognitive heuristics, offer promising new avenues for modelling vaccination behaviour.

Can rewiring strategy control the epidemic spreading?

Relation existed in the social contact network can affect individuals' behaviors greatly. Considering the diversity of relation intimacy among network nodes, an epidemic propagation model is proposed by incorporating the link-breaking threshold, which is normally neglected in the rewiring strategy. The impact of rewiring strategy on the epidemic spreading in the weighted adaptive network is explored. The results show that the rewiring strategy cannot always control the epidemic prevalence, especially when the link-breaking threshold is low. Meanwhile, as well as strong links, weak links also play a significant role on epidemic spreading.

Mathematical and computational approaches to epidemic modeling: a comprehensive review

Mathematical and computational approaches are important tools for understanding epidemic spread patterns and evaluating policies of disease control. In recent years, epidemiology has become increasingly integrated with mathematics, sociology, management science, complexity science, and computer science. The cross of multiple disciplines has caused rapid development of mathematical and computational approaches to epidemic modeling. In this article, we carry out a comprehensive review of epidemic models to provide an insight into the literature of epidemic modeling and simulation. We introduce major epidemic models in three directions, including mathematical models, complex network models, and agent-based models. We discuss the principles, applications, advantages, and limitations of these models. Meanwhile, we also propose some future research directions in epidemic modeling.

Disease Interventions Can Interfere with One Another through Disease-Behaviour Interactions

Theoretical models of disease dynamics on networks can aid our understanding of how infectious diseases spread through a population. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. However, these two interventions are usually modelled separately. Here, we construct a simulation model of influenza transmission through a contact network, where individuals can choose whether to become vaccinated and/or practice NPIs. These decisions are based on previous experience with the disease, the current state of infection amongst one's contacts, and the personal and social impacts of the choices they make. We find that the interventions interfere with one another: because of negative feedback between intervention uptake and infection prevalence, it is difficult to simultaneously increase uptake of all interventions by changing utilities or perceived risks. However, on account of vaccine efficacy being higher than NPI efficacy, measures to expand NPI practice have only a small net impact on influenza incidence due to strongly mitigating feedback from vaccinating behaviour, whereas expanding vaccine uptake causes a significant net reduction in influenza incidence, despite the reduction of NPI practice in response. As a result, measures that support expansion of only vaccination (such as reducing vaccine cost), or measures that simultaneously support vaccination and NPIs (such as emphasizing harms of influenza infection, or satisfaction from preventing infection in others through both interventions) can significantly reduce influenza incidence, whereas measures that only support expansion of NPI practice (such as making hand sanitizers more available) have little net impact on influenza incidence. (However, measures that improve NPI efficacy may fare better.) We conclude that the impact of interference on programs relying on multiple interventions should be more carefully studied, for both influenza and other infectious diseases.

Universal scaling for the dilemma strength in evolutionary games

Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.

The structure and dynamics of multilayer networks

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.

Evolutionary prisoner's dilemma game on graphs and social networks with external constraint

A game-theoretical model is constructed to capture the effect of external constraint on the evolution of cooperation. External constraint describes the case where individuals are forced to cooperate with a given probability in a society. Mathematical analyses are conducted via pair approximation and diffusion approximation methods. The results show that the condition for cooperation to be favored on graphs with constraint is b¯/c¯>k/A¯ (A¯=1+kp/(1-p)), where b¯ and c¯ represent the altruistic benefit and cost, respectively, k is the average degree of the graph and p is the probability of compulsory cooperation by external enforcement. Moreover, numerical simulations are also performed on a repeated game with three strategies, always defect (ALLD), tit-for-tat (TFT) and always cooperate (ALLC). These simulations demonstrate that a slight enforcement of ALLC can only promote cooperation when there is weak network reciprocity, while the catalyst effect of TFT on cooperation is verified. In addition, the interesting phenomenon of stable coexistence of the three strategies can be observed. Our model can represent evolutionary dynamics on a network structure which is disturbed by a specified external constraint.

Effects of behavioral response and vaccination policy on epidemic spreading--an approach based on evolutionary-game dynamics

How effective are governmental incentives to achieve widespread vaccination coverage so as to prevent epidemic outbreak? The answer largely depends on the complex interplay among the type of incentive, individual behavioral responses, and the intrinsic epidemic dynamics. By incorporating evolutionary games into epidemic dynamics, we investigate the effects of two types of incentives strategies: partial-subsidy policy in which certain fraction of the cost of vaccination is offset, and free-subsidy policy in which donees are randomly selected and vaccinated at no cost. Through mean-field analysis and computations, we find that, under the partial-subsidy policy, the vaccination coverage depends monotonically on the sensitivity of individuals to payoff difference, but the dependence is non-monotonous for the free-subsidy policy. Due to the role models of the donees for relatively irrational individuals and the unchanged strategies of the donees for rational individuals, the free-subsidy policy can in general lead to higher vaccination coverage. Our findings indicate that any disease-control policy should be exercised with extreme care: its success depends on the complex interplay among the intrinsic mathematical rules of epidemic spreading, governmental policies, and behavioral responses of individuals.

Aspiration-based partner switching boosts cooperation in social dilemmas

Most previous studies concerning linking dynamics often assumed that links pairing individuals should be identified and treated differently during topology adjusting procedure, in order to promote cooperation. A common assumption was that cooperators were expected to avoid being exploited by quickly breaking up relationships with defectors. Then the so-called prosocial links linking two cooperators (abbreviated as CC links hereafter) would be much favored by evolution, whereby cooperation was promoted. However, we suggest that this is not always necessary. Here, we developed a minimal model in which an aspiration-based partner switching mechanism was embedded to regulate the evolution of cooperation in social dilemmas. Individuals adjusted social ties in a self-questioning manner in line with the learning theory. Less game information was involved during dynamic linking and all links were tackled anonymously irrespective of their types (i.e., CD links, DD links, or CC links). The main results indicate that cooperation flourishes for a broad range of parameters. The denser the underlying network, the more difficult the evolution of cooperation. More importantly, moderate aspirations do much better in promoting the evolution of altruistic behavior and for most cases there exists the optimal aspiration level that most benefits cooperation. Too strong or too weak selection intensity turns out to be pretty conducive to the evolution of cooperation in such a dynamical system.

A belief-based model for characterizing the spread of awareness and its impacts on individuals' vaccination decisions

During an epidemic, individuals' decisions on whether or not to take vaccine may affect the dynamics of disease spread and, therefore, the effectiveness of disease control. Empirical studies have shown that such decisions can be subjected to individuals' awareness about disease and vaccine, such as their perceived disease severity and vaccine safety. The aim of this paper is to gain a better understanding of individuals' vaccination behaviour by modelling the spread of awareness in a group of socially connected individuals and examining the associated impacts on their vaccination decision-making. In our model, we examine whether or not individuals will get vaccinated as well as when they would. In doing so, we consider three possible decisions from an individual, i.e., to accept, to reject, and yet to decide, and further associate them with a set of belief values. Next, we extend the Dempster-Shafer theory to characterize individuals' belief value updates and their decision-making, having incorporated the awareness obtained from their connected neighbours. Furthermore, we examine two factors that will affect individuals' vaccination decisions: (i) reporting rates of disease- and vaccine-related events, and (ii) fading coefficient of awareness spread. By doing so, we can assess the impacts of awareness spread by evaluating the vaccination dynamics in terms of the number of vaccinated individuals. The results have demonstrated that the former influences the ratio of vaccinated individuals, whereas the latter affects the time when individuals decide to take vaccine.

Effect of vaccination strategies on the dynamic behavior of epidemic spreading and vaccine coverage

The transmission of infectious, yet vaccine-preventable, diseases is a typical complex social phenomenon, where the increasing level of vaccine update in the population helps to inhibit the epidemic spreading, which in turn, however, discourages more people to participate in vaccination campaigns, due to the "externality effect" raised by vaccination. We herein study the impact of vaccination strategies, pure, continuous (rather than adopt vaccination definitely, the individuals choose to taking vaccine with some probabilities), or continuous with randomly mutation, on the vaccination dynamics with a spatial susceptible-vaccinated-infected-recovered (SVIR) epidemiological model. By means of extensive Monte-Carlo simulations, we show that there is a crossover behavior of the final vaccine coverage between the pure-strategy case and the continuous-strategy case, and remarkably, both the final vaccination level and epidemic size in the continuous-strategy case are less than them in the pure-strategy case when vaccination is cheap. We explain this phenomenon by analyzing the organization process of the individuals in the continuous-strategy case in the equilibrium. Our results are robust to the SVIR dynamics defined on other spatial networks, like the Erdős-Rényi and Barabási-Albert networks.

Evolutionary dynamics in finite populations with zealots

We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations. Zealots are assumed to take either strategy regardless of the fitness. When the strategy selected by the zealots is the same, the fixation of the strategy selected by the zealots is a trivial outcome. We study fixation time in this scenario. We show that the fixation time is divided into three main regimes, in one of which the fixation time is short, and in the other two the fixation time is exponentially long in terms of the population size. Different from the case without zealots, there is a threshold selection intensity below which the fixation is fast for an arbitrary payoff matrix. We illustrate our results with examples of various social dilemma games.

Free-riding behavior in vaccination decisions: an experimental study

Individual decision-making regarding vaccination may be affected by the vaccination choices of others. As vaccination produces externalities reducing transmission of a disease, it can provide an incentive for individuals to be free-riders who benefit from the vaccination of others while avoiding the cost of vaccination. This study examined an individual's decision about vaccination in a group setting for a hypothetical disease that is called “influenza” using a computerized experimental game. In the game, interactions with others are allowed. We found that higher observed vaccination rate within the group during the previous round of the game decreased the likelihood of an individual's vaccination acceptance, indicating the existence of free-riding behavior. The free-riding behavior was observed regardless of parameter conditions on the characteristics of the influenza and vaccine. We also found that other predictors of vaccination uptake included an individual's own influenza exposure in previous rounds increasing the likelihood of vaccination acceptance, consistent with existing empirical studies. Influenza prevalence among other group members during the previous round did not have a statistically significant effect on vaccination acceptance in the current round once vaccination rate in the previous round was controlled for.

Behavior of susceptible-vaccinated-infected-recovered epidemics with diversity in the infection rate of individuals

We study a susceptible-vaccinated-infected-recovered (SVIR) epidemic-spreading model with diversity of infection rate of the individuals. By means of analytical arguments as well as extensive computer simulations, we demonstrate that the heterogeneity in infection rate can either impede or accelerate the epidemic spreading, which depends on the amount of vaccinated individuals introduced in the population as well as the contact pattern among the individuals. Remarkably, as long as the individuals with different capability of acquiring the disease interact with unequal frequency, there always exist a cross point for the fraction of vaccinated, below which the diversity of infection rate hinders the epidemic spreading and above which expedites it. The overall results are robust to the SVIR dynamics defined on different population models; the possible applications of the results are discussed.

Braess's paradox in epidemic game: better condition results in less payoff

Facing the threats of infectious diseases, we take various actions to protect ourselves, but few studies considered an evolving system with competing strategies. In view of that, we propose an evolutionary epidemic model coupled with human behaviors, where individuals have three strategies: vaccination, self-protection and laissez faire, and could adjust their strategies according to their neighbors' strategies and payoffs at the beginning of each new season of epidemic spreading. We found a counter-intuitive phenomenon analogous to the well-known Braess's Paradox, namely a better condition may lead to worse performance. Specifically speaking, increasing the successful rate of self-protection does not necessarily reduce the epidemic size or improve the system payoff. The range and degree of the Braess's Paradox are sensitive to both the parameters characterizing the epidemic spreading and the strategy payoff, while the existence of the Braess's Paradox is insensitive to the network topologies. This phenomenon can be well explained by a mean-field approximation. Our study demonstrates an important fact that a better condition for individuals may yield a worse outcome for the society.

Effects of adaptive dynamical linking in networked games

The role of dynamical topologies in the evolution of cooperation has received considerable attention, as some studies have demonstrated that dynamical networks are much better than static networks in terms of boosting cooperation. Here we study a dynamical model of evolution of cooperation on stochastic dynamical networks in which there are no permanent partners to each agent. Whenever a new link is created, its duration is randomly assigned without any bias or preference. We allow the agent to adaptively adjust the duration of each link during the evolution in accordance with the feedback from game interactions. By Monte Carlo simulations, we find that cooperation can be remarkably promoted by this adaptive dynamical linking mechanism both for the game of pairwise interactions, such as the Prisoner's Dilemma game (PDG), and for the game of group interactions, illustrated by the public goods game (PGG). And the faster the adjusting rate, the more successful the evolution of cooperation. We also show that in this context weak selection favors cooperation much more than strong selection does. What is particularly meaningful is that the prosperity of cooperation in this study indicates that the rationality and selfishness of a single agent in adjusting social ties can lead to the progress of altruism of the whole population.

Evolutionary vaccination dilemma in complex networks

In this work we analyze the evolution of voluntary vaccination in networked populations by entangling the spreading dynamics of an influenza-like disease with an evolutionary framework taking place at the end of each influenza season so that individuals take or do not take the vaccine upon their previous experience. Our framework thus puts in competition two well-known dynamical properties of scale-free networks: the fast propagation of diseases and the promotion of cooperative behaviors. Our results show that when vaccine is perfect, scale-free networks enhance the vaccination behavior with respect to random graphs with homogeneous connectivity patterns. However, when imperfection appears we find a crossover effect so that the number of infected (vaccinated) individuals increases (decreases) with respect to homogeneous networks, thus showing the competition between the aforementioned properties of scale-free graphs.

Coevolution of quantum and classical strategies on evolving random networks

We study the coevolution of quantum and classical strategies on weighted and directed random networks in the realm of the prisoner's dilemma game. During the evolution, agents can break and rewire their links with the aim of maximizing payoffs, and they can also adjust the weights to indicate preferences, either positive or negative, towards their neighbors. The network structure itself is thus also subject to evolution. Importantly, the directionality of links does not affect the accumulation of payoffs nor the strategy transfers, but serves only to designate the owner of each particular link and with it the right to adjust the link as needed. We show that quantum strategies outperform classical strategies, and that the critical temptation to defect at which cooperative behavior can be maintained rises, if the network structure is updated frequently. Punishing neighbors by reducing the weights of their links also plays an important role in maintaining cooperation under adverse conditions. We find that the self-organization of the initially random network structure, driven by the evolutionary competition between quantum and classical strategies, leads to the spontaneous emergence of small average path length and a large clustering coefficient.

Policy trap and optimal subsidization policy under limited supply of vaccines

We adopt a susceptible-infected-susceptible (SIS) model on a Barabási and Albert (BA) network to investigate the effects of different vaccine subsidization policies. The goal is to control the prevalence of the disease given a limited supply and voluntary uptake of vaccines. The results show a uniform subsidization policy is always harmful and increases the prevalence of the disease, because the lower degree individuals' demand for vaccine crowds out the higher degree individuals' demand. In the absence of an effective uniform policy, we explore a targeted subsidization policy which relies on a proxy variable instead of individuals' connectivity. Findings show a poor proxy-based targeted program can still increase the disease prevalence and become a policy trap. The results are robust to general scale-free networks.

Impacts of subsidy policies on vaccination decisions in contact networks

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

The increased risk of joint venture promotes social cooperation

The joint venture of many members is common both in animal world and human society. In these public enterprizes, highly cooperative groups are more likely to while low cooperative groups are still possible but not probable to succeed. Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly. We here institute a model addressing this public goods dilemma with incorporating the public resource foraging failure risk. Risk-averse individuals tend to lead a autarkic life, while risk-preferential ones tend to participate in the risky public goods game. For participants, group's success relies on its cooperativeness, with increasing contribution leading to increasing success likelihood. We introduce a function with one tunable parameter to describe the risk removal pattern and study in detail three representative classes. Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear. Depending on the way that group's success relies on its cooperativeness, either cooperators pervade the entire population or they coexist with defectors. Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing. The harder the joint venture succeeds, the higher level of cooperation once cooperators can win the evolutionary race. Our work may enrich the literature concerning the risky public goods games.

Vaccination, herd behavior, and herd immunity

BACKGROUND

During the 2009 outbreak of novel influenza AH1N1, insufficient data were available to adequately inform decision makers about benefits and risks of vaccination and disease. We hypothesized that individuals would opt to mimic their peers, having no better decision anchor. We used Game Theory, decision analysis, and transmission models to simulate the impact of subjective risks and preference estimates on vaccination behavior.

METHODS

We asked 95 students to provide estimates of risk and health state valuations with regard to AH1N1 infection, complications, and expectations of vaccine benefits and risks. These estimates were included in a sequential chain of models: a dynamic epidemic model, a decision tree, and a population-level model. Additionally, participants' intentions to vaccinate or not at varying vaccination rates were documented.

RESULTS

The model showed that at low vaccination rates, vaccination dominated. When vaccination rates increased above 78%, nonvaccination was the dominant strategy. We found that vaccination intentions did not correspond to the shift in strategy dominance and segregated to 3 types of intentions: regardless of what others do 29/95 (31%) intended to vaccinate while 27/95 (28%) did not; among 39 of 95 (41%) intention was positively associated with putative vaccination rates.

CONCLUSIONS

Some people conform to the majority's choice, either shifting epidemic dynamics toward herd immunity or, conversely, limiting societal goals. Policy leaders should use models carefully, noting their limitations and theoretical assumptions. Behavior drivers were not explicitly explored in this study, and the discrepant results beg further investigation. Models including real subjective perceptions with empiric or subjective probabilities can provide insight into deviations from expected rational behavior and suggest interventions in order to provide better population outcomes.

A computational approach to characterizing the impact of social influence on individuals' vaccination decision making

In modeling individuals vaccination decision making, existing studies have typically used the payoff-based (e.g., game-theoretical) approaches that evaluate the risks and benefits of vaccination. In reality, whether an individual takes vaccine or not is also influenced by the decisions of others, i.e., due to the impact of social influence. In this regard, we present a dual-perspective view on individuals decision making that incorporates both the cost analysis of vaccination and the impact of social influence. In doing so, we consider a group of individuals making their vaccination decisions by both minimizing the associated costs and evaluating the decisions of others. We apply social impact theory (SIT) to characterize the impact of social influence with respect to individuals interaction relationships. By doing so, we propose a novel modeling framework that integrates an extended SIT-based characterization of social influence with a game-theoretical analysis of cost minimization. We consider the scenario of voluntary vaccination against an influenza-like disease through a series of simulations. We investigate the steady state of individuals' decision making, and thus, assess the impact of social influence by evaluating the coverage of vaccination for infectious diseases control. Our simulation results suggest that individuals high conformity to social influence will increase the vaccination coverage if the cost of vaccination is low, and conversely, will decrease it if the cost is high. Interestingly, if individuals are social followers, the resulting vaccination coverage would converge to a certain level, depending on individuals' initial level of vaccination willingness rather than the associated costs. We conclude that social influence will have an impact on the control of an infectious disease as they can affect the vaccination coverage. In this respect, our work can provide a means for modeling the impact of social influence as well as for estimating the effectiveness of a voluntary vaccination program.

Policy resistance undermines superspreader vaccination strategies for influenza

Theoretical models of infection spread on networks predict that targeting vaccination at individuals with a very large number of contacts (superspreaders) can reduce infection incidence by a significant margin. These models generally assume that superspreaders will always agree to be vaccinated. Hence, they cannot capture unintended consequences such as policy resistance, where the behavioral response induced by a new vaccine policy tends to reduce the expected benefits of the policy. Here, we couple a model of influenza transmission on an empirically-based contact network with a psychologically structured model of influenza vaccinating behavior, where individual vaccinating decisions depend on social learning and past experiences of perceived infections, vaccine complications and vaccine failures. We find that policy resistance almost completely undermines the effectiveness of superspreader strategies: the most commonly explored approaches that target a randomly chosen neighbor of an individual, or that preferentially choose neighbors with many contacts, provide at best a 2% relative improvement over their non-targeted counterpart as compared to 12% when behavioral feedbacks are ignored. Increased vaccine coverage in super spreaders is offset by decreased coverage in non-superspreaders, and superspreaders also have a higher rate of perceived vaccine failures on account of being infected more often. Including incentives for vaccination provides modest improvements in outcomes. We conclude that the design of influenza vaccine strategies involving widespread incentive use and/or targeting of superspreaders should account for policy resistance, and mitigate it whenever possible.

Behavioral Epidemiology of Infectious Diseases: An Overview

The focus of the growing discipline of behavioral epidemiology (BE) of infectious diseases is on individual behavior as a key determinant of infection trajectories. This overview departs from the central, but static, role of human behavior in traditional mathematical models of infection to motivate the importance of including behavior into epidemiological models. Our aim is threefold. First, we attempt to motivate the historical and cultural background underpinning the BE revolution, focusing on the issue of rational opposition to vaccines as a natural endpoint of the changed relation between man and disease in modern industrialized countries. Second, we review those contributions, from both mathematical epidemiology and economics, that forerun the current “epidemic” of studies on BE. Last, we offer a more detailed overview of the current epidemic phase of BE studies and, still motivated by the issue of immunization choices, introduce some baseline ideas and models.

Impact of committed individuals on vaccination behavior

We study how the presence of committed vaccinators, a small fraction of individuals who consistently hold the vaccinating strategy and are immune to influence, impact the vaccination dynamics in well-mixed and spatially structured populations. For this purpose, we develop an epidemiological game-theoretic model of a flu-like vaccination by integrating an epidemiological process into a simple agent-based model of adaptive learning, where individuals (except for those committed ones) use anecdotal evidence to estimate costs and benefits of vaccination. We show that the committed vaccinators, acting as "steadfast role models" in the populations, can efficiently avoid the clustering of susceptible individuals and stimulate other imitators to take vaccination, hence contributing to the promotion of vaccine uptake. We substantiate our findings by making comparative studies of our model on a full lattice and on a randomly diluted one. Our work is expected to provide valuable information for decision-making and design more effective disease-control strategy.

Epidemic spreading with information-driven vaccination

Epidemic spreading has been well studied in the past decade, where the main concentration is focused on the influence of network topology but little attention is paid to the individual's crisis awareness. We here study how the crisis awareness, i.e., personal self-protection, influences the epidemic spreading by presenting a susceptible-infected-recovered model with information-driven vaccination. We introduce two parameters to quantitatively characterize the crisis awareness. One is the information creation rate λ and the other is the information sensitivity η. We find that the epidemic spreading can be significantly suppressed in both the homogeneous and heterogeneous networks when both λ and η are relatively large. More interesting is that the needed vaccine will be significantly reduced when the information is well spread, which is a good news for the poor countries and regions with limited resources.

Universal fungal vaccines: could there be light at the end of the tunnel?

The complex nature of fungal pathogens, the intricate host-pathogen relationship and the health status of subjects in need of antifungal vaccination continue to hamper efforts to develop fungal vaccines for clinical use. That said, the rise of the universal vaccine concept is hoped to revive fungal vaccine research by expanding the pool of vaccine candidates worthy of clinical evaluation. It can do so through antigenic commonality-based screening for vaccine candidates from a wide range of pathogens and by reassessing the sizable collection of already available experimental and approved vaccines. Development of experimental vaccines protective against multiple fungal pathogens is evidence of the utility of this concept in fungal vaccine research. However, universal fungal vaccines are not without difficulties; for instance, development of vaccines with differential effectiveness is an issue that should be addressed. Additionally, rationalizing the development of universal fungal vaccines on health or economic basis could be contentious. Herein, universal fungal vaccines are discussed in terms of their potential usefulness and possible drawbacks.