Imitation dynamics of vaccination behaviour on social networks

Accounting for farmers' control decisions in a model of pathogen spread through animal trade

Accounting for individual decisions in mechanistic epidemiological models remains a challenge, especially for unregulated endemic animal diseases for which control is not compulsory. We propose a new integrative model by combining two sub-models. The first one for the dynamics of a livestock epidemic on a metapopulation network, grounded on demographic and animal trade data. The second one for farmers' behavior regarding the adoption of a control measure against the disease spread in their herd. The measure is specified as a protective vaccine with given economic implications, and the model is numerically studied through intensive simulations and sensitivity analyses. While each tested parameter of the model has an impact on the overall model behavior, the most important factor in farmers' decisions is their frequency, as this factor explained almost 30% of the variation in decision-related outputs of the model. Indeed, updating frequently local health information impacts positively vaccination, and limits strongly the propagation of the pathogen. Our study is relevant for the understanding of the interplay between decision-related human behavior and livestock epidemic dynamics. The model can be used for other structures of epidemic models or different interventions, by adapting its components.

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.

Noncompliance With Safety Guidelines as a Free-Riding Strategy: An Evolutionary Game-Theoretic Approach to Cooperation During the COVID-19 Pandemic

Evolutionary game theory and public goods games offer an important framework to understand cooperation during pandemics. From this perspective, the COVID-19 situation can be conceptualized as a dilemma where people who neglect safety precautions act as free riders, because they get to enjoy the benefits of decreased health risk from others' compliance with policies despite not contributing to or even undermining public safety themselves. At the same time, humans appear to carry a suite of evolved psychological mechanisms aimed at curbing free riding in order to ensure the continued provision of public goods, which can be leveraged to develop more effective measures to promote compliance with regulations. We also highlight factors beyond free riding that reduce compliance rates, such as the emergence of conspiratorial thinking, which seriously undermine the effectiveness of measures to suppress free riding. Together, the current paper outlines the social dynamics that occur in public goods dilemmas involving the spread of infectious disease, highlights the utility and limits of evolutionary game-theoretic approaches for COVID-19 management, and suggests novel directions based on emerging challenges to cooperation.

A game-theoretical dynamic imitation model on networks

A game-theoretical model is constructed to capture the effect of imitation on the evolution of cooperation. This imitation describes the case where successful individuals are more likely to be imitated by newcomers who will employ their strategies and social networks. Two classical repeated strategies 'always defect (ALLD)' and 'tit-for-tat (TFT)' are adopted. Mathematical analyses are mainly conducted by the method of coalescence theory. Under the assumption of a large population size and weak selection, the results show that the evolution of cooperation is promoted in this dynamic network. As we observed that the critical benefit-to-cost ratio is smaller compared to that in well-mixed populations. The critical benefit-to-cost ratio approaches a specific value which depends on three parameters, the repeated rounds of the game, the effective strategy mutation rate, and the effective link mutation rate. Specifically, for a very high value of the effective link mutation rate, the critical benefit-to-cost ratio approaches 1. Remarkably, for a low value of the effective link mutation rate, by letting the effective strategy mutation is nearly equal to zero, the critical benefit-to-cost ratio approaches [Formula: see text] for the resulting highly connected networks, which allows TFT to be evolutionary stable. It illustrates that dominance of TFTs is associated with more connected networks. This research can enrich the theory of the coevolution of game strategy and network structure with dynamic imitation.

Flexible imitation suppresses epidemics through better vaccination

The decision of whether or not to vaccinate is a complex one. It involves the contribution both to a social good-herd immunity-and to one's own well-being. It is informed by social influence, personal experience, education, and mass media. In our work, we investigate a situation in which individuals make their choice based on how social neighbourhood responded to previous epidemics. We do this by proposing a minimalistic model using components from game theory, network theory and the modelling of epidemic spreading, and opinion dynamics. Individuals can use the information about the neighbourhood in two ways-either they follow the majority or the best-performing neighbour. Furthermore, we let individuals learn which of these two decision-making strategies to follow from their experience. Our results show that the flexibility of individuals to choose how to integrate information from the neighbourhood increases the vaccine uptake and decreases the epidemic severity if the following conditions are fulfilled. First, the initial fraction of individuals who imitate the neighbourhood majority should be limited, and second, the memory of previous outbreaks should be sufficiently long. These results have implications for the acceptance of novel vaccines and raising awareness about vaccination, while also pointing to promising future research directions.

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.

An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics

During pandemic events, strategies such as social distancing can be fundamental to reduce simultaneous infections and mitigate the disease spreading, which is very relevant to the risk of a healthcare system collapse. Although these strategies can be recommended, or even imposed, their actual implementation may depend on the population perception of the risks associated with a potential infection. The current COVID-19 crisis, for instance, is showing that some individuals are much more prone than others to remain isolated. To better understand these dynamics, we propose an epidemiological SIR model that uses evolutionary game theory for combining in a single process social strategies, individual risk perception, and viral spreading. In particular, we consider a disease spreading through a population, whose agents can choose between self-isolation and a lifestyle careless of any epidemic risk. The strategy adoption is individual and depends on the perceived disease risk compared to the quarantine cost. The game payoff governs the strategy adoption, while the epidemic process governs the agent's health state. At the same time, the infection rate depends on the agent's strategy while the perceived disease risk depends on the fraction of infected agents. Our results show recurrent infection waves, which are usually seen in previous historic epidemic scenarios with voluntary quarantine. In particular, such waves re-occur as the population reduces disease awareness. Notably, the risk perception is found to be fundamental for controlling the magnitude of the infection peak, while the final infection size is mainly dictated by the infection rates. Low awareness leads to a single and strong infection peak, while a greater disease risk leads to shorter, although more frequent, peaks. The proposed model spontaneously captures relevant aspects of a pandemic event, highlighting the fundamental role of social strategies.

SIR Dynamics with Vaccination in a Large Configuration Model

We consider an SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of optimal controls for the limiting equations formulated in the framework of game theory, both in the centralized and decentralized setting. We show how the characteristics of the graph (degree distribution) influence the vaccination efficiency for optimal strategies, and we compute the limiting final size of the epidemic depending on the degree distribution of the graph and the parameters of infection, recovery and vaccination. We also present several simulations for two types of vaccination, showing how the optimal controls allow to decrease the number of infections and underlining the crucial role of the network characteristics in the propagation of the disease and the vaccination program.

Economic and Behavioral Influencers of Vaccination and Antimicrobial Use

Despite vast improvements in global vaccination coverage during the last decade, there is a growing trend in vaccine hesitancy and/or refusal globally. This has implications for the acceptance and coverage of a potential vaccine against COVID-19. In the United States, the number of children exempt from vaccination for “philosophical belief-based” non-medical reasons increased in 12 of the 18 states that allowed this policy from 2009 to 2017 (1). Meanwhile, the overuse and misuse of antibiotics, especially in young children, have led to increasing rates of drug resistance that threaten our ability to treat infectious diseases. Vaccine hesitancy and antibiotic overuse exist side-by-side in the same population of young children, and it is unclear why one modality (antibiotics) is universally seen as safe and effective, while the other (vaccines) is seen as potentially hazardous by some. In this review, we consider the drivers shaping the use of vaccines and antibiotics in the context of three factors: individual incentives, risk perceptions, and social norms and group dynamics. We illustrate how these factors contribute to the societal and individual costs of vaccine underuse and antimicrobial overuse. Ultimately, we seek to understand these factors that are at the nexus of infectious disease epidemiology and social science to inform policy-making.

Game theoretic modelling of infectious disease dynamics and intervention methods: a review

We review research studies which use game theory to model the decision-making of individuals during an epidemic, attempting to classify the literature and identify the emerging trends in this field. The literature is classified based on (i) type of population modelling (classical or network-based), (ii) frequency of the game (non-repeated or repeated), and (iii) type of strategy adoption (self-learning or imitation). The choice of model is shown to depend on many factors such as the immunity to the disease, the strength of immunity conferred by the vaccine, the size of population and the level of mixing therein. We highlight that while early studies used classical compartmental modelling with self-learning games, in recent years, there is a substantial growth of network-based modelling with imitation games. The review indicates that game theory continues to be an effective tool to model decision-making by individuals with respect to intervention (vaccination or social distancing).

Oscillatory dynamics in the dilemma of social distancing

Social distancing as one of the main non-pharmaceutical interventions can help slow down the spread of diseases, like in the COVID-19 pandemic. Effective social distancing, unless enforced as drastic lockdowns and mandatory cordon sanitaire, requires consistent strict collective adherence. However, it remains unknown what the determinants for the resultant compliance of social distancing and their impact on disease mitigation are. Here, we incorporate into the epidemiological process with an evolutionary game theory model that governs the evolution of social distancing behaviour. In our model, we assume an individual acts in their best interest and their decisions are driven by adaptive social learning of the real-time risk of infection in comparison with the cost of social distancing. We find interesting oscillatory dynamics of social distancing accompanied with waves of infection. Moreover, the oscillatory dynamics are dampened with a non-trivial dependence on model parameters governing decision-makings and gradually cease when the cumulative infections exceed the herd immunity. Compared to the scenario without social distancing, we quantify the degree to which social distancing mitigates the epidemic and its dependence on individuals' responsiveness and rationality in their behaviour changes. Our work offers new insights into leveraging human behaviour in support of pandemic response.

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.

Vaccinating SIS epidemics under evolving perception in heterogeneous networks

ABSTRACT

Vaccination is an effective intervention against epidemics. Previous work has demonstrated that psychological cognition affects individual behavior. However, perceptual differences between individuals, as well as the dynamics of perceptual evolution, are not taken into account. In order to explore how these realistic characteristics of psychological cognition influence collective vaccination behavior, we propose a prospect theory based evolutionary vaccination game model, where the evolution of reference points is used to characterize changes in perception. We compare the fractions of vaccinated individuals and infected individuals under variable reference points with those under the expected utility theory and the fixed reference point, and highlight the role of evolving perception in promoting vaccination and contributing to epidemic control. We find that the epidemic size under variable reference point is always less than that under the expected utility theory. Finding that there exists a vaccination cost threshold for the cognitive effect, we develop a novel mixed-reference-point mechanism by combining individual psychological characteristics with network topological feature. The effectiveness of this mechanism in controlling the network epidemics is verified with numerical simulations. Compared with pure reference points, the mixed-reference-point mechanism can effectively reduce the final epidemic size, especially at a large vaccination cost.

Social efficiency deficit deciphers social dilemmas

What do corruption, resource overexploitation, climate inaction, vaccine hesitancy, traffic congestion, and even cancer metastasis have in common? All these socioeconomic and sociobiological phenomena are known as social dilemmas because they embody in one form or another a fundamental conflict between immediate self-interest and long-term collective interest. A shortcut to the resolution of social dilemmas has thus far been reserved solely for highly stylised cases reducible to dyadic games (e.g., the Prisoner’s Dilemma), whose nature and outcome coalesce in the concept of dilemma strength. We show that a social efficiency deficit, measuring an actor’s potential gain in utility or fitness by switching from an evolutionary equilibrium to a social optimum, generalises dilemma strength irrespective of the underlying social dilemma’s complexity. We progressively build from the simplicity of dyadic games for which the social efficiency deficit and dilemma strength are mathematical duals, to the complexity of carcinogenesis and a vaccination dilemma for which only the social efficiency deficit is numerically calculable. The results send a clear message to policymakers to enact measures that increase the social efficiency deficit until the strain between what is and what could be incentivises society to switch to a more desirable state.

The Singaporean model in public goods dilemmas with benevolent leaders and bribery

Public goods dilemmas are at the heart of some of the greatest challenges of our time, including climate inaction, growing inequality, and the overuse of natural resources. The public goods game in which cooperators contribute to a common pool that is then shared equally with defectors who contribute nothing captures the gist of the problem. Cooperators therefore cannot prevail, which ultimately leads to the tragedy of the commons. Actions such as punishment, rewards, and exclusion have been shown to help, but they are costly, therefore rendering cooperators second-order free-riders due to their lack of participation in these actions. In the search for a remedy, we study the public goods game with benevolent leaders who, at a personal cost, have the ability to exclude defectors from using common pool resources. We also consider bribers who can pay the leaders to relax their exclusion efforts. In a traditional setting, this setup yields the standard second-order free-rider problem, where, ironically, the leaders are overcome by cooperators, who then themselves succumb to defectors. We show, however, that the Singaporean model - where a leader's payoff is determined not only by the regular sharing income from the firm production but also by the success of gross firm production as an incentive - can resolve the second-order free-rider problem. We also show that the detrimental effect of bribery can always be, no matter how high the bribe, held in check as long as the number of individuals engaged in this activity is low compared to the number of benevolent leaders. Otherwise, an abrupt transition to a cooperator-less state becomes unavoidable. We discuss the implications of our research for designing successful cooperation and anti-corruption strategies in public goods dilemmas.

Design and Feasibility Study of the Mobile Application StopTheSpread

The emergence of recent disease outbreaks calls for the design of new educational games aimed at increasing awareness in disease prevention. This article presents StopTheSpread, an educational mobile application that seeks to improve awareness about the best practices to prevent the spreading of seasonal flu in the general public. StopTheSpread integrates concepts in network science and epidemiology, within a freely available mobile application that provides a unique learning experience for free-choice learners about flu prevention. StopTheSpread teaches users basic concepts about flu prevention, within a series of games of increasing difficulty that maintain user engagement and offers a user-friendly design. StopTheSpread provides a summary of the best practices to prevent flu spreading according to the guidelines of the Centers for Disease Control and Prevention, and the World Health Organization, while connecting users to citizen science projects aimed at worldwide flu tracking. Through Facebook, Twitter, and email we reached volunteers during the COVID-19 confinement, to conduct an online feasibility study, toward assessing learning outcome in playing with our mobile application. Our results indicate that the use of StopTheSpread increased by 20% the awareness about the spreading mechanism of flu, compared with the baseline population.

High endemic levels of typhoid fever in rural areas of Ghana may stem from optimal voluntary vaccination behaviour

Typhoid fever has long established itself endemically in rural Ghana despite the availability of cheap and effective vaccines. We used a game-theoretic model to investigate whether the low vaccination coverage in Ghana could be attributed to rational human behaviour. We adopted a version of an epidemiological model of typhoid fever dynamics, which accounted not only for chronic life-long carriers but also for a short-cycle transmission in the immediate environment and a long-cycle transmission via contamination of the water supply. We calibrated the model parameters based on the known incidence data. We found that unless the (perceived) cost of vaccination is negligible, the individually optimal population vaccination rate falls significantly short of the societally optimal population vaccination rate needed to reach herd immunity. We expressed both the herd immunity and the optimal equilibrium vaccination rates in terms of only a few observable parameters such as the incidence rate, demographics, vaccine waning rate and the perceived cost of vaccination relative to the cost of infection. This allowed us not to rely on other uncertain epidemiological model parameters and, in particular, to bypass uncertainties about the role of the carriers in the transmission.

Optimal public health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period

Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to 'pseudo-rational' behaviours: parents overweigh real and imaginary side effects of vaccines. Nonetheless, the 'Public Health System' (PHS) may enact public campaigns to favour vaccine uptake. To determine the optimal time profiles for such campaigns, we apply the optimal control theory to an extension of the susceptible-infectious-removed (SIR)-based behavioural vaccination model by d'Onofrio et al. (2012, PLoS ONE, 7, e45653). The new model is of susceptible-exposed-infectious-removed (SEIR) type under seasonal fluctuations of the transmission rate. Our objective is to minimize the total costs of the disease: the disease burden, the vaccination costs and a less usual cost: the economic burden to enact the PHS campaigns. We apply the Pontryagin minimum principle and numerically explore the impact of seasonality, human behaviour and latency rate on the control and spread of the target disease. We focus on two noteworthy case studies: the low (resp. intermediate) relative perceived risk of vaccine side effects and relatively low (resp. very low) speed of imitation. One general result is that seasonality may produce a remarkable impact on PHS campaigns aimed at controlling, via an increase of the vaccination uptake, the spread of a target infectious disease. In particular, a higher amplitude of the seasonal variation produces a higher effort and this, in turn, beneficially impacts the induced vaccine uptake since the larger is the strength of seasonality, the longer the vaccine propensity remains large. However, such increased effort is not able to fully compensate the action of seasonality on the prevalence.

Decisions and disease: a mechanism for the evolution of cooperation

In numerous contexts, individuals may decide whether they take actions to mitigate the spread of disease, or not. Mitigating the spread of disease requires an individual to change their routine behaviours to benefit others, resulting in a 'disease dilemma' similar to the seminal prisoner's dilemma. In the classical prisoner's dilemma, evolutionary game dynamics predict that all individuals evolve to 'defect.' We have discovered that when the rate of cooperation within a population is directly linked to the rate of spread of the disease, cooperation evolves under certain conditions. For diseases which do not confer immunity to recovered individuals, if the time scale at which individuals receive accurate information regarding the disease is sufficiently rapid compared to the time scale at which the disease spreads, then cooperation emerges. Moreover, in the limit as mitigation measures become increasingly effective, the disease can be controlled; the number of infections tends to zero. It has been suggested that disease spreading models may also describe social and group dynamics, indicating that this mechanism for the evolution of cooperation may also apply in those contexts.

Vaccinating behaviour guided by imitation and aspiration

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

The Impact of Pre-exposure Prophylaxis for Human Immunodeficiency Virus on Gonorrhea Prevalence

Pre-exposure prophylaxis (PrEP) has been shown to be highly effective in reducing the risk of HIV infection in gay and bisexual men who have sex with men (GbMSM). However, PrEP does not protect against other sexually transmitted infections (STIs). In some populations, PrEP has also led to riskier behavior such as reduced condom usage, with the result that the prevalence of bacterial STIs like gonorrhea has increased. Here, we develop a compartmental model of the transmission of HIV and gonorrhea and the impacts of PrEP, condom usage, STI testing frequency and potential changes in sexual risk behavior stemming from the introduction of PrEP in a population of GbMSM. We find that introducing PrEP causes an increase in gonorrhea prevalence for a wide range of parameter values, including at the currently recommended frequency of STI testing once every three months for individuals on PrEP. Moreover, the model predicts that a higher STI testing frequency alone is not enough to prevent a rise in gonorrhea prevalence, unless the testing frequency is increased to impractical levels. However, testing every 2 months in combination with a 10-25 % reduction in risky behavior by individuals on PrEP would maintain gonorrhea prevalence at pre-PrEP levels. The results emphasize that programs making PrEP more available should be accompanied by efforts to support condom usage and frequent STI testing, in order to avoid an increase in the prevalence of gonorrhea and other bacterial STIs.

Modelling anti-vaccine sentiment as a cultural pathogen

Culturally transmitted traits that have deleterious effects on health-related traits can be regarded as cultural pathogens. A cultural pathogen can produce coupled dynamics with its associated health-related traits, so that understanding the dynamics of a health-related trait benefits from consideration of the dynamics of the associated cultural pathogen. Here, we treat anti-vaccine sentiment as a cultural pathogen, modelling its 'infection' dynamics with the infection dynamics of the associated vaccine-preventable disease. In a coupled susceptible-infected-resistant (SIR) model, consisting of an SIR model for the anti-vaccine sentiment and an interacting SIR model for the infectious disease, we explore the effect of anti-vaccine sentiment on disease dynamics. We find that disease endemism is contingent on the presence of the sentiment, and that presence of sentiment can enable diseases to become endemic when they would otherwise have disappeared. Furthermore, the sentiment dynamics can create situations in which the disease suddenly returns after a long period of dormancy. We study the effect of assortative sentiment-based interactions on the dynamics of sentiment and disease, identifying a tradeoff whereby assortative meeting aids the spread of a disease but hinders the spread of sentiment. Our results can contribute to finding strategies that reduce the impact of a cultural pathogen on disease, illuminating the value of cultural evolutionary modelling in the analysis of disease dynamics.

A game-theoretical analysis of poliomyelitis vaccination

Poliomyelitis is a worldwide disease that has nearly been eradicated thanks to the Global Polio Eradication Initiative. Nevertheless, the disease is currently still endemic in three countries. In this paper, we incorporate the vaccination in a two age-class model of polio dynamics. Our main objective is to see whether mandatory vaccination policy is needed or if polio could be almost eradicated by a voluntary vaccination. We perform game theoretical analysis and compare the herd immunity vaccination levels with the Nash equilibrium vaccination levels. We show that the gap between two vaccination levels is too large. We conclude that the mandatory vaccination policy is therefore needed to achieve a complete eradication.

Cooperation on Interdependent Networks by Means of Migration and Stochastic Imitation

Evolutionary game theory in the realm of network science appeals to a lot of research communities, as it constitutes a popular theoretical framework for studying the evolution of cooperation in social dilemmas. Recent research has shown that cooperation is markedly more resistant in interdependent networks, where traditional network reciprocity can be further enhanced due to various forms of interdependence between different network layers. However, the role of mobility in interdependent networks is yet to gain its well-deserved attention. Here we consider an interdependent network model, where individuals in each layer follow different evolutionary games, and where each player is considered as a mobile agent that can move locally inside its own layer to improve its fitness. Probabilistically, we also consider an imitation possibility from a neighbor on the other layer. We show that, by considering migration and stochastic imitation, further fascinating gateways to cooperation on interdependent networks can be observed. Notably, cooperation can be promoted on both layers, even if cooperation without interdependence would be improbable on one of the layers due to adverse conditions. Our results provide a rationale for engineering better social systems at the interface of networks and human decision making under testing dilemmas.

Misinformation making a disease outbreak worse: outcomes compared for influenza, monkeypox, and norovirus

Health misinformation can exacerbate infectious disease outbreaks. Especially pernicious advice could be classified as "fake news": manufactured with no respect for accuracy and often integrated with emotive or conspiracy-framed narratives. We built an agent-based model that simulated separate but linked circulating contagious disease and sharing of health advice (classified as useful or harmful). Such advice has potential to influence human risk-taking behavior and therefore the risk of acquiring infection, especially as people are more likely in observed social networks to share bad advice. We test strategies proposed in the recent literature for countering misinformation. Reducing harmful advice from 50% to 40% of circulating information, or making at least 20% of the population unable to share or believe harmful advice, mitigated the influence of bad advice in the disease outbreak outcomes. How feasible it is to try to make people "immune" to misinformation or control spread of harmful advice should be explored.

The Impact of School and After-School Friendship Networks on Adolescent Vaccination Behavior

Psychological and social characteristics of individuals are important determinants of their health choices and behaviors. Social networks represent "pipes" through which information and opinions circulate and spread out in the social circle surrounding individuals, influencing their propensity toward important health care interventions. This paper aims to explore the relationship between students' vaccination health choices and their social networks. We administered a questionnaire to students to collect data on individual students' demographics, knowledge, and attitudes about vaccinations, as well as their social networks. Forty-nine pupils belonging to 4 classrooms in an Italian secondary school were enrolled in the study. We applied a logistic regression quadratic assignment procedure (LR-QAP) by regressing students' positive responsive behavior similarity as a dependent variable. LRQAP findings indicate that students' vaccination behavior similarity is significantly associated with after-school social ties and related social mechanisms, suggesting that pupils are more likely to share information and knowledge about health behaviors through social relationships maintained after school hours rather than through those established during the school day. Moreover, we found that vaccination behaviors are more similar for those students having the same ethnicity as well as for those belonging to the same class. Our findings may help policymakers in implementing effective vaccination strategies.

Role of vaccine efficacy in the vaccination behavior under myopic update rule on complex networks

How to effectively prevent the diffusion of infectious disease has become an intriguing topic in the field of public hygienics. To be noted that, for the non-periodic infectious diseases, many people hope to obtain the vaccine of epidemics in time to be inoculated, rather than at the end of the epidemic. However, the vaccine may fail as a result of invalid storage, transportation and usage, and then vaccinated individuals may become re-susceptible and be infected again during the outbreak. To this end, we build a new framework that considers the imperfect vaccination during the one cycle of infectious disease within the spatially structured and heterogeneous population. Meanwhile, we propose a new vaccination update rule: myopic update rule, which is only based on one focal player's own perception regarding the disease outbreak, and one susceptible individual makes a decision to adopt the vaccine just by comparing the perceived payoffs vaccination with the perceived ones of being infected. Extensive Monte-Carlo simulations are performed to demonstrate the imperfect vaccination behavior under the myopic update rule in the spatially structured and heterogeneous population. The results indicate that healthy individuals are often willing to inoculate the vaccine under the myopic update rule, which can stop the infectious disease from being spread, in particular, it is found that the vaccine efficacy influences the fraction of vaccinated individuals much more than the relative cost of vaccination on the regular lattice, Meanwhile, vaccine efficacy is more sensitive on the heterogeneous scale-free network. Current results are helpful to further analyze and model the choice of vaccination strategy during the disease outbreaks.

Behavioral incentives in a vaccination-dilemma setting with optional treatment

Social dilemmas are situations wherein individuals choose between selfish interest and common good. One example of this is the vaccination dilemma, in which an individual who vaccinates at a cost protects not only himself but also others by helping maintain a common good called herd immunity. There is, however, a strong incentive to forgo vaccination, thus avoiding the associated cost, all the while enjoying the protection of herd immunity. To analyze behavioral incentives in a vaccination-dilemma setting in which an optional treatment is available to infected individuals, we combined epidemiological and game-theoretic methodologies by coupling a disease-spreading model with treatment and an evolutionary decision-making model. Extensive numerical simulations show that vaccine characteristics are more important in controlling the treatment adoption than the cost of treatment itself. The main effect of the latter is that expensive treatment incentivizes vaccination, which somewhat surprisingly comes at a little cost to society. More surprising is that the margin for a true synergy between vaccine and treatment in reducing the final epidemic size is very small. We furthermore find that society-centered decision making helps protect herd immunity relative to individual-centered decision making, but the latter may be better in establishing a novel vaccine. These results point to useful policy recommendations as well as to intriguing future research directions.

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.

A single 'weight-lifting' game covers all kinds of games

Game theory has been studied extensively to answer why cooperation is promoted in human and animal societies. All games are classified into five games: the Prisoner's Dilemma, chicken game (including hawk-dove game), stag hunt game and two trivial games of either all cooperation or all defect, which are studied separately. Here, we propose a new game that covers all five game categories: the weight-lifting game. The player choose either to (1) carry a weight (cooperate: pay a cost) or (2) pretend to carry it (defect: pay no cost). The probability of success in carrying the weight depends on the number of cooperators, and the players either gain the success reward or pay the failure penalty. All five game categories appear in this game depending on the success probabilities for the number of cooperators. We prove that this game is exactly equivalent to the combination of all five games in terms of a pay-off matrix. This game thus provides a unified framework for studying all five types of games.

Epidemic spreading with awareness and different timescales in multiplex networks

One of the major issues in theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thompson rumor model. Flexibility on the timescale between information and disease spreading is also included. We verify that the velocity characterizing the diffusion of information awareness greatly influences the disease prevalence. We also show that a reduction in the fraction of unaware individuals does not always imply a decrease of the prevalence, as the relative timescale between disease and awareness spreading plays a crucial role in the systems' dynamics. This result is shown to be independent of the network topology. We finally calculate the epidemic threshold of our model, and show that it does not depend on the relative timescale. Our results provide a new view on how information influence disease spreading and can be used for the development of more efficient methods for disease control.

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.

The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model

We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered SIR-network model captures a class of vaccination behaviours influenced by epidemic characteristics, interaction topology, and imitation dynamics. Our focus is the resultant vaccination coverage, produced under voluntary vaccination schemes, in response to these varying factors. Using the next generation matrix method, we analytically derive and compare expressions for the basic reproduction number R 0 for the proposed SIR-network models. Furthermore, we simulate the epidemic dynamics over time for the considered models, and show that if individuals are sufficiently responsive towards the changes in the disease prevalence, then the more expansive travelling patterns encourage convergence to the endemic, mixed equilibria. On the contrary, if individuals are insensitive to changes in the disease prevalence, we find that they tend to remain unvaccinated. Our results concur with earlier studies in showing that residents from highly connected residential areas are more likely to get vaccinated. We also show that the existence of the individuals committed to receiving vaccination reduces R 0 and delays the disease prevalence, and thus is essential to containing epidemics.

Epidemic prevalence information on social networks can mediate emergent collective outcomes in voluntary vaccine schemes

The effectiveness of a mass vaccination program can engender its own undoing if individuals choose to not get vaccinated believing that they are already protected by herd immunity. This would appear to be the optimal decision for an individual, based on a strategic appraisal of her costs and benefits, even though she would be vulnerable during subsequent outbreaks if the majority of the population argues in this manner. We investigate how voluntary vaccination can nevertheless emerge in a social network of rational agents, who make informed decisions whether to be vaccinated, integrated with a model of epidemic dynamics. The information available to each agent includes the prevalence of the disease in their local network neighborhood and/or globally in the population, as well as the fraction of their neighbors that are protected against the disease. Crucially, the payoffs governing the decision of agents vary with disease prevalence, resulting in the vaccine uptake behavior changing in response to contagion spreading. The collective behavior of the agents responding to local prevalence can lead to a significant reduction in the final epidemic size, particularly for less contagious diseases having low basic reproduction number [Formula: see text]. Near the epidemic threshold ([Formula: see text]) the use of local prevalence information can result in divergent responses in the final vaccine coverage. Our results suggest that heterogeneity in the risk perception resulting from the spatio-temporal evolution of an epidemic differentially affects agents' payoffs, which is a critical determinant of the success of voluntary vaccination schemes.

The impact of rare but severe vaccine adverse events on behaviour-disease dynamics: a network model

The propagation of rumours about rare but severe adverse vaccination or infection events through social networks can strongly impact vaccination uptake. Here we model a coupled behaviour-disease system where individual risk perception regarding vaccines and infection are shaped by their personal experiences and the experiences of others. Information about vaccines and infection either propagates through the network or becomes available through globally available sources. Dynamics are studied on a range of network types. Individuals choose to vaccinate according to their personal perception of risk and information about infection prevalence. We study events ranging from common and mild, to severe and rare. We find that vaccine and infection adverse events have asymmetric impacts. Vaccine (but not infection) adverse events may significantly prolong the tail of an outbreak. Similarly, introducing a small risk of a vaccine adverse event may cause a steep decline in vaccine coverage, especially on scale-free networks. Global dissemination of information about infection prevalence boosts vaccine coverage more than local dissemination. Taken together, these findings highlight the dangers associated with vaccine rumour propagation through scale-free networks such as those exhibited by online social media, as well as the benefits of disseminating public health information through mass media.

Modeling Behavioral Response to Vaccination Using Public Goods Game

Epidemics of infectious disease can be traced back to the early days of mankind. Only in the last two centuries vaccination has become a viable strategy to prevent such epidemics. In addition to the clinical efficacy of this strategy, the behavior and public attitudes affect the success of vaccines. This paper describes modeling the efficacy of vaccination considering the cost and benefit of vaccination to individual players. The model is based on the public goods game and is presented as a spatial game on a lattice. Using this model, individuals can contribute to the public health by paying the cost of vaccination or choose to be protected by the public who is vaccinated rather than pay the cost and share the risk of vaccination. Thus, in this model individuals can choose to stay susceptible, can become infected, or choose to vaccinate once in each episode. This paper presents the behavioral changes of the population and the cost to the society as a function of the cost of vaccines, cost of being infected, and the "fear factor" created by the public media.

Imperfect vaccine and hysteresis

Addressing vaccine compliance problems is of particular relevance and significance to public health. Despite resurgence of vaccine-preventable diseases and public awareness of vaccine importance, why is it so challenging to boost population vaccination coverage to desired levels especially in the wake of declining vaccine uptake? To understand this puzzling phenomenon, here we study how social imitation dynamics of vaccination can be impacted by the presence of imperfect vaccine, which only confers partial protection against the disease. Besides weighing the perceived cost of vaccination with the risk of infection, the effectiveness of vaccination is also an important factor driving vaccination decisions. We discover that there can exist multiple stable vaccination equilibria if vaccine efficacy is below a certain threshold. Furthermore, our bifurcation analysis reveals the occurrence of hysteresis loops of vaccination rate with respect to changes in the perceived vaccination cost as well as in the vaccination effectiveness. Moreover, we find that hysteresis is more likely to arise in spatial populations than in well-mixed populations, even for parameter choices that do not allow for bifurcation in the latter. Our work shows that hysteresis can appear as an unprecedented roadblock for the recovery of vaccination uptake, thereby helping explain the persistence of vaccine compliance problem.

Optimal Control of Heterogeneous Mutating Viruses

Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results.

Interplay between cost and benefits triggers nontrivial vaccination uptake

The containment of epidemic spreading is a major challenge in science. Vaccination, whenever available, is the best way to prevent the spreading, because it eventually immunizes individuals. However, vaccines are not perfect, and total immunization is not guaranteed. Imperfect immunization has driven the emergence of antivaccine movements that totally alter the predictions about the epidemic incidence. Here, we propose a mathematically solvable mean-field vaccination model to mimic the spontaneous adoption of vaccines against influenzalike diseases and the expected epidemic incidence. The results are in agreement with extensive Monte Carlo simulations of the epidemics and vaccination coevolutionary processes. Interestingly, the results reveal a nonmonotonic behavior on the vaccination coverage that increases with the imperfection of the vaccine and after decreases. This apparent counterintuitive behavior is analyzed and understood from stability principles of the proposed mathematical model.

Scaling the phase-planes of social dilemma strengths shows game-class changes in the five rules governing the evolution of cooperation

Game theory has been extensively applied to help explain how cooperative behaviour is promoted in human and animal societies. How do humans and animals establish reciprocity when confronting a social dilemma? In 2006, Nowak theoretically proved that numerous mechanisms and models for evolving cooperative behaviour reported over the last few decades can be distilled into five reciprocity mechanisms (rules). Additionally, universal scaling parameters were proposed to measure two different types of dilemmas, namely, the gamble-intending dilemma (GID) and risk-averting dilemma (RAD). In this work, by drawing a RAD-GID phase-plane diagram for pair-wise games, we prove that these five rules are indeed quite different for the resolution (relaxation) of the two dilemmas. These diagrams also demonstrate whether and when game-class change (resolution of a dilemma) occurs, thus implying how defectors can be eliminated.

Coupling dynamics of epidemic spreading and information diffusion on complex networks

The interaction between disease and disease information on complex networks has facilitated an interdisciplinary research area. When a disease begins to spread in the population, the corresponding information would also be transmitted among individuals, which in turn influence the spreading pattern of the disease. In this paper, firstly, we analyze the propagation of two representative diseases (H7N9 and Dengue fever) in the real-world population and their corresponding information on Internet, suggesting the high correlation of the two-type dynamical processes. Secondly, inspired by empirical analyses, we propose a nonlinear model to further interpret the coupling effect based on the SIS (Susceptible-Infected-Susceptible) model. Both simulation results and theoretical analysis show that a high prevalence of epidemic will lead to a slow information decay, consequently resulting in a high infected level, which shall in turn prevent the epidemic spreading. Finally, further theoretical analysis demonstrates that a multi-outbreak phenomenon emerges via the effect of coupling dynamics, which finds good agreement with empirical results. This work may shed light on the in-depth understanding of the interplay between the dynamics of epidemic spreading and information diffusion.

The impact of individual heterogeneity on the coupled awareness-epidemic dynamics in multiplex networks

Awareness of disease outbreaks can trigger changes in human behavior and has a significant impact on the spread of epidemics. Previous studies usually considered the coupled awareness-epidemic dynamics to be two competing processes that interact in the information and epidemic layers. However, these studies mostly assumed that all aware individuals have the same reduced infectivity and that different neighbors have the same influence on one's perception, ignoring the heterogeneity of individuals. In this paper, we propose a coupled awareness-epidemic spreading model in multiplex networks incorporating three types of heterogeneity: (1) the heterogeneity of individual responses to disease outbreaks, (2) the influence heterogeneity in the epidemic layer, and (3) the influence heterogeneity in the information layer. The theoretical analysis shows that the influence heterogeneity in the information layer has two-stage effects on the epidemic threshold. Moreover, we find that the epidemic threshold in the higher stage depends on the heterogeneity of individual responses and the influence heterogeneity in the epidemic layer, while the epidemic threshold in the lower stage is independent of awareness spreading and individual behaviors. The results give us a better understanding of how individual heterogeneity affects epidemic spreading and provide some practical implications for the control of epidemics.

Changes in political party systems arising from conflict and transfer among political parties

Conflict that arises between two groups of different paradigms is an inevitable phenomenon, and a representative example of the conflict among different groups is a conflict phenomenon caused by competition among political parties. In this paper, we study the dynamical behavior of a political party system. Considering three major political parties, we investigate how political party systems can be changed by employing a mathematical model. By considering the transfer mechanism of recruitment as well as conflict of competition between political parties, we found that all parties are likely to coexist when both the competition and transfer between the parties are weak, or if either mechanism can occur at a relatively low level. Otherwise, a political party system is changed to a single-party system. In addition, we found that when a party system was changed into a single-party system, it appeared to be either bistable or multistable, and has been elucidate by linear stability analysis. Our results may provide insights to understand mechanisms how political party systems can be changed by conflict and transfer.

Increasing Vaccination: Putting Psychological Science Into Action

Vaccination is one of the great achievements of the 20th century, yet persistent public-health problems include inadequate, delayed, and unstable vaccination uptake. Psychology offers three general propositions for understanding and intervening to increase uptake where vaccines are available and affordable. The first proposition is that thoughts and feelings can motivate getting vaccinated. Hundreds of studies have shown that risk beliefs and anticipated regret about infectious disease correlate reliably with getting vaccinated; low confidence in vaccine effectiveness and concern about safety correlate reliably with not getting vaccinated. We were surprised to find that few randomized trials have successfully changed what people think and feel about vaccines, and those few that succeeded were minimally effective in increasing uptake. The second proposition is that social processes can motivate getting vaccinated. Substantial research has shown that social norms are associated with vaccination, but few interventions examined whether normative messages increase vaccination uptake. Many experimental studies have relied on hypothetical scenarios to demonstrate that altruism and free riding (i.e., taking advantage of the protection provided by others) can affect intended behavior, but few randomized trials have tested strategies to change social processes to increase vaccination uptake. The third proposition is that interventions can facilitate vaccination directly by leveraging, but not trying to change, what people think and feel. These interventions are by far the most plentiful and effective in the literature. To increase vaccine uptake, these interventions build on existing favorable intentions by facilitating action (through reminders, prompts, and primes) and reducing barriers (through logistics and healthy defaults); these interventions also shape behavior (through incentives, sanctions, and requirements). Although identification of principles for changing thoughts and feelings to motivate vaccination is a work in progress, psychological principles can now inform the design of systems and policies to directly facilitate action.

Infection prevention behaviour and infectious disease modelling: a review of the literature and recommendations for the future

Background

Given the importance of person to person transmission in the spread of infectious diseases, it is critically important to ensure that human behaviour with respect to infection prevention is appropriately represented within infectious disease models. This paper presents a large scale scoping review regarding the incorporation of infection prevention behaviour in infectious disease models. The outcomes of this review are contextualised within the psychological literature concerning health behaviour and behaviour change, resulting in a series of key recommendations for the incorporation of human behaviour in future infectious disease models.

Methods

The search strategy focused on terms relating to behaviour, infectious disease and mathematical modelling. The selection criteria were developed iteratively to focus on original research articles that present an infectious disease model with human-human spread, in which individuals’ self-protective health behaviour varied endogenously within the model. Data extracted included: the behaviour that is modelled; how this behaviour is modelled; any theoretical background for the modelling of behaviour, and; any behavioural data used to parameterise the models.

Results

Forty-two papers from an initial total of 2987 were retained for inclusion in the final review. All of these papers were published between 2002 and 2015. Many of the included papers employed a multiple, linked models to incorporate infection prevention behaviour. Both cognitive constructs (e.g., perceived risk) and, to a lesser extent, social constructs (e.g., social norms) were identified in the included papers. However, only five papers made explicit reference to psychological health behaviour change theories. Finally, just under half of the included papers incorporated behavioural data in their modelling.

Conclusions

By contextualising the review outcomes within the psychological literature on health behaviour and behaviour change, three key recommendations for future behavioural modelling are made. First, modellers should consult with the psychological literature on health behaviour/ behaviour change when developing new models. Second, modellers interested in exploring the relationship between behaviour and disease spread should draw on social psychological literature to increase the complexity of the social world represented within infectious disease models. Finally, greater use of context-specific behavioural data (e.g., survey data, observational data) is recommended to parameterise models.

Electronic supplementary material

The online version of this article (10.1186/s12889-018-5223-1) contains supplementary material, which is available to authorized users.