A game dynamic model for delayer strategies in vaccinating behaviour for pediatric infectious diseases

A mathematical model of visceral leishmaniasis transmission and control: Impact of ITNs on VL prevention and elimination in the Indian subcontinent

Visceral Leishmaniasis (VL) is a deadly, vector-borne, parasitic, neglected tropical disease, particularly prevalent on the Indian subcontinent. Sleeping under the long-lasting insecticide-treated nets (ITNs) was considered an effective VL prevention and control measures, until KalaNet, a large trial in Nepal and India, did not show enough supporting evidence. In this paper, we adapt a biologically accurate, yet relatively simple compartmental ordinary differential equations (ODE) model of VL transmission and explicitly model the use of ITNs and their role in VL prevention and elimination. We also include a game-theoretic analysis in order to determine an optimal use of ITNs from the individuals' perspective. In agreement with the previous more detailed and complex model, we show that the ITNs coverage amongst the susceptible population has to be unrealistically high (over 96%) in order for VL to be eliminated. However, we also show that if the whole population, including symptomatic and asymptomatic VL cases adopt about 90% ITN usage, then VL can be eliminated. Our model also suggests that ITN usage should be accompanied with other interventions such as vector control.

Dynamical vaccination behavior with risk perception and vaccination rewards

Vaccination is the most effective way to control the epidemic spreading. However, the probability of people getting vaccinated changes with the epidemic situation due to personal psychology. Facing various risks, some people are reluctant to vaccinate and even prefer herd immunity. To encourage people to get vaccinated, many countries set up reward mechanisms. In this paper, we propose a disease transmission model combining vaccination behaviors based on the SIR (Susceptible-Infected-Recovered) model and introduce three vaccination mechanisms. We analyze the impact of the infection rate and the recovery rate on the total cost and the epidemic prevalence. Numerical simulations fit with our intuitive feelings. Then, we study the impact of vaccination rewards on the total social cost. We find that when vaccination rewards offset vaccination costs, both the total cost and the epidemic prevalence reach the lowest levels. Finally, this paper suggests that encouraging people to get vaccinated at the beginning of an epidemic has the best effect.

Parameter estimation in behavioral epidemic models with endogenous societal risk-response

Behavioral epidemic models incorporating endogenous societal risk-response, where changes in risk perceptions prompt adjustments in contact rates, are crucial for predicting pandemic trajectories. Accurate parameter estimation in these models is vital for validation and precise projections. However, few studies have examined the problem of identifiability in models where disease and behavior parameters must be jointly estimated. To address this gap, we conduct simulation experiments to assess the effect on parameter estimation accuracy of a) delayed risk response, b) neglecting behavioral response in model structure, and c) integrating disease and public behavior data. Our findings reveal systematic biases in estimating behavior parameters even with comprehensive and accurate disease data and a well-structured simulation model when data are limited to the first wave. This is due to the significant delay between evolving risks and societal reactions, corresponding to the duration of a pandemic wave. Moreover, we demonstrate that conventional SEIR models, which disregard behavioral changes, may fit well in the early stages of a pandemic but exhibit significant errors after the initial peak. Furthermore, early on, relatively small data samples of public behavior, such as mobility, can significantly improve estimation accuracy. However, the marginal benefits decline as the pandemic progresses. These results highlight the challenges associated with the joint estimation of disease and behavior parameters in a behavioral epidemic model.

Modeling the "F" in "SAFE": The dynamic game of facial cleanliness in trachoma prevention

Trachoma, a neglected tropical disease (NTDs) caused by bacterium Chlamydia trachomatis, is a leading cause of infectious blindness. Efforts are underway to eliminate trachoma as a public health problem by using the "SAFE" strategy. While mathematical models are now standard tools used to support elimination efforts and there are a variety of models studying different aspects of trachoma transmission dynamics, the "F" component of the strategy corresponding to facial cleanliness has received very little attention so far. In this paper, we incorporate human behavior into a standard epidemiological model and develop a dynamical game during which individuals practice facial cleanliness based on their epidemiological status and perceived benefits and costs. We found that the number of infectious individuals generally increases with the difficulty to access a water source. However, this increase happens only during three transition periods and the prevalence stays constant otherwise. Consequently, improving access to water can help eliminate trachoma, but the improvement needs to be significant enough to cross at least one of the three transition thresholds; otherwise the improved access will have no noticeable effect.

Social divisions and risk perception drive divergent epidemics and large later waves

During infectious disease outbreaks, individuals may adopt protective measures like vaccination and physical distancing in response to awareness of disease burden. Prior work showed how feedbacks between epidemic intensity and awareness-based behaviour shape disease dynamics. These models often overlook social divisions, where population subgroups may be disproportionately impacted by a disease and more responsive to the effects of disease within their group. We develop a compartmental model of disease transmission and awareness-based protective behaviour in a population split into two groups to explore the impacts of awareness separation (relatively greater in- vs. out-group awareness of epidemic severity) and mixing separation (relatively greater in- vs. out-group contact rates). Using simulations, we show that groups that are more separated in awareness have smaller differences in mortality. Fatigue (i.e. abandonment of protective measures over time) can drive additional infection waves that can even exceed the size of the initial wave, particularly if uniform awareness drives early protection in one group, leaving that group largely susceptible to future infection. Counterintuitively, vaccine or infection-acquired immunity that is more protective against transmission and mortality may indirectly lead to more infections by reducing perceived risk of infection and therefore vaccine uptake. Awareness-based protective behaviour, including awareness separation, can fundamentally alter disease dynamics. Social media summary: Depending on group division, behaviour based on perceived risk can change epidemic dynamics & produce large later waves.

An evolutionary game model of individual choices and bed net use: elucidating key aspect in malaria elimination strategies

Insecticide-treated net (ITN) is the most applicable and cost-effective malaria intervention measure in sub-Saharan Africa and elsewhere. Although ITNs have been widely distributed to malaria-endemic regions in the past, their success has been threatened by misuses (in fishing, agriculture etc.) and decay in ITN efficacy. Decision-making in using the ITNs depends on multiple coevolving factors: malaria prevalence, mosquito density, ITN availability and its efficacy, and other socio-economic determinants. While ITN misuse increases as the efficacy of ITNs declines, high efficacy also impedes proper use due to free-riding. This irrational usage leads to increased malaria prevalence, thereby worsening malaria control efforts. It also remains unclear if the optimum ITN use for malaria elimination can be achieved under such an adaptive social learning process. Here, we incorporate evolutionary game theory into a disease transmission model to demonstrate these behavioural interactions and their impact on malaria prevalence. We show that social optimum usage is a function of transmission potential, ITN efficacy and mosquito demography. Under specific parameter regimes, our model exhibits patterns of ITN usage similar to observed data from parts of Africa. Our study suggests that the provision of financial incentives as prompt feedback to improper ITN use can reduce misuse and contribute positively towards malaria elimination efforts in Africa and elsewhere.

Coevolution of vaccination behavior and perceived vaccination risk can lead to a stag-hunt-like game

Voluntary vaccination is effective to prevent infectious diseases from spreading. Both vaccination behavior and cognition of the vaccination risk play important roles in individual vaccination decision making. However, it is not clear how the coevolution of the two shapes population-wide vaccination behavior. We establish a coupled dynamics of epidemic, vaccination behavior, and perceived vaccination risk with three different time scales. We assume that the increase of vaccination level inhibits the rise of perceived vaccination risk, and the increase of perceived vaccination risk inhibits the rise of vaccination level. It is shown that the resulting vaccination behavior is similar to the stag-hunt game, provided that the basic reproductive ratio is moderate and that the epidemic dynamics evolves sufficiently fast. This is in contrast with the previous view that vaccination is a snowdriftlike game. And we find that epidemic breaks out repeatedly and eventually leads to vaccine scares if these three dynamics evolve on a similar time scale. Furthermore, we propose some ways to promote vaccination behavior, such as controlling side-effect bias and perceived vaccination costs. Our work sheds light on epidemic control via vaccination by taking into account the coevolutionary dynamics of cognition and behavior.

Vaccination games in prevention of infectious diseases with application to COVID-19

Vaccination coverage is crucial for disease prevention and control. An appropriate combination of compulsory vaccination with voluntary vaccination is necessary to achieve the goal of herd immunity for some epidemic diseases such as measles and COVID-19. A mathematical model is proposed that incorporates both compulsory vaccination and voluntary vaccination, where a decision of voluntary vaccination is made on the basis of game evaluation by comparing the expected returns of different strategies. It is shown that the threshold of disease invasion is determined by the reproduction numbers, and an over-response in magnitude or information interval in the dynamic games could induce periodic oscillations from the Hopf bifurcation. The theoretical results are applied to COVID-19 to find out the strategies for protective immune barrier against virus variants.

Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review

This review presents and reviews various solved and open problems in developing, analyzing, and mitigating epidemic spreading processes under human decision-making. We provide a review of a range of epidemic models and explain the pros and cons of different epidemic models. We exhibit the art of coupling between epidemic models and decision models in the existing literature. More specifically, we provide answers to fundamental questions in human decision-making amid epidemics, including what interventions to take to combat the disease, who are decision-makers, and when and how to take interventions, and how to make interventions. Among many decision models, game-theoretic models have become increasingly crucial in modeling human responses or behavior amid epidemics in the last decade. In this review, we motivate the game-theoretic approach to human decision-making amid epidemics. This review provides an overview of the existing literature by developing a multi-dimensional taxonomy, which categorizes existing literature based on multiple dimensions, including (1) types of games, such as differential games, stochastic games, evolutionary games, and static games; (2) types of interventions, such as social distancing, vaccination, quarantine, and taking antidotes; (3) the types of decision-makers, such as individuals, adversaries, and central authorities at different hierarchical levels. A fine-grained dynamic game framework is proposed to capture the essence of game-theoretic decision-making amid epidemics. We showcase three representative frameworks with unique ways of integrating game-theoretic decision-making into the epidemic models from a vast body of literature. Each of the three frameworks has their unique way of modeling and analyzing and develops results from different angles. In the end, we identify several main open problems and research gaps left to be addressed and filled.

The effect of human vaccination behaviour on strain competition in an infectious disease: An imitation dynamic approach

Strain competition plays an important role in shaping the dynamics of multiple pathogen outbreaks in a population. Competition may lead to exclusion of some pathogens, while it may influence the invasion of an emerging mutant in the population. However, little emphasis has been given to understand the influence of human vaccination choice on pathogen competition or strain invasion for vaccine-preventable infectious diseases. Coupling game dynamic framework of vaccination choice and compartmental disease transmission model of two strains, we explore invasion and persistence of a mutant in the population despite having a lower reproduction rate than the resident one. We illustrate that higher perceived strain severity and lower perceived vaccine efficacy are necessary conditions for the persistence of a mutant strain. The numerical simulation also extends these invasion and persistence analyses under asymmetric cross-protective immunity of these strains. We show that the dynamics of this cross-immunity model under human vaccination choices is determined by the interplay of parameters defining the cross-immune response function, perceived risk of infection, and vaccine efficacy, and it can exhibit invasion and persistence of mutant strain, even complete exclusion of resident strain in the regime of sufficiently high perceived risk. We conclude by discussing public health implications of the results, that proper risk communication in public about the severity of the disease is an important task to reduce the chance of mutant invasion. Thus, understanding pathogen competitions under social interactions and choices may be an important component for policymakers for strategic decision-making.

Vaccine uptake and constrained decision making: The case of Covid-19

Policy makers require support in conceptualizing and assessing the impact that vaccination policies can have on the proportion of the population being vaccinated against COVID-19. To this purpose, we propose a behavioural economics-based framework to model vaccination choices. We calibrate our model using up-to-date surveys on people attitudes toward vaccination as well as estimates of COVID-19 infection and mortality rates and vaccine efficacy for the UK population. Our findings show that vaccine campaigns hardly reach herd immunity if the sceptics have real-time information on the proportion of the population being vaccinated and the negationists do not change their attitudes toward vaccination. Based on our results, we discuss the main implications of the model's application in the context of nudging and voluntariness versus mandatory rule-based policies.

Human choice to self-isolate in the face of the COVID-19 pandemic: A game dynamic modelling approach

Non-pharmaceutical interventions (NPIs) involving social-isolation strategies such as self-quarantine (SQ) and social-distancing (SD) are useful in controlling the spread of infections that are transmitted through human-to–human contacts, e.g., respiratory diseases such as COVID-19. In the absence of a safe and effective cure or vaccine during the first ten months of the COVID-19 pandemic, countries around the world implemented these social-isolation strategies and other NPIs to reduce COVID-19 transmission. But, individual and public perception play a crucial role in the success of any social-isolation measure. Thus, in spite of governments’ initiatives to use NPIs to combat COVID-19 in many countries around the world, individual choices rendered social-isolation unsuccessful in some of these countries. This resulted in huge outbreaks that imposed a substantial morbidity, mortality, hospitalization, economic, etc., toll on human lives. In particular, human choices pose serious challenges to public health strategic decision-making in controlling the COVID-19 pandemic. To unravel the impact of this behavioral response to social-isolation on the burden of the COVID-19 pandemic, we develop a model framework that integrates COVID-19 transmission dynamics with a multi-strategy evolutionary game approach of individual decision-making. We use this integrated framework to characterize the evolution of human choices in social-isolation as the disease progresses and public health control measures such as mandatory lockdowns are implemented. Analysis of the model illustrates that SD plays a major role in reducing the burden of the disease compared to SQ. Parameter estimation using COVID-19 incidence data, as well as different lockdown data sets from India, and scenario analysis involving a combination of Voluntary-Mandatory implementation of SQ and SD shows that the effectiveness of this approach depends on the type of isolation, and the time and period of implementation of the selected isolation measure during the outbreak.

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).

The Prediction of Infectious Diseases: A Bibliometric Analysis

OBJECTIVE

The outbreak of infectious diseases has a negative influence on public health and the economy. The prediction of infectious diseases can effectively control large-scale outbreaks and reduce transmission of epidemics in rapid response to serious public health events. Therefore, experts and scholars are increasingly concerned with the prediction of infectious diseases. However, a knowledge mapping analysis of literature regarding the prediction of infectious diseases using rigorous bibliometric tools, which are supposed to offer further knowledge structure and distribution, has been conducted infrequently. Therefore, we implement a bibliometric analysis about the prediction of infectious diseases to objectively analyze the current status and research hotspots, in order to provide a reference for related researchers.

METHODS

We viewed "infectious disease*" and "prediction" or "forecasting" as search theme in the core collection of Web of Science from inception to 1 May 2020. We used two effective bibliometric tools, i.e., CiteSpace (Drexel University, Philadelphia, PA, USA) and VOSviewer (Leiden University, Leiden, The Netherlands) to objectively analyze the data of the prediction of infectious disease domain based on related publications, which can be downloaded from the core collection of Web of Science. Then, the leading publications of the prediction of infectious diseases were identified to detect the historical progress based on collaboration analysis, co-citation analysis, and co-occurrence analysis.

RESULTS

1880 documents that met the inclusion criteria were extracted from Web of Science in this study. The number of documents exhibited a growing trend, which can be expressed an increasing number of experts and scholars paying attention to the field year by year. These publications were published in 427 different journals with 11 different document types, and the most frequently studied types were articles 1618 (83%). In addition, as the most productive country, the United States has provided a lot of scientific research achievements in the field of infectious diseases.

CONCLUSION

Our study provides a systematic and objective view of the field, which can be useful for readers to evaluate the characteristics of publications involving the prediction of infectious diseases and for policymakers to take timely scientific responses.

Uptake of Diagnostic Tests by Livestock Farmers: A Stochastic Game Theory Approach

Game theory examines strategic decision-making in situations of conflict, cooperation, and coordination. It has become an established tool in economics, psychology and political science, and more recently has been applied to disease control. Used to examine vaccination uptake in human medicine, game theory shows that when vaccination is voluntary some individuals will choose to "free-ride" on the protection provided by others, resulting in insufficient coverage for control of a vaccine-preventable disease. Here, we use game theory to examine farmer uptake of a new diagnostic ELISA test for sheep scab-a highly infectious disease with an estimated cost exceeding £8M per year to the UK industry. The stochastic game models decisions made by neighboring farmers when deciding whether to adopt the newly available test, which can detect subclinical infestation. A key element of the stochastic game framework is that it allows multiple states. Depending on infestation status and test adoption decisions in the previous year, a farm may be at high, medium or low risk of infestation this year-a status which influences the decision the farmer makes and the farmer payoffs. Ultimately, each farmer's decision depends on the costs of using the diagnostic test vs. the benefits of enhanced disease control, which may only accrue in the longer term. The extent to which a farmer values short-term over long-term benefits reflects external factors such as inflation or individual characteristics such as patience. Our results show that when using realistic parameters and with a test cost around 50% more than the current clinical diagnosis, the test will be adopted in the high-risk state, but not in the low-risk state. For the medium risk state, test adoption will depend on whether the farmer takes a long-term or short-term view. We show that these outcomes are relatively robust to change in test costs and, moreover, that whilst the farmers adopting the test would not expect to see large gains in profitability, substantial reduction in sheep scab (and associated welfare implications) could be achieved in a cost-neutral way to the industry.

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.

Game dynamic model of optimal budget allocation under individual vaccination choice

Communicable diseases are leading cause of child mortality in developing and under-developed countries. Public health ministries in states and country allocate a considerable amount of budget every year for vaccination campaigns to control infections. Even third-party agencies such as Gates Foundation, UNDP, GAVI, World Bank, WHO also allocate huge funds to under-developed and developing countries for vaccination programs and disease eliminations. However, economic constraints and current disease prevalence are not enough driving factors for optimal decisions in budget allocations for vaccinations and controlling the disease. In a population under voluntary vaccination campaign, high vaccine coverage cannot be taken for granted, as individuals' free-riding behaviour plays a significant role in achieving the herd immunity level coverage. Individual-level vaccine exemptions and ignoring this important component by the policymakers are key determinants for failure of disease elimination program these days in many under-developed and developing countries. We integrate evolutionary game theory and compartmental model of disease transmission to analyze how individual vaccination choice influence the budget allocations and vice-versa. Our model illustrates that individuals' perceived risk plays an important role in optimal budget allocations to minimize infections. Analyses of our model indicate that the optimal distribution of third-party funds may be very different than usual, especially in multiple populations with contrasting demographic and economic profiles. These findings are certainly useful to public health policymakers and may help to quantify certain parameters in budget allocations to control vaccine-preventable diseases.

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.

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.

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.

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.

Self-enforcing regional vaccination agreements

In a highly interconnected world, immunizing infections are a transboundary problem, and their control and elimination require international cooperation and coordination. In the absence of a global or regional body that can impose a universal vaccination strategy, each individual country sets its own strategy. Mobility of populations across borders can promote free-riding, because a country can benefit from the vaccination efforts of its neighbours, which can result in vaccination coverage lower than the global optimum. Here we explore whether voluntary coalitions that reward countries that join by cooperatively increasing vaccination coverage can solve this problem. We use dynamic epidemiological models embedded in a game-theoretic framework in order to identify conditions in which coalitions are self-enforcing and therefore stable, and thus successful at promoting a cooperative vaccination strategy. We find that countries can achieve significantly greater vaccination coverage at a lower cost by forming coalitions than when acting independently, provided a coalition has the tools to deter free-riding. Furthermore, when economically or epidemiologically asymmetric countries form coalitions, realized coverage is regionally more consistent than in the absence of coalitions.

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.

A game-theoretic approach to valuating toxoplasmosis vaccination strategies

The protozoan Toxoplasma gondii is a parasite often found in wild and domestic cats, and it is the cause of the disease toxoplasmosis. More than 60 million people in the United States carry the parasite, and the Centers for Disease Control have placed toxoplasmosis in their disease classification group Neglected Parasitic Infections as one of five parasitic diseases targeted as priorities for public health action. In recent years, there has been significant progress toward the development of a practical vaccine, so vaccination programs may soon be a viable approach to controlling the disease. Anticipating the availability of a toxoplasmosis vaccine, we are interested in determining when cat owners should vaccinate their own pets. We have created a mathematical model describing the conditions under which vaccination is advantageous. Our model can be used to predict the average vaccination level in the population. We find that there is a critical vaccine cost threshold above which no one will use the vaccine. A vaccine cost slightly below this threshold, however, results in high usage of the vaccine, and consequently in a significant reduction in population seroprevalence. Not surprisingly, we find that populations may achieve herd immunity only if the cost of vaccine is zero.

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.

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 interplay of public intervention and private choices in determining the outcome of vaccination programmes

After a long period of stagnation, traditionally explained by the voluntary nature of the programme, a considerable increase in routine measles vaccine uptake has been recently observed in Italy after a set of public interventions aiming to promote MMR immunization, whilst retaining its voluntary aspect. To account for this take-off in coverage we propose a simple SIR transmission model with vaccination choice, where, unlike similar works, vaccinating behaviour spreads not only through the diffusion of "private" information spontaneously circulating among parents of children to be vaccinated, which we call imitation, but also through public information communicated by the public health authorities. We show that public intervention has a stabilising role which is able to reduce the strength of imitation-induced oscillations, to allow disease elimination, and to even make the disease-free equilibrium where everyone is vaccinated globally attractive. The available Italian data are used to evaluate the main behavioural parameters, showing that the proposed model seems to provide a much more plausible behavioural explanation of the observed take-off of uptake of vaccine against measles than models based on pure imitation alone.

A game dynamic model for vaccine skeptics and vaccine believers: measles as an example

Widespread avoidance of Measles-Mumps-Rubella vaccination (MMR), with a consequent increase in the incidence of major measles outbreaks, demonstrates that the effectiveness of vaccination programs can be thwarted by the public misperceptions of vaccine risk. By coupling game theory and epidemic models, we examine vaccination choice among populations stratified into two behavioral groups: vaccine skeptics and vaccine believers. The two behavioral groups are assumed to be heterogeneous with respect to their perceptions of vaccine and infection risks. We demonstrate that the pursuit of self-interest among vaccine skeptics often leads to vaccination levels that are suboptimal for a population, even if complete coverage is achieved among vaccine believers. The demand for measles vaccine across populations driven by individual self-interest was found to be more sensitive to the proportion of vaccine skeptics than to the extent to which vaccine skeptics misperceive the risk of vaccine. Furthermore, as the number of vaccine skeptics increases, the probability of infection among vaccine skeptics increases initially, but it decreases once the vaccine skeptics begin receiving the vaccination, if both behavioral groups are vaccinated according to individual self-interest. Our results show that the discrepancy between the coverages of measles vaccine that are driven by self-interest and those driven by population interest becomes larger when the cost of vaccination increases. This research illustrates the importance of public education on vaccine safety and infection risk in order to maintain vaccination levels that are sufficient to maintain herd immunity.

"Wait and see" vaccinating behaviour during a pandemic: a game theoretic analysis

During the 2009 H1N1 pandemic, many individuals did not seek vaccination immediately but rather decided to "wait and see" until further information was available on vaccination costs. This behaviour implies two sources of strategic interaction: as more individuals become vaccinated, both the perceived vaccination cost and the probability that susceptible individuals become infected decline. Here we analyze the outcome of these two strategic interactions by combining game theory with a disease transmission model during an outbreak of a novel influenza strain. The model exhibits a "wait and see" Nash equilibrium strategy, with vaccine delayers relying on herd immunity and vaccine safety information generated by early vaccinators. This strategic behaviour causes the timing of the epidemic peak to be strongly conserved across a broad range of plausible transmission rates, in contrast to models without such adaptive behaviour. The model exhibits not only feedback mechanisms but also a feed-forward mechanism: a high initial perceived vaccination cost perpetuates high perceived vaccine costs (and lower vaccine coverage) throughout the remainder of the outbreak. This suggests that any effect of risk communication at the start of a pandemic outbreak will be amplified compared to the same amount of risk communication effort distributed throughout the outbreak.