Funded Grants

Developing and applying game theoretic human papillomavirus vaccination models with psychological data

Human papillomavirus (HPV) is one of the world’s most prevalent sexually transmitted diseases. It is estimated that 5.5 million HPV infections arise annually in the US alone. HPV is the primary cause of cervical carcinoma, which is in turn the second most common malignancy among women and a leading cause of cancer death worldwide. HPV is also associated with genital warts in both females and males.

Prophylactic HPV vaccines will be available soon. Vaccination has recently been advocated by the Centers for Disease Control and Prevention (CDC) as an integral strategy for reducing the public health burden of HPV. The CDC currently recommends vaccination of young women only. However, the feasibility of optimal community vaccination depends on population adherence.

The utilities (or values) of vaccination decisions to individuals and to their communities are governed by the interplay between two complex systems: epidemiological systems and social systems. We will quantitatively and experimentally assess the interaction between disease transmission and social decision-making, with specific application to HPV infection and vaccination decisions. We will determine h ow epidemiological complexity affects decision-making. In turn, we will explore how aggregate decision making influences a complex biological system. We propose to take an interdisciplinary approach that combines epidemiology, mathematical modeling, economics and game theory, in addition to model parameterization and verification from experimental and psychological data. We will define policies that encourage adherence to optimal vaccination strategies for the community-wide control of HPV.

When vaccination is voluntary, medical decisions are made by individuals. Collectively, individual decisions determine the level of population immunity and thus the magnitude of an epidemic. Vaccination protects not only the people who are vaccinated, but others in the community who are thereby less likely to become infected. Conversely, when people choose not to be vaccinated, they not only take on a risk to themselves, but also put others at risk. In the case of HPV, the risks for the two sexes are different: women have much greater incentives to vaccinate than men. HPV vaccination confers protection against cervical cancer for women, whereas men receive protection against the much less grave condition of genital warts (in the case of the Merck vaccine) or even no personal incentive (in the case of the SmithKline Beecham vaccine). Consequently, if men are not vaccinated, they take on relatively small personal risk, but they cause a risk to their sexual partners directly and to the community indirectly.

We will integrate results from models and experiments that capture both individual- and population-scale dynamics. On an individual scale, questionnaires and experimental game studies will be conducted to examine how an individual's vaccination decisions are influenced by the decisions of others, and to estimate the influence of altruism on vaccination decisions. Combining individual and population scales of analysis, we will combine a game-theoretic model of gender-specific vaccine demand with a model of HPV epidemiology, parameterized and verified with results from our questionnaire and experimental game studies. Our integration of these scales of analysis will facilitate the development of public health policies that take into account barriers to population adherence, and delineate the importance of such adherence in reducing HPV prevalence and cervical cancer.

Most vaccination decision models have been formulated from a purely economic or sociological perspective, while studies from the public health perspective have not addressed the temporal dynamics of disease transmission. Conversely, e pidemiological models usually ignore economic constraints and incentives that are fundamental to the successful application of public health programs. A burgeoning area in which applied mathematical models can play a significant role is in addressing questions of the game-theoretic determinants of health outcomes. In a game-theoretic context, individuals are strategists who strive to maximize their expected utility, defined as the value of anticipated benefits minus the cost of anticipated risks. Indeed, survey data indicates that individuals attempt to do this, within the constraints of their knowledge and perceptions. We have previously formulated the conflict between individual and group interest as a population game, and have shown that the pursuit of self-interest can lead to suboptimal vaccination coverage for a community. The benefit to an individual of vaccination drops as the system approaches herd immunity, a level of community vaccination at which a disease would be eradicated. However, classical game theoretic models assume that individuals are perfectly rational and have complete knowledge. The next challenge is to parameterize epidemiological game theory models with empirically collected psychological data to include perceptions and attitudes about vaccination that differ from reality. For example, people tend to over-estimate risks of adverse effects of vaccines.

We propose to conduct the first application of epidemiological game theoretic modeling to HPV vaccination policy. To achieve this objective, we will incorporate a model of HPV transmission into a game-theoretic framework that calculates the utilities to an individual dependent on their gender and on the strategies adopted by the rest of the population. We will compare group-optimal strategies versus individual-optimal strategies for HPV vaccination implementation, and the potential public health repercussions of imperfect adherence. This model will be applied to survey and experimental data designed specifically to parameterize and verify the model. We will propose ways in which population adherence to group-optimal public health policies can be enhanced. We will investigate two important sources of discrepancies that affect vaccination levels. Firstly, there are discrepancies generated by the discordance of incentives between women and men to vaccinate. Secondly, there are discrepancies caused by differences between perception and reality of HPV epidemiological parameters.

The early history of game theory, as developed by John von Neumann and others from the 1920's to the 1940's focused on 2-person games where the winnings of one player were the losses of the other player. In 1950, John Nash radically expanded the scope of game theory.  He developed game theory with 3 or more players and introduced the idea of a "Nash equilibrium", which is now a central tool in contemporary microeconomic theory.  At a Nash equilibrium, no individuals can increase their utility by switching to a different strategy. However, an individual’s utility at the Nash equilibrium is not necessarily optimal for the individual or for the community. Cooperation may generate a higher utility, but may not be socially stable, because an individual can increase his utility by ‘defecting’ – in the vaccination case, refusal to vaccinate is a defection. Calculating Nash equilibria for heterogeneous (in our case gender-structured) populations is challenging because it requires simultaneously determining the best response strategy for every heterogeneous group, dependent upon overall population behavior. Thus, w e will develop an algorithm for determining Nash equilibria of vaccination behavior governed by self-interest, in addition to utilitarian vaccine allocation strategies. We will identify the parameters that have the greatest impact on aligning individual-optimal and group-optimal vaccination strategies, such as attitudes toward vaccine efficacy, cost and risk. To determine the likely influence of improving dissemination of information about HPV and its vaccine, we will compare actual parameter values with perceived parameter values, the latter of which will be obtained from our psychological data.

To examine how an individual's vaccination decisions are influenced by the dynamics of disease transmission and aggregate vaccination behavior, we will conduct a questionnaire studies and experimental games. Interdependent social and epidemiological dynamics have been unrecognized in previous questionnaire studies of vaccination decisions. Our interdisciplinary collaboration will equip us to take into account these complex dynamics. These studies will quantify the extent to which people accurately estimate the relative risks and costs of HPV vaccination compared to the illness itself. We will assess how the behavior of others and concern for others HPV vaccination decisions. We will use our empirical results to parameterize our game theoretic model of vaccination and predict discrepancies between collective individual behavior and the societal utilitarian strategy. Our results will be applicable to other social decision-making contexts in which costs and benefits must be evaluated and the behavior of others taken into account.

Ultimately, policy makers must balance health, social, economic, ethical and political considerations when developing optimal public health policies. Our aim is to inform vaccine allocation and adherence promotion strategies that minimize the public health burden of HPV. Our interdisciplinary approach combines the development of theoretical models with psychological data collection and parameterization, economics with epidemiology, and individual decision making with population-level public health outcomes. The development of game theoretic models and parameterization will be useful for studying vaccination dynamics of other infectious diseases; to the further application of game theory to population dynamics, psychology and health; and to public policy in general.