Vaccination and the theory of games

Abstract

Voluntary vaccination policies for childhood diseases present parents with a subtle challenge: if a sufficient proportion of the population is already immune, either naturally or by vaccination, then even the slightest risk associated with vaccination will outweigh the risk from infection. As a result, individual self-interest might preclude complete eradication of a vaccine-preventable disease. We show that a formal game theoretical analysis of this problem leads to new insights that help to explain human decisionmaking with respect to vaccination. Increases in perceived vaccine risk will tend to induce larger declines in vaccine uptake for pathogens that cause more secondary infections (such as measles and pertussis). After a vaccine scare, even if perceived vaccine risk is greatly reduced, it will be relatively difficult to restore prescare vaccine coverage levels.T he history of vaccination policy includes numerous bouts of public resistance, often in the form of vaccine scares (1-4). In the United Kingdom, for example, a pertussis vaccine scare in the 1970s caused a decline in the level of vaccine coverage, resulting in substantial increases in morbidity and mortality from whooping cough (4). Currently, measles-mumps-rubella vaccine uptake is declining in the United Kingdom, with mounting concern that widespread outbreaks of measles may recur (5).In deciding whether to vaccinate their children, parents consider the risk of morbidity from vaccination, the probability that their child will become infected, and the risk of morbidity from such an infection. The decisions of individual parents are indirectly influenced by the decisions of all other parents, because the sum of these decisions yields the vaccine coverage levels in the population and hence the course of epidemics.Game theory (6-9) attempts to predict individual behavior in such a setting, where the payoff to strategies chosen by individuals depends on the strategies adopted by others in the population. Here, we integrate epidemic modeling (10) into a game theoretical framework to analyze population behavior under voluntary vaccination policies for childhood diseases. This approach allows us to quantify how risk perception influences expected vaccine uptake and coverage levels and what role is played by the epidemiological characteristics of the pathogens.The Vaccination Game Description of Game. For simplicity, we imagine that all individuals are provided with the same information and use this information in the same way to assess risks. An individual's strategy is the probability P that s͞he will choose to vaccinate. The vaccine uptake level in the population is the proportion of newborns who will be vaccinated and hence is the mean of all strategies adopted by individuals in the population. We ignore any delay between changes in vaccine uptake and corresponding changes in overall vaccine coverage in the population; consequently, if no diseaserelated or vaccine-related mortality occurs, then the proportion of the population vaccinated, p, will be ...

The impact of vaccine side effects on the natural history of immunization programmes: An imitation-game approach

“…In the US approximately 1 30,000 reports of Vaccine Adverse Events are notified annually, with 10-15% classified as serious [4]. In such circumstances the perception of the public will likely rank the perceived risk of suffering a vaccine side effect (VSE) as much higher than the corresponding risk of infection [1,2,6,7]. A common example is poliomyelitis in industrialized countries.…”

“…the parents' decision not to vaccinate children after comparing the perceived risk of disease and the perceived risk of vaccine side effects [1,2,6]. Vaccination free riding [3,10,13,1,2,6,7,9,21,22,11] makes eradication impossible (unless special contact structures are considered [19]) and triggers stable oscillations in the infection prevalence. Previous studies on the impact of vaccination free riding on endemic infections have focused on scenarios where the vaccine demand is driven by the time changes in the perceived risk of disease, measured through the current (or past) infection prevalence.…”

Vaccine demand driven by vaccine side effects: Dynamic implications for SIR diseases

“…causing disability, hospitalization, life-threatening illness or death [7]. In such circumstances it is natural to expect that the perceived risk of experiencing a VSE will outweight the perceived risk from infection [3,4,11]. A commonly brought example is Poliomyelitis 1 ([33] and references therein).…”

“…Vaccination free riding results in the family's decision not to vaccinate children after a seemingly rational comparison between the perceived risk of infection and the perceived risk of VSE. Vaccination free riding can take profit of the high degree of herd immunity existing in communities with high vaccine uptake [2,3,4,11]. In our previous work [11,12] we have described vaccination free-riding as "rational exemption", in order to distinguish it from other forms of exemption observed in the history of vaccination, e.g.…”

Provisioning of Public Health Can Be Designed to Anticipate Public Policy Responses

“…Gersovitz [17] and Gersovitz and Hammer [18] discussed the economic aspects of the control of infectious diseases, investigating the decisions of social planners and the representative decision-making agents who directly control preventive and therapeutic efforts. Research articles using game theory study individuals' responses to the incentives associated with vaccination [15,6,3,2,9,11,29,30] and transmission reduction [8,28,31,19,10]. These advances indicate that game theory gives a way to analyze how people may respond to economic and epidemiological pressures.…”