Dipartimento di Statistica & Matematica Applicata all'Economia, Facoltà di Economia, Università di Pisa, Via Ridolfi 10, I-56124 Pisa, Italy.
Vaccine. 2009 Dec 10;28(1):98-109. doi: 10.1016/j.vaccine.2009.09.109. Epub 2009 Nov 4.
A threat for vaccination policies might be the onset of "rational" exemption, i.e. the family's decision not to vaccinate children after a seemingly rational comparison between the perceived risk of infection and the perceived risk of vaccine side effects. We study the implications of rational exemption by models of vaccination choice. By a simple model of individual choice we first prove the "elimination impossible" result in presence of informed families, i.e. aware of herd immunity, and suggest that limited information might explain patterns of universal vaccination. Next, we investigate vaccination choice in a game-theoretic framework for communities stratified into two groups, "pro" and "anti" vaccinators, having widely different perceived costs of infection and of vaccine side effects. We show that under informed families neither a Nash nor a Stackelberg behaviour (characterized, respectively, by players acting simultaneously and by an asymmetric situation with a "leader" and a "follower) allow elimination, unless "pro-vaccinators" assign no costs to vaccine side effects. Elimination turns out to be possible when cooperation is encouraged by a social planner, provided, however, he incorporates in the "social loss function" the preferences of anti-vaccinators only. This allows an interpretation of the current Italian vaccination policy.
接种政策可能面临的一个威胁是“理性”豁免的出现，即家庭在对感染风险和疫苗副作用风险的感知进行看似理性的比较后，决定不为孩子接种疫苗。我们通过接种选择模型研究理性豁免的含义。首先，通过一个简单的个体选择模型，我们证明了在知情家庭（即了解群体免疫）存在的情况下“消除不可能”的结果，并认为有限的信息可能解释了普遍接种的模式。接下来，我们在社区分层为“赞成”和“反对”接种者的博弈论框架中研究接种选择，这两个群体对感染和疫苗副作用的感知成本存在很大差异。我们表明，在知情家庭中，无论是纳什均衡还是斯塔克伯格均衡（分别由同时行动的参与者和一个具有“领导者”和“追随者”的不对称情况所决定）都无法消除，除非“赞成接种者”不认为疫苗副作用有任何成本。当社会规划者通过鼓励合作来消除时，合作就成为可能，但前提是他将反疫苗接种者的偏好纳入“社会损失函数”。这使得人们可以对意大利目前的疫苗接种政策进行解读。
