A game theoretic approach to discuss the positive secondary effect of vaccination scheme in an infinite and well-mixed population
A game theoretic approach to discuss the positive secondary effect of vaccination scheme in an infinite and well-mixed population
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DOI：
10.1016/j.chaos.2019.05.031
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发表时间：
2019-08-01
影响因子：
7.8
通讯作者：
Tanimoto, Jun
中科院分区：
文献类型：
--
作者：
Alam, Muntasir;Tanaka, Masaki;Tanimoto, Jun
预防接种政策用于控制传染病的快速传播，被认为是人类面临的最具挑战性的问题之一，多年来造成了巨大的死亡人数。本文研究了早期接种疫苗的个体不能获得完全免疫力所带来的两难效应。因此，我们提出了一个新的理论模型，减缓了感染的传播，也有利于更快的恢复时间比以前的模型，即使接种者未能获得完美的免疫力。我们将这种效应称为疫苗接种的“正二次效应”，因为它为接种者提供了第二次机会，从而抑制了快速传播，有助于产生更好的社会平均回报，并保持最终的流行规模较小。此外，为了更精确地解决正二次效应，我们引入了两个不同的参数;即，松弛参数（eta）和福斯特参数（delta）在两个不同的方向，以量化每个参数空间产生的个体效应以及它们的叠加效应。深入的讨论集中在我们提出的模型通过折扣和更快的恢复效果所发挥的影响作用，同时给接种者第二次机会。此外，我们也研究了当eta所带来的贴现效应远胜于delta所控制的快速恢复以及叠加效应时的情形。与以往研究疫苗接种博弈不同的是，本文着重研究了不完全疫苗接种政策的二次效应。我们提出的理论方案完全再现了选择一个不完美的规定，基于进化博弈论的广泛使用的SIR（易感-感染-传播）流行病模型的决策过程。在不考虑任何空间结构和完善的疫苗接种政策的情况下，我们的模型假设人口是无限的，并且是混合的，以数学方式表示感染传播动力学。本研究始终采用所谓的理论方法进行。此外，基于演化博弈理论，我们还考虑了三种不同的更新规则，以研究所有可能的情况。随后，我们绘制了2D全相图，定量显示了最终的流行规模、疫苗接种覆盖率和平均社会收益。最后，我们的理论结果进行了比较，从多智能体仿真（MAS）的方法得到的结果和一个很好的协议，因此，所提出的模型的适当性是完全合理的。(C)2019爱思唯尔有限公司版权所有。
Pre-emptive vaccination policy used in controlling the rapid spreading of infectious diseases is considered as one of the most challenging issues imposed to mankind, causing enormous death tolls over the years. This paper dedicatedly studies the dilemma effect coming from the failure of getting perfect immunity to those individuals who committed vaccination earlier. Therefore, we propose a new theoretical model that slows down the infection spreading and also facilitates quicker recovery time than what the previous model does even if a vaccinator fails to obtain perfect immunity. We name this effect as the "positive secondary effect" of vaccination as it gives a second chance to the vaccinators which in return subdues the rapid spreading that helps in producing better social average payoff as well as keeping the final epidemic size smaller. Moreover, to address the positive secondary effect more precisely, we introduce two different parameters; namely, relaxation parameter (eta) and foster parameter (delta) in two different directions to quantify the individual effects resulting from each of the parameter space as well as their superposition effect. An in-depth discussion focuses on the influential role played by our proposed model via discounting and faster recovery effects while a second chance is given to the vaccinators. In addition, we also examine the situation when discounting effect brought by eta outperforms very much than its faster recovery controlled by delta as well as the superposition effects. Unlike all previous studies dealing with vaccination game, we pay much attention to investigating the secondary effect of imperfect vaccination policy. Our proposed theoretical scheme completely reproduces the decision-making process of choosing an imperfect provision based on evolutionary game theory entailed with the widely used SIR (Susceptible-Infected-Recovered) epidemic model. Without considering any spatial structure and perfect vaccination policy, our model presumes the population being infinite and well-mixed to represent the infection spreading dynamics mathematically. This study is conducted throughout using the so-called theoretical approach. Besides that, three different updating rules based on evolutionary game theory have also been considered to investigate all possible situations. Later on, we draw 2D full phase diagrams showing the final epidemic size, vaccination coverage, and average social payoff quantitatively. Finally, our theoretical result is compared with the counterpart result obtained from the multi-agent simulation (MAS) approach and a good agreement is found, hence the appropriateness of the proposed model is fully justified. (C) 2019 Elsevier Ltd. All rights reserved.