Bai Fan
Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany.
J Theor Biol. 2021 Oct 7;526:110795. doi: 10.1016/j.jtbi.2021.110795. Epub 2021 Jun 5.
We study the influence of population heterogeneity on herd immunity level and on individual's vaccination decision making process. We first formulate the mathematical model in a population with two subgroups, based on different activity levels or different susceptibilities. The herd immunity threshold is derived and discussed. It is calculated that the required vaccine coverage level for herd immunity in a heterogeneous mixing population can be varied significantly. The required vaccine coverage level is lower than the classical herd immunity level, if the vaccine coverage level in the more active group or more susceptible group is higher than the other subgroup. It is suggested that the classical herd immunity levels can be misleading in the process of planning mass vaccination programs. The analysis is further extended to study the population with more subgroups. We then study the formal vaccination games to simulate the process of vaccination decision making, in either homogeneous or heterogeneous mixing populations. It is proved that the Nash equilibrium in the vaccination game is not unique if population heterogeneity is considered. Moreover, herd immunity is not achieved if individuals are solely driven by self-interests.
我们研究了人群异质性对群体免疫水平以及个体疫苗接种决策过程的影响。我们首先基于不同的活动水平或易感性，在一个包含两个亚组的人群中建立数学模型。推导并讨论了群体免疫阈值。经计算得出，在异质混合人群中实现群体免疫所需的疫苗接种覆盖率水平可能会有显著差异。如果较活跃组或较易感组的疫苗接种覆盖率高于另一亚组，那么所需的疫苗接种覆盖率水平会低于经典的群体免疫水平。这表明在规划大规模疫苗接种计划的过程中，经典的群体免疫水平可能会产生误导。进一步扩展分析以研究包含更多亚组的人群。然后我们研究正式的疫苗接种博弈，以模拟在同质或异质混合人群中的疫苗接种决策过程。结果证明，如果考虑人群异质性，疫苗接种博弈中的纳什均衡并非唯一。此外，如果个体仅受自身利益驱动，则无法实现群体免疫。
