Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.
PLoS One. 2021 Feb 19;16(2):e0247445. doi: 10.1371/journal.pone.0247445. eCollection 2021.
In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while minimizing the costs incurred by the introduction of societal control measures (such as closing schools, social distancing, lockdowns, etc.), under the constraint that the infected fraction of the population does never exceed a certain maximum corresponding to public health system capacity. Optimality is derived and verified by variational and numerical methods for a number of model cost functions. The effects of immune response decay after recovery are taken into account and discussed in terms of the feasibility of strategies based on herd immunity.
在同质易感染-恢复（SIR）模型框架内，我们使用控制理论方法来确定最佳的大流行缓解策略。我们推导出了在满足人口中感染比例永远不会超过对应公共卫生系统容量的某个最大值的约束下，同时最小化引入社会控制措施（如关闭学校、社交距离、封锁等）所产生的成本，以达到群体免疫的一般条件。我们通过变分和数值方法对一些模型成本函数进行了最优性推导和验证。我们还考虑了恢复后免疫反应衰减的影响，并根据基于群体免疫的策略的可行性进行了讨论。
