Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

中文翻译：

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从流行病到地方病的浪潮：病毒突变、免疫变化和政策反应

非药物干预措施 (NPI) 是应对 COVID-19 等流行病的重要工具。有些很便宜；有些则很便宜。其他的则扰乱经济、教育和社会活动。后者迫使政府在减少感染和死亡所带来的健康效益与更广泛的封锁引发的社会成本之间进行权衡。一篇文献开发了如何随着流行病的发展优化调整封锁强度的模型。本文通过用额外的状态和流增强经典的 SIR 模型来扩展该文献，捕获疫苗赋予的免疫力随时间的衰减、突变产生削弱免疫力的变体的可能性，以及针对感染的保护比针对严重疾病的保护更快地削弱。与过去的模型一样，我们发现参数值的微小变化可能会导致非常不同的解决方案之间的最佳响应，但这里考虑的扩展创建了新类型的解决方案。在某些情况下，即使不受控制的感染流行率会稳定在稳定的中间水平，但引发持续的流行病波可能是最佳选择。