Long-Term Regulation of Prolonged Epidemic Outbreaks in Large Populations via Adaptive Control: A Singular Perturbation Approach
Long-Term Regulation of Prolonged Epidemic Outbreaks in Large Populations via Adaptive Control: A Singular Perturbation Approach
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DOI：
10.1109/lcsys.2021.3083983
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发表时间：
2022-01-01
影响因子：
3
通讯作者：
Sontag, Eduardo D.
中科院分区：
文献类型：
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作者：
Al-Radhawi, M. Ali;Sadeghi, Mahdiar;Sontag, Eduardo D.
为了控制高传染性和长期爆发，公共卫生当局进行干预，制定社交距离，封锁政策和其他非药物干预措施（NPI）。由于非营利机构的社会、教育、心理和经济成本很高，当局调整它们，或者收紧或放松规则，结果实际上导致相对平稳的感染率。例如，于2020年夏季，美国部分地区的每日COVID-19感染人数降至平稳水平。这封信的方法NPI调整作为一个控制理论问题，从一个简单的动态模型的基础上的经典SIR流行病模型的社会距离。使用奇异摄动方法，高原成为一个准稳态（QSS）的减少二维SIR模型调节自适应动态反馈。结果表明，QSS是可以分配的，它是全局渐近稳定的。有趣的是，社会距离的动态模型可以被解释为一个非线性积分控制器。研究了该模型的数据拟合和参数可辨识性问题。这封信还讨论了这个简单的模型如何允许对人口规模，疫苗接种和第二波出现的影响进行有意义的研究。
In order to control highly-contagious and prolonged outbreaks, public health authorities intervene to institute social distancing, lock-down policies, and other Non-Pharmaceutical Interventions (NPIs). Given the high social, educational, psychological, and economic costs of NPIs, authorities tune them, alternatively tightening up or relaxing rules, with the result that, in effect, a relatively flat infection rate results. For example, during the summer of 2020 in parts of the United States, daily COVID-19 infection numbers dropped to a plateau. This letter approaches NPI tuning as a control-theoretic problem, starting from a simple dynamic model for social distancing based on the classical SIR epidemics model. Using a singular-perturbation approach, the plateau becomes a Quasi-Steady-State (QSS) of a reduced two-dimensional SIR model regulated by adaptive dynamic feedback. It is shown that the QSS can be assigned and it is globally asymptotically stable. Interestingly, the dynamic model for social distancing can be interpreted as a nonlinear integral controller. Problems of data fitting and parameter identifiability are also studied for this model. This letter also discusses how this simple model allows for a meaningful study of the effect of population size, vaccinations, and the emergence of second waves.