{"title":"论新病毒爆发初期的优化控制","authors":"Alexandra Smirnova, Xiaojing Ye","doi":"10.1016/j.idm.2024.05.006","DOIUrl":null,"url":null,"abstract":"<div><p>We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available. At that stage, control is often limited to non-medical interventions like social distancing and other behavioral changes. For the SIR optimal control problem, we show that the running cost of control satisfying mild, practically justified conditions generates an optimal strategy, <em>u</em>(<em>t</em>), <em>t</em> ∈ [0, <em>T</em>], that is sustainable up until some moment <em>τ</em> ∈ [0, <em>T</em>). However, for any <em>t</em> ∈ [<em>τ</em>, <em>T</em>], the function <em>u</em>(<em>t</em>) will decline as <em>t</em> approaches <em>T</em>, which may cause the number of newly infected people to increase. So, the window from 0 to <em>τ</em> is the time for public health officials to prepare alternative mitigation measures, such as vaccines, testing, antiviral medications, and others. In addition to theoretical study, we develop a fast and stable computational method for solving the proposed optimal control problem. The efficiency of the new method is illustrated with numerical examples of optimal control trajectories for various cost functions and weights. Simulation results provide a comprehensive demonstration of the effects of control on the epidemic spread and mitigation expenses, which can serve as invaluable references for public health officials.</p></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8000,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2468042724000721/pdfft?md5=5b1b4e071f72a65d370b1dd97514faf5&pid=1-s2.0-S2468042724000721-main.pdf","citationCount":"0","resultStr":"{\"title\":\"On optimal control at the onset of a new viral outbreak\",\"authors\":\"Alexandra Smirnova, Xiaojing Ye\",\"doi\":\"10.1016/j.idm.2024.05.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available. At that stage, control is often limited to non-medical interventions like social distancing and other behavioral changes. For the SIR optimal control problem, we show that the running cost of control satisfying mild, practically justified conditions generates an optimal strategy, <em>u</em>(<em>t</em>), <em>t</em> ∈ [0, <em>T</em>], that is sustainable up until some moment <em>τ</em> ∈ [0, <em>T</em>). However, for any <em>t</em> ∈ [<em>τ</em>, <em>T</em>], the function <em>u</em>(<em>t</em>) will decline as <em>t</em> approaches <em>T</em>, which may cause the number of newly infected people to increase. So, the window from 0 to <em>τ</em> is the time for public health officials to prepare alternative mitigation measures, such as vaccines, testing, antiviral medications, and others. In addition to theoretical study, we develop a fast and stable computational method for solving the proposed optimal control problem. The efficiency of the new method is illustrated with numerical examples of optimal control trajectories for various cost functions and weights. Simulation results provide a comprehensive demonstration of the effects of control on the epidemic spread and mitigation expenses, which can serve as invaluable references for public health officials.</p></div>\",\"PeriodicalId\":36831,\"journal\":{\"name\":\"Infectious Disease Modelling\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":8.8000,\"publicationDate\":\"2024-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2468042724000721/pdfft?md5=5b1b4e071f72a65d370b1dd97514faf5&pid=1-s2.0-S2468042724000721-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Infectious Disease Modelling\",\"FirstCategoryId\":\"3\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2468042724000721\",\"RegionNum\":3,\"RegionCategory\":\"医学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Medicine\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Infectious Disease Modelling","FirstCategoryId":"3","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468042724000721","RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Medicine","Score":null,"Total":0}
引用次数: 0
摘要
我们提出了一个灵活选择控制措施的多功能模型,用于在疫苗/药物尚未问世的情况下预防大流行病的早期爆发。在这一阶段,控制通常仅限于非医疗干预,如社会疏远和其他行为改变。对于 SIR 最佳控制问题,我们表明,满足温和、实际合理条件的控制运行成本会产生一个最佳策略 u(t),t ∈ [0, T],该策略可持续到某个时刻 τ∈ [0, T)。然而,对于任意 t∈ [τ, T],函数 u(t) 会随着 t 接近 T 而下降,这可能会导致新感染人数增加。因此,从 0 到 τ 的窗口期是公共卫生官员准备其他缓解措施的时间,如疫苗、检测、抗病毒药物等。除了理论研究,我们还开发了一种快速稳定的计算方法来解决所提出的最优控制问题。新方法的效率通过各种成本函数和权重的最优控制轨迹的数值示例来说明。模拟结果全面展示了控制对疫情传播和减灾支出的影响,可为公共卫生官员提供宝贵的参考。
On optimal control at the onset of a new viral outbreak
We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available. At that stage, control is often limited to non-medical interventions like social distancing and other behavioral changes. For the SIR optimal control problem, we show that the running cost of control satisfying mild, practically justified conditions generates an optimal strategy, u(t), t ∈ [0, T], that is sustainable up until some moment τ ∈ [0, T). However, for any t ∈ [τ, T], the function u(t) will decline as t approaches T, which may cause the number of newly infected people to increase. So, the window from 0 to τ is the time for public health officials to prepare alternative mitigation measures, such as vaccines, testing, antiviral medications, and others. In addition to theoretical study, we develop a fast and stable computational method for solving the proposed optimal control problem. The efficiency of the new method is illustrated with numerical examples of optimal control trajectories for various cost functions and weights. Simulation results provide a comprehensive demonstration of the effects of control on the epidemic spread and mitigation expenses, which can serve as invaluable references for public health officials.
期刊介绍:
Infectious Disease Modelling is an open access journal that undergoes peer-review. Its main objective is to facilitate research that combines mathematical modelling, retrieval and analysis of infection disease data, and public health decision support. The journal actively encourages original research that improves this interface, as well as review articles that highlight innovative methodologies relevant to data collection, informatics, and policy making in the field of public health.