首页/论文/2012.00698

arXiv 2012.006982020-12-21math.OCphysics.soc-ph

Data-driven optimal control of a SEIR model for COVID-19

Hailiang Liu, Xuping Tian

备注：: 20 pages, 5 figures

英文摘要：

We present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. We use a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model, the model parameters are time-varying and learned from the data. This approach serves to forecast the evolution of the outbreak over a relatively short time period and provide scheduled controls of the epidemic. We provide efficient numerical algorithms based on a generalized Pontryagin Maximum Principle associated with the optimal control theory. Numerical experiments demonstrate the effective performance of the proposed model and its numerical approximations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

COVID-19传播的空间SEIR-HCD模型的可辨识性

Identifiability of the spatial SEIR-HCD model of COVID-19 propagation

本文基于Sobol敏感性分析和贝叶斯方法，研究了COVID-19传播的空间SEIR-HCD模型的可辨识性，缩小了未知参数边界并指出辨识扩散系数需额外信息。

2024-12-25math.OCphysics.soc-phq-bio.PE

Optimal control of vaccination and plasma transfusion with potential usefulness for COVID-19

The SEIR model is a compartmental model used to simulate the dynamics of an epidemic. In this chapter, we introduce two control functions in the compartmental SEIR model representing vaccination and plasma transfusion. Optimal control problems are proposed to study the effects of these two control measures, on the reduction of infected individuals and increase of recovered ones, with minimal costs. Up to our knowledge, the plasma transfusion treatment has never been considered as a control strategy for epidemics mitigation. The proposed vaccination and treatment strategies may have a real appl…

2020-10-08math.OCq-bio.PE

Optimal quarantine strategies for COVID-19 control models

Optimal control problems reflecting the finding of effective quarantine strategies are considered for two control SEIR~type models describing the spread of the COVID-19 virus in the human population. The properties of the corresponding optimal controls are established analytically by applying the Pontryagin maximum principle. The optimal solutions are obtained numerically using BOCOP 2.0.5 software. The behavior of the appropriate optimal solutions and their dependence on the basic reproductive ratio and length of quarantine are discussed in detail. Necessary conclusions are made.

2020-11-27math.OC

网络化SEIRS传染病过程中人口流动的分析与应用

Analysis and Applications of Population Flows in a Networked SEIRS Epidemic Process

本文提出网络化SEIRS模型刻画人口流动驱动的传染病传播，分析健康状态稳定性与地方病状态存在唯一性，并利用明尼苏达州COVID-19数据验证参数估计和到达时间预测方法。

2023-09-20math.OC

Control Strategies for COVID-19 Epidemic with Vaccination, Shield Immunity and Quarantine: A Metric Temporal Logic Approach

Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can …

2020-08-13cs.SYeess.SYmath.OC

Containment strategies after the first wave of COVID-19 using mobility data

In their response to the COVID-19 outbreak, governments face the dilemma to balance public health and economy. Mobility plays a central role in this dilemma because the movement of people enables both economic activity and virus spread. We use mobility data in the form of counts of travelers between regions, to extend the often-used SEIR models to include mobility between regions. We quantify the trade-off between mobility and infection spread in terms of a single parameter, to be chosen by policy makers, and propose strategies for restricting mobility so that the restrictions are minimal whil…

2020-10-27math.OCphysics.soc-ph

更多相关论文收起更多论文

Transport and Optimal Control of Vaccination Dynamics for COVID-19

We develop a mathematical model for transferring the vaccine BNT162b2 based on the heat diffusion equation. Then, we apply optimal control theory to the proposed generalized SEIR model. We introduce vaccination for the susceptible population to control the spread of the COVID-19 epidemic. For this, we use the Pontryagin minimum principle to find the necessary optimality conditions for the optimal control. The optimal control problem and the heat diffusion equation are solved numerically. Finally, several simulations are done to study and predict the spread of the COVID-19 epidemic in Italy. In…

2022-04-21math.OCq-bio.PE

Contact rate epidemic control of COVID-19: an equilibrium view

We consider the control of the COVID-19 pandemic through a standard SIR compartmental model. This control is induced by the aggregation of individuals' decisions to limit their social interactions: when the epidemic is ongoing, an individual can diminish his/her contact rate in order to avoid getting infected, but this effort comes at a social cost. If each individual lowers his/her contact rate, the epidemic vanishes faster, but the effort cost may be high. A Mean Field Nash equilibrium at the population level is formed, resulting in a lower effective transmission rate of the virus. We prove …

2020-05-10math.OCphysics.soc-phq-bio.PE

Optimal Control to Limit the Spread of COVID-19 in Italy

We apply optimal control theory to a generalized SEIR-type model. The proposed system has three controls, representing social distancing, preventive means, and treatment measures to combat the spread of the COVID-19 pandemic. We analyze such optimal control problem with respect to real data transmission in Italy. Our results show the appropriateness of the model, in particular with respect to the number of quarantined/hospitalized (confirmed and infected) and recovered individuals. Considering the Pontryagin controls, we show how in a perfect world one could have drastically diminish the numbe…

2021-07-25math.OCq-bio.PE

Optimal Lockdown for Pandemic Control

As a common strategy of contagious disease containment, lockdowns will inevitably weaken the economy. The ongoing COVID-19 pandemic underscores the trade-off arising from public health and economic cost. An optimal lockdown policy to resolve this trade-off is highly desired. Here we propose a mathematical framework of pandemic control through an optimal stabilizing non-uniform lockdown, where our goal is to reduce the economic activity as little as possible while decreasing the number of infected individuals at a prescribed rate. This framework allows us to efficiently compute the optimal stab…

2022-01-25math.OCphysics.soc-ph

Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm

University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）；Princeton University（普林斯顿大学）

Game theory has been an effective tool in the control of disease spread and in suggesting optimal policies at both individual and area levels. In this paper, we propose a multi-region SEIR model based on stochastic differential game theory, aiming to formulate optimal regional policies for infectious diseases. Specifically, we enhance the standard epidemic SEIR model by taking into account the social and health policies issued by multiple region planners. This enhancement makes the model more realistic and powerful. However, it also introduces a formidable computational challenge due to the hi…

2021-03-08cs.LGmath.DSmath.OC

Data-Driven Control of the COVID-19 Outbreak via Non-Pharmaceutical Interventions: A Geometric Programming Approach

In this paper we propose a data-driven model for the spread of SARS-CoV-2 and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of our data-driven model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on indi…

2020-11-03cs.SYeess.SYmath.OC