SIR类型新型冠状病毒肺炎多阶段最优控制模型

doi:10.15960/j.cnki.issn.1007-6093.2023.01.003

Abstract

Abstract:

The coronavirus disease 2019 (COVID-19) spreads all over the world, and it makes serious threat to people's health. Being faced with the data of anticipated development of COVID-19, we need to determine the epidemic spreading parameters under limited medical resources to give guidance for implementation intensities of the main epidemic prevention and control measures. In this paper, we describe the development of COVID-19 based on the SIR model. What's more, we propose a multi-stage optimal control model to determine the epidemic spreading parameters. In order to determine the values of parameters efficiently, we construct an SDP approximation model which is a polynomial-time computable problem. Based on the data of COVID-19 published by WHO, we apply our approximation model to obtain the epidemic spreading parameters which describe the development of COVID-19 in the USA within a given period of time, and analyze the epidemic prevention and control strategies.

Key words: coronavirus disease 2019, multi-stage optimal control model, SDP problem

CLC Number:

O221

Jintao XU, Wenxun XING. SIR type COVID-19 multi-stage optimal control model[J]. Operations Research Transactions, 2023, 27(1): 43-52.

Figures/Tables 5

References 14

1	张彦平. 新型冠状病毒肺炎流行病学特征分析[J]. 中华流行病学杂志, 2020, 41 (2): 145- 151.
2	严杰, 李明远, 孙爱华, 等. 2019新型冠状病毒及其感染性肺炎[J]. 中华微生物学和免疫学杂志, 2020, 40 (1): 1- 6.
3	徐宝丽, 管甲亮, 术超, 等. 新型冠状病毒COVID-19相关研究进展[J]. 中华医院感染学杂志, 2020, 30 (6): 839- 844.
4	陈兴志, 田宝单, 王代文, 等. 基于SEIR模型的COVID-19疫情防控效果评估和预测[J]. 应用数学和力学, 2021, 42 (2): 199- 211.
5	Xu C , Yu Y , Chen Y , et al. Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model[J]. Nonlinear Dynamics, 2020, 101, 1621- 1634. doi: 10.1007/s11071-020-05946-3
6	Mahrouf M , Boukhouima A , Zine H , et al. Modeling and forecasting of COVID-19 spreading by delayed stochastic differential equations[J]. Axioms, 2021, 10 (1): 18. doi: 10.3390/axioms10010018
7	Khyar O , Allali K . Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic[J]. Nonlinear Dynamics, 2020, 102, 489- 509. doi: 10.1007/s11071-020-05929-4
8	Arcede J P , Caga-anan R L , Mentuda C Q , et al. Accounting for symptomatic and asymptomatic in a SEIR-type model of COVID-19[J]. Mathematical Modelling of Natural Phenomena, 2020, 15, 34.
9	Zhang Z , Zeb A , Hussain S , et al. Dynamics of COVID-19 mathematical model with stochastic perturbation[J]. Advances in Difference Equations, 2020, 2020, 451.
10	薛毅. 数学建模基础[M]. 北京: 科学出版社, 2011.
11	吴尊友. 新型冠状病毒肺炎无症状感染者在疫情传播中的作用与防控策略[J]. 中华流行病学杂志, 2020, 41 (6): 801- 805.
12	Nesterov Y. Squared functional systems and optimization problems[M]//High Performance Optimization, Boston: Springer, 2000: 405-440.
13	邢文训, 方述诚. 线性锥优化导论[M]. 北京: 清华大学出版社, 2020.
14	美国最快12月11日接种新冠疫苗一线医护人员率先接种[EB/OL]. (2020-11-24)[2021-03-06]. https://xw.qq.com/cmsid/20201124V03H5I00.

$\lambda_{a}$	相邻两阶段易感者($\rm S$)被新冠病毒感染, 转变为无症状感染者($\rm I_{a}$) 的比例
$\lambda_{s}$	相邻两阶段易感者($\rm S$)被新冠病毒感染, 转变为有症状感染者($\rm I_{s}$) 的比例
$\mu_{a}$	相邻两阶段无症状感染者($\rm I_{a}$)痊愈的比例
$\mu_{s}$	相邻两阶段有症状感染者($\rm I_{s}$)痊愈的比例
$\gamma $	相邻两阶段易感者($\rm S$)通过接种疫苗获得免疫的比例
$\delta_{S}$	相邻两阶段易感者($\rm S$)保持不变的比例
$\delta_{I_{a}}$	相邻两阶段无症状感染者($\rm I_{a}$)保持不变的比例
$\delta_{I_{s}}$	相邻两阶段有症状感染者($\rm I_{s}$)保持不变的比例
$\delta_{R}$	相邻两阶段免疫者($\rm R$)保持不变的比例
$\beta_{S1}$	相邻两阶段由于输入输出导致的易感者($\rm S$)人数变化量
$\beta_{S2}$	相邻两阶段内新生儿人数
$\beta_{I_{a}}$	相邻两阶段由于输入输出导致的无症状感染者($\rm I_{a}$)人数变化量
$\beta_{I_{s}}$	相邻两阶段由于输入输出导致的有症状感染者($\rm I_{s}$)人数变化量
$\beta_{R}$	相邻两阶段由于输入输出导致的免疫者($\rm R$)人数变化量

方程组(1)疫情传播参数需满足的关系式	原因解释
$L_{1}\leq \delta_{S}+\lambda_{a}+\lambda_{s}+\gamma\leq U_{1}$	易感者($\rm S$)存在死亡率
$L_{2}\leq \delta_{I_{a}}+\mu_{a}\leq U_{2}$	无症状感染者($\rm I_{a}$)存在死亡率
$L_{3}\leq \delta_{I_{s}}+\mu_{s}\leq U_{3}$	有症状感染者($\rm I_{s}$)存在死亡率
$L_{4}\leq \delta_{R}\leq U_{4}$	免疫者($\rm R$)存在死亡率
$9\lambda_{a}\leq \lambda_{s}$	依据文献[11], 本文的合理假设
$L_{5}\leq \gamma\leq U_{5}$	本文的合理假设

$\tilde{U}$的取值	0.6	1	2
AMOCM的最优值	0.363 729	0.110 419	0.003 306 57

矩阵及向量	$\lambda_{a}$	$\lambda_{s}$	$\gamma$	$\delta_{I_{a}}$	$\delta_{I_{s}}$	$\delta_{S}$	$\mu_{a}$	$\mu_{s}$	$\beta_{I_{a}}$
$A_{0}$, $b_{0}$	0.000 46	0.004 14	0	0.325 18	0.315 17	0.995 4	0.674 82	0.677 55	-0.000 06
$A_{1}$, $b_{1}$	0.000 09	0.000 82	0.000 32	0.441 04	0.555 47	0.998 77	0.558 96	0.420 39	0.000 04

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SIR type COVID-19 multi-stage optimal control model

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