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SIRC 传染病爆发的最优控制。

Optimal control for SIRC epidemic outbreak.

机构信息

Department of Computer, Control and Management Engineering Antonio Ruberti - Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy.

出版信息

Comput Methods Programs Biomed. 2013 Jun;110(3):333-42. doi: 10.1016/j.cmpb.2013.01.006. Epub 2013 Feb 8.

DOI:10.1016/j.cmpb.2013.01.006
PMID:23399104
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7126881/
Abstract

In this paper the mathematical SIRC epidemic model is considered. It efficiently describes diseases in which a cross immune class (C) is present, along with the susceptible (S), the infected (I) and the removed (R) ones. Controlling epidemic diseases corresponds to the introduction of vaccination, quarantine and treatment strategies; generally only one of these actions is considered. In this paper the possibility of optimal controls both over the susceptible and the infected subjects is assumed, taking into account also limitations of resources. A suitable cost index is introduced and via the Pontryagin's Minimum Principle the optimal control strategy is determined and the existence of the optimal solution is assessed. Numerical results are developed analyzing the effects of different control strategies.

摘要

本文考虑了数学 SIRC 传染病模型。它有效地描述了存在交叉免疫类（C）的疾病，同时还有易感者（S）、感染者（I）和清除者（R）。控制传染病对应于引入疫苗接种、隔离和治疗策略；通常只考虑其中一种措施。本文假设对易感者和感染者都可以进行最优控制，同时还考虑了资源的限制。引入了一个合适的成本指数，并通过庞特里亚金最小原理确定了最优控制策略，并评估了最优解的存在性。通过分析不同控制策略的效果，得出了数值结果。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/0c33353eedf8/gr11_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/f16162710b6e/gr1_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/6c3696a474c2/gr2_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/32ccf1a60f47/gr3_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/f85afc0cbdec/gr4_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/58713545afe8/gr5_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/ca04732452c4/gr6_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/84915177c96e/gr7_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/0e16a36793d0/gr8_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/d65f0cbe54cd/gr9_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/dfd300cb958a/gr10_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/0c33353eedf8/gr11_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/f16162710b6e/gr1_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/6c3696a474c2/gr2_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/32ccf1a60f47/gr3_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/f85afc0cbdec/gr4_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/58713545afe8/gr5_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/ca04732452c4/gr6_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/84915177c96e/gr7_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/0e16a36793d0/gr8_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/d65f0cbe54cd/gr9_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/dfd300cb958a/gr10_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/da36/7126881/0c33353eedf8/gr11_lrg.jpg

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