Bézier curve parametrisation and echo state network methods for solving optimal control problems of SIR model
In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the infective and susceptible individuals. To solve the control problem, we use direct Bernstein–Bézier parametrisation of the control variables and...
Saved in:
| Published in | BioSystems Vol. 186; p. 104029 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Ireland
Elsevier B.V
01.12.2019
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0303-2647 1872-8324 1872-8324 |
| DOI | 10.1016/j.biosystems.2019.104029 |
Cover
| Abstract | In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the infective and susceptible individuals. To solve the control problem, we use direct Bernstein–Bézier parametrisation of the control variables and metaheuristic optimisation methods of an objective function, and indirect methods, adaptive critic design (ACD) with echo state networks (ESNs) and Pontryagin's maximum principle. We propose Bernstein–Bézier parametrisation and ESNs based algorithms to solve optimal control problems for systems governed by differential equations. We use ACD with ESNs to approximate co-state equations. Our simulations have shown that the proposed two methods are able to solve optimal control problems. |
|---|---|
| AbstractList | In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the infective and susceptible individuals. To solve the control problem, we use direct Bernstein-Bézier parametrisation of the control variables and metaheuristic optimisation methods of an objective function, and indirect methods, adaptive critic design (ACD) with echo state networks (ESNs) and Pontryagin's maximum principle. We propose Bernstein-Bézier parametrisation and ESNs based algorithms to solve optimal control problems for systems governed by differential equations. We use ACD with ESNs to approximate co-state equations. Our simulations have shown that the proposed two methods are able to solve optimal control problems.In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the infective and susceptible individuals. To solve the control problem, we use direct Bernstein-Bézier parametrisation of the control variables and metaheuristic optimisation methods of an objective function, and indirect methods, adaptive critic design (ACD) with echo state networks (ESNs) and Pontryagin's maximum principle. We propose Bernstein-Bézier parametrisation and ESNs based algorithms to solve optimal control problems for systems governed by differential equations. We use ACD with ESNs to approximate co-state equations. Our simulations have shown that the proposed two methods are able to solve optimal control problems. In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the infective and susceptible individuals. To solve the control problem, we use direct Bernstein-Bézier parametrisation of the control variables and metaheuristic optimisation methods of an objective function, and indirect methods, adaptive critic design (ACD) with echo state networks (ESNs) and Pontryagin's maximum principle. We propose Bernstein-Bézier parametrisation and ESNs based algorithms to solve optimal control problems for systems governed by differential equations. We use ACD with ESNs to approximate co-state equations. Our simulations have shown that the proposed two methods are able to solve optimal control problems. |
| ArticleNumber | 104029 |
| Author | Kmet, Tibor Kmetova, Maria |
| Author_xml | – sequence: 1 givenname: Tibor surname: Kmet fullname: Kmet, Tibor email: kmett@ujs.sk organization: J. Selye University, Department of Mathematics and Informatics, Bratislavska Cesta 3322, 945 01 Komarno, Slovakia – sequence: 2 givenname: Maria surname: Kmetova fullname: Kmetova, Maria email: mkmetova@ukf.sk organization: Constantine the Philosopher University, Faculty of Natural Sciences, Department of Mathematics, Nitra, Slovakia |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/31540680$$D View this record in MEDLINE/PubMed |
| BookMark | eNqNkctOHDEQRS0EguHxC5GX2fTEr552b5AA5YGEFImEteW2q8ETtz2xPRORP8p38GN4MqBI2STelGydulW-9xjthxgAIUzJnBK6eLecDy7mx1xgynNGaF-fBWH9HppR2bFGcib20Yxwwhu2EN0ROs55SeppJT1ER5y2giwkmaFw-fTrp4OEzTptAK900hOU5LIuLgasg8VgHiLORRfAAcqPmL7hijxEm_EYE87Rb1y4x3FV3KQ9NjGUFD1epTj4uh-OI_5yfYunaMGfooNR-wxnL_UE3X14__XqU3Pz-eP11cVNY3gnSsM0E_1AxQJq6VphDR0FgOGEWF5vjAPhHRDBek6ZloJbybtKG6kHQwU_QW93unWL72vIRU0uG_BeB4jrrBjrWyHbvtuib17Q9TCBVatUv5Ee1atHFTjfASbFnBOMyrjy256StPOKErUNRS3Vn1DUNhS1C6UKyL8EXmf8R-vlrhWqWZuak8rGQTBgXQJTlI3u3yLPgDavbw |
| CitedBy_id | crossref_primary_10_1007_s12652_022_03796_y crossref_primary_10_1088_2632_072X_ac24f3 crossref_primary_10_1016_j_cmpb_2021_106411 crossref_primary_10_1038_s41467_024_55461_x |
| Cites_doi | 10.1017/S0305004100030401 10.1016/j.engappai.2011.04.005 10.1016/j.ins.2018.04.056 10.1016/j.matcom.2016.11.010 10.1016/j.asoc.2014.12.015 10.1016/j.ecoinf.2006.07.003 10.1016/j.neucom.2014.01.078 10.1016/j.knosys.2016.06.022 10.1016/S0377-0427(03)00417-5 10.1049/iet-map.2008.0188 10.1016/j.engappai.2012.09.019 10.1016/j.ejor.2011.11.041 10.1016/j.biosystems.2008.05.004 10.1109/TSMCB.2008.926599 10.1016/j.biosystems.2011.02.001 10.1016/j.neunet.2007.04.003 10.1016/j.biosystems.2009.05.006 10.1016/j.ins.2018.12.019 10.1098/rspa.1927.0118 10.1016/j.swevo.2011.12.001 10.1016/j.mbs.2013.10.006 10.1016/j.cnsns.2016.12.025 10.1016/j.neucom.2013.05.063 10.1126/science.1091277 |
| ContentType | Journal Article |
| Copyright | 2019 Elsevier B.V. Copyright © 2019 Elsevier B.V. All rights reserved. |
| Copyright_xml | – notice: 2019 Elsevier B.V. – notice: Copyright © 2019 Elsevier B.V. All rights reserved. |
| DBID | AAYXX CITATION CGR CUY CVF ECM EIF NPM 7X8 |
| DOI | 10.1016/j.biosystems.2019.104029 |
| DatabaseName | CrossRef Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed MEDLINE - Academic |
| DatabaseTitle | CrossRef MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) MEDLINE - Academic |
| DatabaseTitleList | MEDLINE - Academic MEDLINE |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: EIF name: MEDLINE url: https://proxy.k.utb.cz/login?url=https://www.webofscience.com/wos/medline/basic-search sourceTypes: Index Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Biology |
| EISSN | 1872-8324 |
| ExternalDocumentID | 31540680 10_1016_j_biosystems_2019_104029 S0303264718301096 |
| Genre | Journal Article |
| GroupedDBID | --- --K --M -~X .GJ .~1 0R~ 1B1 1RT 1~. 1~5 23N 4.4 457 4G. 53G 5GY 5VS 7-5 71M 8P~ 9JM 9JN AABVA AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALCJ AALRI AAOAW AAQFI AATCM AATLK AAXUO ABAOU ABFNM ABGRD ABGSF ABJNI ABMAC ABUDA ABXDB ABYKQ ABZDS ACAZW ACDAQ ACGFS ACIUM ACNCT ACRLP ADBBV ADEZE ADGUI ADQTV ADUVX AEBSH AEHWI AEKER AENEX AEQOU AFKWA AFTJW AFXIZ AGHFR AGRDE AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALCLG ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CBWCG CS3 DOVZS DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HLV HVGLF HZ~ H~9 IHE J1W KOM LW9 M41 MHUIS MO0 MVM N9A O-L O9- OAUVE OGGZJ OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SAB SDF SDG SDP SES SEW SPC SPCBC SSA SSP SSU SSW SSZ T5K WH7 WUQ XPP ZGI ZMT ZXP ~02 ~G- AATTM AAXKI AAYWO AAYXX ACLOT ACVFH ADCNI AEIPS AEUPX AFJKZ AFPUW AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD CGR CUY CVF ECM EIF NPM 7X8 |
| ID | FETCH-LOGICAL-c374t-2a249b146e49b754dc1f4eec300d34dc23e037e0429312a843d8376e4c8abc143 |
| IEDL.DBID | .~1 |
| ISSN | 0303-2647 1872-8324 |
| IngestDate | Mon Sep 29 01:57:09 EDT 2025 Wed Feb 19 02:30:49 EST 2025 Thu Oct 09 00:24:02 EDT 2025 Thu Apr 24 23:05:17 EDT 2025 Fri Feb 23 02:50:48 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Adaptive critic design Numerical examples Particle swarm optimisation SIR model Optimal control problem Echo state networks Bernstein–Bézier curve Invasive weed optimisation |
| Language | English |
| License | Copyright © 2019 Elsevier B.V. All rights reserved. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c374t-2a249b146e49b754dc1f4eec300d34dc23e037e0429312a843d8376e4c8abc143 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| PMID | 31540680 |
| PQID | 2295485974 |
| PQPubID | 23479 |
| ParticipantIDs | proquest_miscellaneous_2295485974 pubmed_primary_31540680 crossref_citationtrail_10_1016_j_biosystems_2019_104029 crossref_primary_10_1016_j_biosystems_2019_104029 elsevier_sciencedirect_doi_10_1016_j_biosystems_2019_104029 |
| PublicationCentury | 2000 |
| PublicationDate | December 2019 2019-12-00 2019-Dec 20191201 |
| PublicationDateYYYYMMDD | 2019-12-01 |
| PublicationDate_xml | – month: 12 year: 2019 text: December 2019 |
| PublicationDecade | 2010 |
| PublicationPlace | Ireland |
| PublicationPlace_xml | – name: Ireland |
| PublicationTitle | BioSystems |
| PublicationTitleAlternate | Biosystems |
| PublicationYear | 2019 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Rodrigues, Monteiro, Torres (bib0170) 2014; 247 Werbos (bib0190) 1990 Beheshti, Shamsuddin (bib0010) 2015; 28 Pontryagin, Boltyanskii, Gamkrelidze, Mischenko (bib0155) 1983 Kirk (bib0120) 1989 Balakrishnan, Ding, Lewis (bib0005) 2008; 38 Zaman, Kang, Jung (bib0205) 2017; 136 Fleming, Rishel (bib0055) 1975 Jaeger (bib0085) 2002 Xu, Xu, Xie, Yang (bib0200) 2017; 48 Zaman, Kang, Jung (bib0210) 2008; 93 Roshanaei, Lucas, Mehrabian (bib0175) 2009; 3 Kermack, Mckendrick (bib0115) 1927; 115 Kar, Batabyal (bib0105) 2011; 104 Bryson (bib0030) 1999 Kandhway, Kuri (bib0100) 2014; 231 Zaman, Kang, Jung (bib0215) 2009; 98 Ferrari, Stengel (bib0050) 2004 Zhou, Luo, He, Wu (bib0225) 2015; 151 Kennedy, Eberhart (bib0110) 1995 Gantmacher (bib0060) 1959 Grothey, Yang (bib0075) 2012; 218 Cao, Xu, Goodman (bib0035) 2018; 453 Farin (bib0045) 1993 Kmet, Kmetova (bib0135) 2017 Penrose (bib0150) 1955; 51 Pourjafari, Mojallali (bib0160) 2012; 4 Zhou, Chen, Zhou (bib0220) 2014; 137 Ongenae, Van Looy, Verstraeten, Verplancke, Decruyenaere (bib0145) 2013; 26 Ghosh, Das, Chowdhury, Giri (bib0065) 2011; 24 Kmet, Kmetova (bib0130) 2017 Kmet, Kmetova (bib0125) 2016 Mehrabian, Lucas (bib0140) 2006; 1 Chen, Wang, Cao, Wu (bib0040) 2019; 482 Jaeger (bib0080) 2001 Verstraeten, Schrauwen, D’Haene, Stroobandt (bib0180) 2007; 20 Borzi (bib0020) 2003; 157 Rabie, El-Khodary, Tharwart (bib0165) 2013; 4 Jung, Lenhart, Feng (bib0095) 2002; 2 Brauer (bib0025) 2001 Jaeger, Haas (bib0090) 2004; 304 Werbos (bib0195) 1992 Wang, Zang, Lin, Zhao, Hu (bib0185) 2016; 109 Binitha, Sathya (bib0015) 2012; 2 Giri, Chowdhury, Ghosh, Das, Abraham, Snasel (bib0070) 2010 Giri (10.1016/j.biosystems.2019.104029_bib0070) 2010 Kermack (10.1016/j.biosystems.2019.104029_bib0115) 1927; 115 Ongenae (10.1016/j.biosystems.2019.104029_bib0145) 2013; 26 Mehrabian (10.1016/j.biosystems.2019.104029_bib0140) 2006; 1 Penrose (10.1016/j.biosystems.2019.104029_bib0150) 1955; 51 Bryson (10.1016/j.biosystems.2019.104029_bib0030) 1999 Wang (10.1016/j.biosystems.2019.104029_bib0185) 2016; 109 Zhou (10.1016/j.biosystems.2019.104029_bib0225) 2015; 151 Pourjafari (10.1016/j.biosystems.2019.104029_bib0160) 2012; 4 Zhou (10.1016/j.biosystems.2019.104029_bib0220) 2014; 137 Werbos (10.1016/j.biosystems.2019.104029_bib0195) 1992 Chen (10.1016/j.biosystems.2019.104029_bib0040) 2019; 482 Kmet (10.1016/j.biosystems.2019.104029_bib0125) 2016 Xu (10.1016/j.biosystems.2019.104029_bib0200) 2017; 48 Roshanaei (10.1016/j.biosystems.2019.104029_bib0175) 2009; 3 Zaman (10.1016/j.biosystems.2019.104029_bib0215) 2009; 98 Grothey (10.1016/j.biosystems.2019.104029_bib0075) 2012; 218 Kmet (10.1016/j.biosystems.2019.104029_bib0135) 2017 Kmet (10.1016/j.biosystems.2019.104029_bib0130) 2017 Kennedy (10.1016/j.biosystems.2019.104029_bib0110) 1995 Ferrari (10.1016/j.biosystems.2019.104029_bib0050) 2004 Kar (10.1016/j.biosystems.2019.104029_bib0105) 2011; 104 Jaeger (10.1016/j.biosystems.2019.104029_bib0085) 2002 Kirk (10.1016/j.biosystems.2019.104029_bib0120) 1989 Gantmacher (10.1016/j.biosystems.2019.104029_bib0060) 1959 Kandhway (10.1016/j.biosystems.2019.104029_bib0100) 2014; 231 Zaman (10.1016/j.biosystems.2019.104029_bib0205) 2017; 136 Jaeger (10.1016/j.biosystems.2019.104029_bib0080) 2001 Ghosh (10.1016/j.biosystems.2019.104029_bib0065) 2011; 24 Werbos (10.1016/j.biosystems.2019.104029_bib0190) 1990 Rabie (10.1016/j.biosystems.2019.104029_bib0165) 2013; 4 Jaeger (10.1016/j.biosystems.2019.104029_bib0090) 2004; 304 Jung (10.1016/j.biosystems.2019.104029_bib0095) 2002; 2 Fleming (10.1016/j.biosystems.2019.104029_bib0055) 1975 Verstraeten (10.1016/j.biosystems.2019.104029_bib0180) 2007; 20 Zaman (10.1016/j.biosystems.2019.104029_bib0210) 2008; 93 Brauer (10.1016/j.biosystems.2019.104029_bib0025) 2001 Farin (10.1016/j.biosystems.2019.104029_bib0045) 1993 Pontryagin (10.1016/j.biosystems.2019.104029_bib0155) 1983 Balakrishnan (10.1016/j.biosystems.2019.104029_bib0005) 2008; 38 Borzi (10.1016/j.biosystems.2019.104029_bib0020) 2003; 157 Rodrigues (10.1016/j.biosystems.2019.104029_bib0170) 2014; 247 Cao (10.1016/j.biosystems.2019.104029_bib0035) 2018; 453 Beheshti (10.1016/j.biosystems.2019.104029_bib0010) 2015; 28 Binitha (10.1016/j.biosystems.2019.104029_bib0015) 2012; 2 |
| References_xml | – volume: 98 start-page: 43 year: 2009 end-page: 50 ident: bib0215 article-title: Optimal treatment of an SIR epidemic model with time delay publication-title: BioSystems – volume: 38 start-page: 913 year: 2008 end-page: 916 ident: bib0005 article-title: Issues on stability of ADP feedback controllers for dynamical systems publication-title: IEEE Trans. Syst. Man Cybern. Part B: Cybern. – volume: 136 start-page: 63 year: 2017 end-page: 77 ident: bib0205 article-title: Optimal strategy of vaccination and treatment in an SIR epidemic model publication-title: Math. Comput. Simul. Biosyst. – year: 1983 ident: bib0155 article-title: Freshwater Ecosystems. Modelling and Simulation, Developments in Environmental Modelling – year: 1959 ident: bib0060 article-title: The Theory of Matrices, Vol. 2 – volume: 231 start-page: 79 year: 2014 end-page: 92 ident: bib0100 article-title: How to run a campaign: optimal control of SIS and SIR information epidemics publication-title: Appl. Math. Comput. – volume: 304 start-page: 78 year: 2004 end-page: 80 ident: bib0090 article-title: Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication publication-title: Science – volume: 4 start-page: 101 year: 2013 end-page: 106 ident: bib0165 article-title: A particle swarm optimization algorithm for the continuous absolute p-center location problem with Euclidean distance publication-title: Int. J. Adv. Comput. Sci. Appl. – volume: 3 start-page: 765 year: 2009 end-page: 773 ident: bib0175 article-title: Adaptive beam forming using a novel numerical optimisation algorithm publication-title: IET Microwaves Anten. Propag. – volume: 109 start-page: 35 year: 2016 end-page: 47 ident: bib0185 article-title: Computational model and optimal control strategies for emotion contagion in the human population in emergencies publication-title: Knowl.-Based Syst. – start-page: 100 year: 2017 end-page: 110 ident: bib0130 article-title: Bézier curve parametrization methods for solving optimal control problems of SIR model publication-title: LNCS 10687 Theory and Practice of Natural Computing – TPNC 2017 – volume: 28 start-page: 345 year: 2015 end-page: 359 ident: bib0010 article-title: Non-parametric particle swarm optimization for global optimization publication-title: Appl. Soft Comput. – volume: 218 start-page: 698 year: 2012 end-page: 707 ident: bib0075 article-title: Approximate dynamic programming with Bézier curves/surfaces for top-percentile traffic routing publication-title: Eur. J. Oper. Res. – volume: 104 start-page: 127 year: 2011 end-page: 135 ident: bib0105 article-title: Stability analysis and optimal control of an SIR epidemic model with vaccination publication-title: Biosyst. Sci. – volume: 137 start-page: 285 year: 2014 end-page: 292 ident: bib0220 article-title: Invasive weed optimization algorithm for optimization no-idle flow shop scheduling problem publication-title: Neurocomputing – start-page: 3166 year: 2010 end-page: 3173 ident: bib0070 article-title: A modified invasive weed optimization algorithm for training of feed-forward neural networks publication-title: IEEE International Conference on Systems Man and Cybernetics – year: 2001 ident: bib0080 article-title: The “Echo State” Approach to Analysing and Training Recurrent Neural Networks. Technical Report GMD 148 – start-page: 468 year: 2016 end-page: 477 ident: bib0125 article-title: Neural networks simulation of distributed control problems with state and control constraints publication-title: LNCS 9886 Artificial Neural Networks and Machine Learning – ICANN 2016 – volume: 453 start-page: 463 year: 2018 end-page: 485 ident: bib0035 article-title: A neighbor-based learning particle swarm optimizer with short-term and long-term memory for dynamic optimization problems publication-title: Inform. Sci. – volume: 26 start-page: 984 year: 2013 end-page: 996 ident: bib0145 article-title: Time series classification for the prediction of dialysis in critically ill patients using echo state networks publication-title: Eng. Appl. Artif. Intell. – start-page: 493 year: 1992 end-page: 525 ident: bib0195 article-title: Approximate dynamic programming for real-time control and neural modelling publication-title: Handbook of intelligent control: Neural Fuzzy, and Adaptive Approaches – volume: 482 start-page: 139 year: 2019 end-page: 155 ident: bib0040 article-title: Gaussian-kernel-based adaptive critic design using two-phase value iteration publication-title: Inform. Sci. – year: 1975 ident: bib0055 article-title: Deterministic and Stochastic Optimal Control – volume: 24 start-page: 1195 year: 2011 end-page: 1203 ident: bib0065 article-title: An ecologically inspired direct search method for solving optimal control problems with Bézier parameterization publication-title: Eng. Appl. Artif. Intell. – volume: 51 start-page: 406 year: 1955 end-page: 413 ident: bib0150 article-title: A generalized inverse for matrices publication-title: Math. Proc. Cambr. Philos. Soc. – start-page: 468 year: 2004 end-page: 477 ident: bib0050 article-title: Model-based adaptive critic designs publication-title: Learning and Approximate Dynamic Programming: Scaling Up to the Real World – volume: 151 start-page: 1227 year: 2015 end-page: 1236 ident: bib0225 article-title: A discrete invasive weed optimization algorithm for solving salesman problem publication-title: Neurocomputing – year: 1999 ident: bib0030 article-title: Dynamic optimization – year: 1993 ident: bib0045 article-title: Curves and Surfaces for Computer Aided Geometric Design – A Practical Guide – start-page: 86 year: 2017 end-page: 96 ident: bib0135 article-title: Echo state networks simulation of sir distributed control publication-title: LNAI 10245 Artificial Intelligence and Soft Computing AISC 2017 – volume: 115 start-page: 700 year: 1927 end-page: 721 ident: bib0115 article-title: Contribution to the mathematical theory of epidemic publication-title: Proc. R. Soc. Lond. Ser. A – volume: 1 start-page: 355 year: 2006 end-page: 366 ident: bib0140 article-title: A novel numerical optimization algorithm inspired from weed colonization publication-title: Ecol. Inform. – volume: 48 start-page: 200 year: 2017 end-page: 210 ident: bib0200 article-title: Optimal control of an SIVRS epidemic model with virus variation based on complex networks publication-title: Commun. Nonlinear Sci. Numer. Simul. – start-page: 493 year: 1990 end-page: 525 ident: bib0190 article-title: A menu of designs for reinforcement learning over time publication-title: Neural Networks for Control – year: 2002 ident: bib0085 article-title: Short Term Memory in Echo State Networks. Technical Report GMD 152 – volume: 4 start-page: 33 year: 2012 end-page: 43 ident: bib0160 article-title: Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering publication-title: Swarm Evol. Comput. – year: 1989 ident: bib0120 article-title: Optimal Control Theory: An Introduction – start-page: 1942 year: 1995 end-page: 1948 ident: bib0110 article-title: Particle swarm optimization publication-title: IEEE International Conference on Neural Networks – volume: 157 start-page: 365 year: 2003 end-page: 382 ident: bib0020 article-title: Multigrid methods for parabolic distributed optimal control problems publication-title: J. Comput. Appl. Math. – volume: 247 start-page: 1 year: 2014 end-page: 12 ident: bib0170 article-title: Vaccination models and optimal control strategies to dengue publication-title: Math. Biosci. – year: 2001 ident: bib0025 article-title: Mathematical Models in Population Biology and Epidemiology – volume: 20 start-page: 414 year: 2007 end-page: 423 ident: bib0180 article-title: An experimental unification of reservoir computing methods publication-title: Neural Netw. – volume: 93 start-page: 240 year: 2008 end-page: 249 ident: bib0210 article-title: Stability analysis and optimal vaccination of an SIR epidemic model publication-title: BioSystems – volume: 2 start-page: 137 year: 2012 end-page: 151 ident: bib0015 article-title: A survey of bio-inspired optimization algorithms publication-title: Int. J. Soft Eng. – volume: 2 start-page: 473 year: 2002 end-page: 482 ident: bib0095 article-title: Optimal control of treatments in a two-strain tuberculosis model publication-title: Discr. Cont. Dyn. Syst. – volume: 51 start-page: 406 year: 1955 ident: 10.1016/j.biosystems.2019.104029_bib0150 article-title: A generalized inverse for matrices publication-title: Math. Proc. Cambr. Philos. Soc. doi: 10.1017/S0305004100030401 – volume: 24 start-page: 1195 year: 2011 ident: 10.1016/j.biosystems.2019.104029_bib0065 article-title: An ecologically inspired direct search method for solving optimal control problems with Bézier parameterization publication-title: Eng. Appl. Artif. Intell. doi: 10.1016/j.engappai.2011.04.005 – start-page: 86 year: 2017 ident: 10.1016/j.biosystems.2019.104029_bib0135 article-title: Echo state networks simulation of sir distributed control – volume: 453 start-page: 463 year: 2018 ident: 10.1016/j.biosystems.2019.104029_bib0035 article-title: A neighbor-based learning particle swarm optimizer with short-term and long-term memory for dynamic optimization problems publication-title: Inform. Sci. doi: 10.1016/j.ins.2018.04.056 – volume: 136 start-page: 63 year: 2017 ident: 10.1016/j.biosystems.2019.104029_bib0205 article-title: Optimal strategy of vaccination and treatment in an SIR epidemic model publication-title: Math. Comput. Simul. Biosyst. doi: 10.1016/j.matcom.2016.11.010 – volume: 2 start-page: 137 year: 2012 ident: 10.1016/j.biosystems.2019.104029_bib0015 article-title: A survey of bio-inspired optimization algorithms publication-title: Int. J. Soft Eng. – year: 2001 ident: 10.1016/j.biosystems.2019.104029_bib0025 – start-page: 493 year: 1992 ident: 10.1016/j.biosystems.2019.104029_bib0195 article-title: Approximate dynamic programming for real-time control and neural modelling – year: 1989 ident: 10.1016/j.biosystems.2019.104029_bib0120 – volume: 28 start-page: 345 year: 2015 ident: 10.1016/j.biosystems.2019.104029_bib0010 article-title: Non-parametric particle swarm optimization for global optimization publication-title: Appl. Soft Comput. doi: 10.1016/j.asoc.2014.12.015 – volume: 1 start-page: 355 issue: 4 year: 2006 ident: 10.1016/j.biosystems.2019.104029_bib0140 article-title: A novel numerical optimization algorithm inspired from weed colonization publication-title: Ecol. Inform. doi: 10.1016/j.ecoinf.2006.07.003 – volume: 151 start-page: 1227 year: 2015 ident: 10.1016/j.biosystems.2019.104029_bib0225 article-title: A discrete invasive weed optimization algorithm for solving salesman problem publication-title: Neurocomputing doi: 10.1016/j.neucom.2014.01.078 – year: 1993 ident: 10.1016/j.biosystems.2019.104029_bib0045 – start-page: 468 year: 2016 ident: 10.1016/j.biosystems.2019.104029_bib0125 article-title: Neural networks simulation of distributed control problems with state and control constraints – volume: 109 start-page: 35 year: 2016 ident: 10.1016/j.biosystems.2019.104029_bib0185 article-title: Computational model and optimal control strategies for emotion contagion in the human population in emergencies publication-title: Knowl.-Based Syst. doi: 10.1016/j.knosys.2016.06.022 – volume: 157 start-page: 365 year: 2003 ident: 10.1016/j.biosystems.2019.104029_bib0020 article-title: Multigrid methods for parabolic distributed optimal control problems publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(03)00417-5 – volume: 3 start-page: 765 issue: 5 year: 2009 ident: 10.1016/j.biosystems.2019.104029_bib0175 article-title: Adaptive beam forming using a novel numerical optimisation algorithm publication-title: IET Microwaves Anten. Propag. doi: 10.1049/iet-map.2008.0188 – year: 1999 ident: 10.1016/j.biosystems.2019.104029_bib0030 – volume: 2 start-page: 473 issue: 4 year: 2002 ident: 10.1016/j.biosystems.2019.104029_bib0095 article-title: Optimal control of treatments in a two-strain tuberculosis model publication-title: Discr. Cont. Dyn. Syst. – volume: 26 start-page: 984 year: 2013 ident: 10.1016/j.biosystems.2019.104029_bib0145 article-title: Time series classification for the prediction of dialysis in critically ill patients using echo state networks publication-title: Eng. Appl. Artif. Intell. doi: 10.1016/j.engappai.2012.09.019 – year: 1975 ident: 10.1016/j.biosystems.2019.104029_bib0055 – volume: 218 start-page: 698 year: 2012 ident: 10.1016/j.biosystems.2019.104029_bib0075 article-title: Approximate dynamic programming with Bézier curves/surfaces for top-percentile traffic routing publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2011.11.041 – year: 2002 ident: 10.1016/j.biosystems.2019.104029_bib0085 – volume: 93 start-page: 240 year: 2008 ident: 10.1016/j.biosystems.2019.104029_bib0210 article-title: Stability analysis and optimal vaccination of an SIR epidemic model publication-title: BioSystems doi: 10.1016/j.biosystems.2008.05.004 – volume: 38 start-page: 913 issue: 4 year: 2008 ident: 10.1016/j.biosystems.2019.104029_bib0005 article-title: Issues on stability of ADP feedback controllers for dynamical systems publication-title: IEEE Trans. Syst. Man Cybern. Part B: Cybern. doi: 10.1109/TSMCB.2008.926599 – year: 2001 ident: 10.1016/j.biosystems.2019.104029_bib0080 – volume: 231 start-page: 79 year: 2014 ident: 10.1016/j.biosystems.2019.104029_bib0100 article-title: How to run a campaign: optimal control of SIS and SIR information epidemics publication-title: Appl. Math. Comput. – volume: 104 start-page: 127 year: 2011 ident: 10.1016/j.biosystems.2019.104029_bib0105 article-title: Stability analysis and optimal control of an SIR epidemic model with vaccination publication-title: Biosyst. Sci. doi: 10.1016/j.biosystems.2011.02.001 – volume: 20 start-page: 414 issue: 3 year: 2007 ident: 10.1016/j.biosystems.2019.104029_bib0180 article-title: An experimental unification of reservoir computing methods publication-title: Neural Netw. doi: 10.1016/j.neunet.2007.04.003 – volume: 98 start-page: 43 year: 2009 ident: 10.1016/j.biosystems.2019.104029_bib0215 article-title: Optimal treatment of an SIR epidemic model with time delay publication-title: BioSystems doi: 10.1016/j.biosystems.2009.05.006 – year: 1959 ident: 10.1016/j.biosystems.2019.104029_bib0060 – start-page: 1942 year: 1995 ident: 10.1016/j.biosystems.2019.104029_bib0110 article-title: Particle swarm optimization – volume: 482 start-page: 139 year: 2019 ident: 10.1016/j.biosystems.2019.104029_bib0040 article-title: Gaussian-kernel-based adaptive critic design using two-phase value iteration publication-title: Inform. Sci. doi: 10.1016/j.ins.2018.12.019 – start-page: 3166 year: 2010 ident: 10.1016/j.biosystems.2019.104029_bib0070 article-title: A modified invasive weed optimization algorithm for training of feed-forward neural networks – volume: 115 start-page: 700 year: 1927 ident: 10.1016/j.biosystems.2019.104029_bib0115 article-title: Contribution to the mathematical theory of epidemic publication-title: Proc. R. Soc. Lond. Ser. A doi: 10.1098/rspa.1927.0118 – start-page: 100 year: 2017 ident: 10.1016/j.biosystems.2019.104029_bib0130 article-title: Bézier curve parametrization methods for solving optimal control problems of SIR model – volume: 4 start-page: 33 year: 2012 ident: 10.1016/j.biosystems.2019.104029_bib0160 article-title: Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering publication-title: Swarm Evol. Comput. doi: 10.1016/j.swevo.2011.12.001 – volume: 247 start-page: 1 year: 2014 ident: 10.1016/j.biosystems.2019.104029_bib0170 article-title: Vaccination models and optimal control strategies to dengue publication-title: Math. Biosci. doi: 10.1016/j.mbs.2013.10.006 – volume: 48 start-page: 200 year: 2017 ident: 10.1016/j.biosystems.2019.104029_bib0200 article-title: Optimal control of an SIVRS epidemic model with virus variation based on complex networks publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2016.12.025 – volume: 137 start-page: 285 year: 2014 ident: 10.1016/j.biosystems.2019.104029_bib0220 article-title: Invasive weed optimization algorithm for optimization no-idle flow shop scheduling problem publication-title: Neurocomputing doi: 10.1016/j.neucom.2013.05.063 – start-page: 468 year: 2004 ident: 10.1016/j.biosystems.2019.104029_bib0050 article-title: Model-based adaptive critic designs – start-page: 493 year: 1990 ident: 10.1016/j.biosystems.2019.104029_bib0190 article-title: A menu of designs for reinforcement learning over time – volume: 304 start-page: 78 year: 2004 ident: 10.1016/j.biosystems.2019.104029_bib0090 article-title: Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication publication-title: Science doi: 10.1126/science.1091277 – year: 1983 ident: 10.1016/j.biosystems.2019.104029_bib0155 – volume: 4 start-page: 101 year: 2013 ident: 10.1016/j.biosystems.2019.104029_bib0165 article-title: A particle swarm optimization algorithm for the continuous absolute p-center location problem with Euclidean distance publication-title: Int. J. Adv. Comput. Sci. Appl. |
| SSID | ssj0000581 |
| Score | 2.2539115 |
| Snippet | In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the... |
| SourceID | proquest pubmed crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 104029 |
| SubjectTerms | Adaptive critic design Algorithms Bernstein–Bézier curve Echo state networks Humans Invasive weed optimisation Models, Theoretical Neural Networks, Computer Numerical examples Optimal control problem Particle swarm optimisation SIR model |
| Title | Bézier curve parametrisation and echo state network methods for solving optimal control problems of SIR model |
| URI | https://dx.doi.org/10.1016/j.biosystems.2019.104029 https://www.ncbi.nlm.nih.gov/pubmed/31540680 https://www.proquest.com/docview/2295485974 |
| Volume | 186 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Baden-Württemberg Complete Freedom Collection (Elsevier) customDbUrl: eissn: 1872-8324 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000581 issn: 0303-2647 databaseCode: GBLVA dateStart: 20110101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier ScienceDirect [Accès UNIL ; CHUV ; HEP Vaud ; Sites BCUL] customDbUrl: eissn: 1872-8324 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000581 issn: 0303-2647 databaseCode: ACRLP dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals [SCFCJ] customDbUrl: eissn: 1872-8324 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000581 issn: 0303-2647 databaseCode: AIKHN dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Science Direct customDbUrl: eissn: 1872-8324 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000581 issn: 0303-2647 databaseCode: .~1 dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals customDbUrl: mediaType: online eissn: 1872-8324 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000581 issn: 0303-2647 databaseCode: AKRWK dateStart: 19670301 isFulltext: true providerName: Library Specific Holdings |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1fS8MwEA9jIvgi_nf-GRF8rWuXtKn4NIcyHe5hU_StpEkGE9eK2wR98Pv4Ofxi3jWpQ1AQfAopSRNy6eWu98v9CDksUnYrE3lhrFOPgw_ipTzinoyGcaB0KHyBt5GvelHnhl_ehXcV0i7vwiCs0ul-q9MLbe2eNNxqNh5Ho8YAtifYHqhcGcZ3MO025wJZDI7e5jAPPyyISrExormEQ_NYjFc6ym3CZEzcHRxjwNMvjM0fj6jfTNDiKDpfIcvOhqQtO81VUjHZGlm0rJIv6yQ7_Xh_hVdRNXt6NhSTe4-RN8vidqjMNDWg9Ghxl4hmFgdOLZX0hIIRS2E_4n8GmoM-GcNIDs9OHfvMhOZDOrjo04JGZ4PcnJ9dtzueo1XwFBN86jUluFwpaEgDhQi5VsGQG6OY72sGtSYzPhMGTyoWNGXMmQYvFlqrWKYK7KtNUs3yzGwTylOhuPKlEQzcSiWkjBn0MVpHcaQ1qxFRrmSiXM5xpL54SEpw2X0yl0GCMkisDGok-Or5aPNu_KHPSSms5NseSuB4-EPvg1K-CXxiGDeRmcln0AhjoTF6XjWyZQX_NScGJijSl-z8a-xdsoQ1C5PZI9Xp08zsg7EzTevFbq6ThdZFt9PDstu_7X4CLv8DCw |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NTtwwEB4BFYILogXK8tO6EtewydqJU3ECBFrahUMBiZvl2F5pKzZZLbtIcOB9eI6-GDOxw6oSlZB6ipJ4YivjzE_8eT6Avbpkt3FZlOa2iATmIFEhMhHprJ8nxqYylrQb-fwi616LHzfpzRwcN3thCFYZbL-36bW1Dlfa4W22R4NB-xKnJ8YeZFw5re9k8_BBpB1JGdj-0wznEac1Uym1JjiXDHAeD_IqBpWvmEyVu5PvtOIZ19Hmmz7qXzFo7YtOV2ElBJHs0I_zI8y58hMselrJhzUoj_48P-KjmJmO7x2j6t5DIs7ywB2mS8scWj1WbyZipQeCM88lfccwimU4IelHA6vQoAyxpwBoZ4F-5o5VfXZ59ovVPDrrcH16cnXcjQKvQmS4FJOoozHnKtBEOjzIVFiT9IVzhsex5XjW4S7m0pGr4klH54JbTGOxtcl1YTDA2oCFsirdJjBRSCNMrJ3kmFcaqXXOUcZZm-WZtbwFsnmTyoSi48R9casadNlvNdOBIh0or4MWJK-SI1944x0yB42y1F-TSKF_eIf0t0a_Cr8xWjjRpaum2IgWQ3NKvVrw2Sv-dUwcY1DiL9n6r76_wlL36rynemcXP7dhme54zMwOLEzGU7eLkc-k-FLP7BcBHgL9 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=B%C3%A9zier+curve+parametrisation+and+echo+state+network+methods+for+solving+optimal+control+problems+of+SIR+model&rft.jtitle=BioSystems&rft.au=Kmet%2C+Tibor&rft.au=Kmetova%2C+Maria&rft.date=2019-12-01&rft.issn=1872-8324&rft.eissn=1872-8324&rft.volume=186&rft.spage=104029&rft_id=info:doi/10.1016%2Fj.biosystems.2019.104029&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0303-2647&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0303-2647&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0303-2647&client=summon |