Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives.
Identifieur interne : 001C49 ( Main/Exploration ); précédent : 001C48; suivant : 001C50Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives.
Auteurs : Khondoker Nazmoon Nabi [Bangladesh] ; Hamadjam Abboubakar [Cameroun] ; Pushpendra Kumar [Inde]Source :
- Chaos, solitons, and fractals [ 0960-0779 ] ; 2020.
Abstract
In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number, R 0 R 0 ( 95 % CI : 2.2 - 4.4 ) ( 95 % CI : 714 - 1654 ) ( 95 % CI : 17 , 343 - 24 , 584 )
DOI: 10.1016/j.chaos.2020.110283
PubMed: 32982078
PubMed Central: PMC7505562
Affiliations:
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives.</title><author><name sortKey="Nabi, Khondoker Nazmoon" sort="Nabi, Khondoker Nazmoon" uniqKey="Nabi K" first="Khondoker Nazmoon" last="Nabi">Khondoker Nazmoon Nabi</name><affiliation wicri:level="1"><nlm:affiliation>Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000, Bangladesh.</nlm:affiliation><country xml:lang="fr">Bangladesh</country><wicri:regionArea>Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000</wicri:regionArea><wicri:noRegion>Dhaka 1000</wicri:noRegion></affiliation></author><author><name sortKey="Abboubakar, Hamadjam" sort="Abboubakar, Hamadjam" uniqKey="Abboubakar H" first="Hamadjam" last="Abboubakar">Hamadjam Abboubakar</name><affiliation wicri:level="1"><nlm:affiliation>Department of Computer Engineering, University Institute of Technology of Ngaoundéré, University of Ngaoundéré, Ngaoundéré, PO Box 455, Cameroon.</nlm:affiliation><country xml:lang="fr">Cameroun</country><wicri:regionArea>Department of Computer Engineering, University Institute of Technology of Ngaoundéré, University of Ngaoundéré, Ngaoundéré, PO Box 455</wicri:regionArea><wicri:noRegion>PO Box 455</wicri:noRegion></affiliation></author><author><name sortKey="Kumar, Pushpendra" sort="Kumar, Pushpendra" uniqKey="Kumar P" first="Pushpendra" last="Kumar">Pushpendra Kumar</name><affiliation wicri:level="1"><nlm:affiliation>Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab 151001, India.</nlm:affiliation><country xml:lang="fr">Inde</country><wicri:regionArea>Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab 151001</wicri:regionArea><wicri:noRegion>Punjab 151001</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PubMed</idno><date when="2020">2020</date><idno type="RBID">pubmed:32982078</idno><idno type="pmid">32982078</idno><idno type="doi">10.1016/j.chaos.2020.110283</idno><idno type="pmc">PMC7505562</idno><idno type="wicri:Area/Main/Corpus">001531</idno><idno type="wicri:explorRef" wicri:stream="Main" wicri:step="Corpus" wicri:corpus="PubMed">001531</idno><idno type="wicri:Area/Main/Curation">001531</idno><idno type="wicri:explorRef" wicri:stream="Main" wicri:step="Curation">001531</idno><idno type="wicri:Area/Main/Exploration">001531</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives.</title><author><name sortKey="Nabi, Khondoker Nazmoon" sort="Nabi, Khondoker Nazmoon" uniqKey="Nabi K" first="Khondoker Nazmoon" last="Nabi">Khondoker Nazmoon Nabi</name><affiliation wicri:level="1"><nlm:affiliation>Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000, Bangladesh.</nlm:affiliation><country xml:lang="fr">Bangladesh</country><wicri:regionArea>Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000</wicri:regionArea><wicri:noRegion>Dhaka 1000</wicri:noRegion></affiliation></author><author><name sortKey="Abboubakar, Hamadjam" sort="Abboubakar, Hamadjam" uniqKey="Abboubakar H" first="Hamadjam" last="Abboubakar">Hamadjam Abboubakar</name><affiliation wicri:level="1"><nlm:affiliation>Department of Computer Engineering, University Institute of Technology of Ngaoundéré, University of Ngaoundéré, Ngaoundéré, PO Box 455, Cameroon.</nlm:affiliation><country xml:lang="fr">Cameroun</country><wicri:regionArea>Department of Computer Engineering, University Institute of Technology of Ngaoundéré, University of Ngaoundéré, Ngaoundéré, PO Box 455</wicri:regionArea><wicri:noRegion>PO Box 455</wicri:noRegion></affiliation></author><author><name sortKey="Kumar, Pushpendra" sort="Kumar, Pushpendra" uniqKey="Kumar P" first="Pushpendra" last="Kumar">Pushpendra Kumar</name><affiliation wicri:level="1"><nlm:affiliation>Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab 151001, India.</nlm:affiliation><country xml:lang="fr">Inde</country><wicri:regionArea>Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab 151001</wicri:regionArea><wicri:noRegion>Punjab 151001</wicri:noRegion></affiliation></author></analytic><series><title level="j">Chaos, solitons, and fractals</title><idno type="ISSN">0960-0779</idno><imprint><date when="2020" type="published">2020</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number, <mml:math><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> of the model has been presented. Cameroon has been considered as a representative for the developing countries and the epidemic threshold, <mml:math><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> has been estimated to be ~ 3.41 <mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>95</mml:mn><mml:mo>%</mml:mo><mml:mspace></mml:mspace><mml:mtext>CI</mml:mtext><mml:mo>:</mml:mo><mml:mn>2.2</mml:mn><mml:mo>-</mml:mo><mml:mn>4.4</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> as of July 9, 2020. Using real data compiled by the Cameroonian government, model calibration has been performed through an optimization algorithm based on renowned trust-region-reflective (TRR) algorithm. Based on our projection results, the probable peak date is estimated to be on August 1, 2020 with approximately 1073 <mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>95</mml:mn><mml:mo>%</mml:mo><mml:mspace></mml:mspace><mml:mtext>CI</mml:mtext><mml:mo>:</mml:mo><mml:mn>714</mml:mn><mml:mo>-</mml:mo><mml:mn>1654</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> daily confirmed cases. The tally of cumulative infected cases could reach ~ 20, 100 <mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>95</mml:mn><mml:mo>%</mml:mo><mml:mspace></mml:mspace><mml:mtext>CI</mml:mtext><mml:mo>:</mml:mo><mml:mn>17</mml:mn><mml:mo>,</mml:mo><mml:mn>343</mml:mn><mml:mo>-</mml:mo><mml:mn>24</mml:mn><mml:mo>,</mml:mo><mml:mn>584</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> cases by the end of August 2020. Later, global sensitivity analysis has been applied to quantify the most dominating model mechanisms that significantly affect the progression dynamics of COVID-19. Importantly, Caputo derivative concept has been performed to formulate a fractional model to gain a deeper insight into the probable peak dates and sizes in Cameroon. By showing the existence and uniqueness of solutions, a numerical scheme has been constructed using the Adams-Bashforth-Moulton method. Numerical simulations have enlightened the fact that if the fractional order <i>α</i> is close to unity, then the solutions will converge to the integer model solutions, and the decrease of the fractional-order parameter (0 < <i>α</i> < 1) leads to the delaying of the epidemic peaks.</div></front></TEI><pubmed><MedlineCitation Status="PubMed-not-MEDLINE" Owner="NLM"><PMID Version="1">32982078</PMID><DateRevised><Year>2020</Year><Month>10</Month><Day>29</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Print">0960-0779</ISSN><JournalIssue CitedMedium="Print"><Volume>141</Volume><PubDate><Year>2020</Year><Month>Dec</Month></PubDate></JournalIssue><Title>Chaos, solitons, and fractals</Title><ISOAbbreviation>Chaos Solitons Fractals</ISOAbbreviation></Journal><ArticleTitle>Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives.</ArticleTitle><Pagination><MedlinePgn>110283</MedlinePgn></Pagination><ELocationID EIdType="doi" ValidYN="Y">10.1016/j.chaos.2020.110283</ELocationID><Abstract><AbstractText>In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number, <mml:math><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> of the model has been presented. Cameroon has been considered as a representative for the developing countries and the epidemic threshold, <mml:math><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> has been estimated to be ~ 3.41 <mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>95</mml:mn><mml:mo>%</mml:mo><mml:mspace></mml:mspace><mml:mtext>CI</mml:mtext><mml:mo>:</mml:mo><mml:mn>2.2</mml:mn><mml:mo>-</mml:mo><mml:mn>4.4</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> as of July 9, 2020. Using real data compiled by the Cameroonian government, model calibration has been performed through an optimization algorithm based on renowned trust-region-reflective (TRR) algorithm. Based on our projection results, the probable peak date is estimated to be on August 1, 2020 with approximately 1073 <mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>95</mml:mn><mml:mo>%</mml:mo><mml:mspace></mml:mspace><mml:mtext>CI</mml:mtext><mml:mo>:</mml:mo><mml:mn>714</mml:mn><mml:mo>-</mml:mo><mml:mn>1654</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> daily confirmed cases. The tally of cumulative infected cases could reach ~ 20, 100 <mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>95</mml:mn><mml:mo>%</mml:mo><mml:mspace></mml:mspace><mml:mtext>CI</mml:mtext><mml:mo>:</mml:mo><mml:mn>17</mml:mn><mml:mo>,</mml:mo><mml:mn>343</mml:mn><mml:mo>-</mml:mo><mml:mn>24</mml:mn><mml:mo>,</mml:mo><mml:mn>584</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> cases by the end of August 2020. Later, global sensitivity analysis has been applied to quantify the most dominating model mechanisms that significantly affect the progression dynamics of COVID-19. Importantly, Caputo derivative concept has been performed to formulate a fractional model to gain a deeper insight into the probable peak dates and sizes in Cameroon. By showing the existence and uniqueness of solutions, a numerical scheme has been constructed using the Adams-Bashforth-Moulton method. Numerical simulations have enlightened the fact that if the fractional order <i>α</i> is close to unity, then the solutions will converge to the integer model solutions, and the decrease of the fractional-order parameter (0 < <i>α</i> < 1) leads to the delaying of the epidemic peaks.</AbstractText><CopyrightInformation>© 2020 Elsevier Ltd. All rights reserved.</CopyrightInformation></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Nabi</LastName><ForeName>Khondoker Nazmoon</ForeName><Initials>KN</Initials><AffiliationInfo><Affiliation>Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000, Bangladesh.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Abboubakar</LastName><ForeName>Hamadjam</ForeName><Initials>H</Initials><AffiliationInfo><Affiliation>Department of Computer Engineering, University Institute of Technology of Ngaoundéré, University of Ngaoundéré, Ngaoundéré, PO Box 455, Cameroon.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Kumar</LastName><ForeName>Pushpendra</ForeName><Initials>P</Initials><AffiliationInfo><Affiliation>Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab 151001, India.</Affiliation></AffiliationInfo></Author></AuthorList><Language>eng</Language><PublicationTypeList><PublicationType UI="D016428">Journal Article</PublicationType></PublicationTypeList><ArticleDate DateType="Electronic"><Year>2020</Year><Month>09</Month><Day>21</Day></ArticleDate></Article><MedlineJournalInfo><Country>England</Country><MedlineTA>Chaos Solitons Fractals</MedlineTA><NlmUniqueID>100971564</NlmUniqueID><ISSNLinking>0960-0779</ISSNLinking></MedlineJournalInfo><KeywordList Owner="NOTNLM"><Keyword MajorTopicYN="N">26A33</Keyword><Keyword MajorTopicYN="N">34D20</Keyword><Keyword MajorTopicYN="N">47H10</Keyword><Keyword MajorTopicYN="N">92D30</Keyword><Keyword MajorTopicYN="N">Adams-Bashforth-Moulton scheme</Keyword><Keyword MajorTopicYN="N">COVID-19</Keyword><Keyword MajorTopicYN="N">Caputo fractional derivative</Keyword><Keyword MajorTopicYN="N">Imperfect quarantine</Keyword><Keyword MajorTopicYN="N">Lockdown</Keyword><Keyword MajorTopicYN="N">TRR algorithm</Keyword></KeywordList><CoiStatement>This work does not have any conflict of interest. No funding is received for this study.</CoiStatement></MedlineCitation><PubmedData><History><PubMedPubDate PubStatus="received"><Year>2020</Year><Month>07</Month><Day>14</Day></PubMedPubDate><PubMedPubDate PubStatus="revised"><Year>2020</Year><Month>08</Month><Day>26</Day></PubMedPubDate><PubMedPubDate PubStatus="accepted"><Year>2020</Year><Month>09</Month><Day>08</Day></PubMedPubDate><PubMedPubDate PubStatus="pubmed"><Year>2020</Year><Month>9</Month><Day>29</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="medline"><Year>2020</Year><Month>9</Month><Day>29</Day><Hour>6</Hour><Minute>1</Minute></PubMedPubDate><PubMedPubDate PubStatus="entrez"><Year>2020</Year><Month>9</Month><Day>28</Day><Hour>5</Hour><Minute>36</Minute></PubMedPubDate></History><PublicationStatus>ppublish</PublicationStatus><ArticleIdList><ArticleId IdType="pubmed">32982078</ArticleId><ArticleId IdType="doi">10.1016/j.chaos.2020.110283</ArticleId><ArticleId IdType="pii">S0960-0779(20)30679-2</ArticleId><ArticleId IdType="pmc">PMC7505562</ArticleId></ArticleIdList><pmc-dir>pmcsd</pmc-dir>
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