Publikation:

A reaction-diffusion model for the transmission dynamics of the Coronavirus pandemic with reinfection and vaccination process

Lade...
Vorschaubild

Dateien

Abboubakar_2-1m20kb5x8fiel7.pdf
Abboubakar_2-1m20kb5x8fiel7.pdfGröße: 6.82 MBDownloads: 202

Datum

2023

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Auflagebezeichnung

DOI (zitierfähiger Link)
ArXiv-ID

Internationale Patentnummer

Angaben zur Forschungsförderung

Projekt

Open Access-Veröffentlichung
Open Access Green
Core Facility der Universität Konstanz

Gesperrt bis

Titel in einer weiteren Sprache

Publikationstyp
Working Paper/Technical Report
Publikationsstatus
Published

Erschienen in

Zusammenfassung

This work aims at deriving and analysing a reaction-diffusion model for the transmission dynamics of the Coronavirus (COVID-19) which takes into account the reinfection and the vaccination process, and to compare it with the ODE model. After formulating the time-dependent ODE model, we compute the control reproduction number $\mathcal{R}_c$ and prove the global stability of the disease-free equilibrium whenever $\mathcal{R}_c<1$. We also demonstrate that if $\mathcal{R}_c>1$, the disease-free equilibrium becomes unstable and coexists with at least one endemic equilibrium point. We then use data from Germany to calibrate our model and estimate some model parameters. We find that $\mathcal{R}_c\approx 1.13$ expressing that the disease persists in the population. To determine key parameters which influence the model dynamics, we perform global sensitivity analysis by computing partial rank correlation coefficients between model parameters and the control reproduction number (respectively model state variables). After that, we include in the previous model the mobility in space by transforming it into a reaction-diffusion PDE model. For this last initial value boundary problem (IVBP), we prove the non-negativity, existence, and uniqueness of solutions. We also prove the local and global stability of the disease-free equilibrium whenever $\mathcal{R}_c<1$, and the fact that $\mathcal{R}_c>1$ implies the instability of the DFE and its coexistence with at least one endemic equilibrium point. To validate our theoretical results, we perform numerous numerical simulations. We then compare the ODE model with the PDE model.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Zitieren

ISO 690ABBOUBAKAR, Hamadjam, Reinhard RACKE, Nicolas SCHLOSSER, 2023. A reaction-diffusion model for the transmission dynamics of the Coronavirus pandemic with reinfection and vaccination process
BibTex
@techreport{Abboubakar2023react-67339,
  year={2023},
  series={Konstanzer Schriften in Mathematik},
  title={A reaction-diffusion model for the transmission dynamics of the Coronavirus pandemic with reinfection and vaccination process},
  number={409},
  author={Abboubakar, Hamadjam and Racke, Reinhard and Schlosser, Nicolas}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/67339">
    <dc:creator>Schlosser, Nicolas</dc:creator>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:creator>Racke, Reinhard</dc:creator>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/67339/4/Abboubakar_2-1m20kb5x8fiel7.pdf"/>
    <dc:creator>Abboubakar, Hamadjam</dc:creator>
    <dc:language>eng</dc:language>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/67339/4/Abboubakar_2-1m20kb5x8fiel7.pdf"/>
    <dcterms:abstract>This work aims at deriving and analysing a reaction-diffusion model for the transmission dynamics of the Coronavirus (COVID-19) which takes into account the reinfection and the vaccination process, and to compare it with the ODE model. After formulating the time-dependent ODE model, we compute the control reproduction number $\mathcal{R}_c$ and prove the global stability of the disease-free equilibrium whenever $\mathcal{R}_c&lt;1$. We also demonstrate that if $\mathcal{R}_c&gt;1$, the disease-free equilibrium becomes unstable and coexists with at least one endemic equilibrium point. We then use data from Germany to calibrate our model and estimate some model parameters. We find that $\mathcal{R}_c\approx 1.13$ expressing that the disease persists in the population. To determine key parameters which influence the model dynamics, we perform global sensitivity analysis by computing partial rank correlation coefficients between model parameters and the control reproduction number (respectively model state variables). After that, we include in the previous model the mobility in space by transforming it into a reaction-diffusion PDE model. For this last initial value boundary problem (IVBP), we prove the non-negativity, existence, and uniqueness of solutions. We also prove the local and global stability of the disease-free equilibrium whenever $\mathcal{R}_c&lt;1$, and the fact that $\mathcal{R}_c&gt;1$ implies the instability of the DFE and its coexistence with at least one endemic equilibrium point. To validate our theoretical results, we perform numerous numerical simulations. We then compare the ODE model with the PDE model.</dcterms:abstract>
    <dc:contributor>Abboubakar, Hamadjam</dc:contributor>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-07-10T12:09:00Z</dc:date>
    <dcterms:issued>2023</dcterms:issued>
    <dc:contributor>Schlosser, Nicolas</dc:contributor>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:title>A reaction-diffusion model for the transmission dynamics of the Coronavirus pandemic with reinfection and vaccination process</dcterms:title>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/67339"/>
    <dc:contributor>Racke, Reinhard</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-07-10T12:09:00Z</dcterms:available>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
  </rdf:Description>
</rdf:RDF>

Interner Vermerk

xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter

Kontakt
URL der Originalveröffentl.

Prüfdatum der URL

Prüfungsdatum der Dissertation

Finanzierungsart

Kommentar zur Publikation

Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
Begutachtet
Diese Publikation teilen