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Mathematical modelling and optimal control strategies of the transmission of enterovirus

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Název: Mathematical modelling and optimal control strategies of the transmission of enterovirus
Autoři: Mabotsa, Malebese
Přispěvatelé: Munganga, J. M. W., Hassan, Adamu Shitu
Rok vydání: 2022
Sbírka: University of South Africa: UNISA Institutional Repository
Témata: Mathematical modelling, Enterovirus, Basic reproduction number, Next generation matrix method, Lyapunov functions, Volterra-Lyapunov matrices, Optimal control, Pontrayagin's Maximum principle, 616.9180015118, Enterovirus diseases -- Transmission -- Mathematical models, Matrix analytic methods, Maximum principles (Mathematics)
Popis: We propose a mathematical model for the transmission dynamics of enterovirus. We prove that if the basic reproduction number R0 1, a suitable Lyapunov function is used to establish the global stability of the disease free equilibrium, in which case the infection will die out over time. Our analysis further establish the global stability of the endemic equilibrium based on the approach of Volterra-Lyapunov matrices if R0 > 1. Our ndings show that when R0 > 1, the endemic equilibrium is globally asymptotically stable. In this case, the enterovirus will invade the population. It is shown that by reducing direct transmission rate by 80%, the basic reproduction number can be reduced below one and thus controlling the infection. Using optimal control with hygiene and sanitation campaigns as control measures, it is shown that the disease can be controlled within a shorter period of time as compared to minimizing the direct contact rate by 80%. Numerical simulations are provided to illustrate the results. ; M. Sc. (Applied Mathematics) ; Mathematical Sciences
Druh dokumentu: doctoral or postdoctoral thesis
Popis souboru: 1 online resource (60 leaves) : black and white illustration, color graphs; application/pdf
Jazyk: English
Relation: https://hdl.handle.net/10500/28986
Dostupnost: https://hdl.handle.net/10500/28986
Přístupové číslo: edsbas.4465FECB
Databáze: BASE
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  – Url: https://hdl.handle.net/10500/28986#
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PubType: Dissertation/ Thesis
PubTypeId: dissertation
PreciseRelevancyScore: 777.000732421875
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Mathematical modelling and optimal control strategies of the transmission of enterovirus
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Mabotsa%2C+Malebese%22">Mabotsa, Malebese</searchLink>
– Name: Author
  Label: Contributors
  Group: Au
  Data: Munganga, J. M. W.<br />Hassan, Adamu Shitu
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2022
– Name: Subset
  Label: Collection
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  Data: University of South Africa: UNISA Institutional Repository
– Name: Subject
  Label: Subject Terms
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+modelling%22">Mathematical modelling</searchLink><br /><searchLink fieldCode="DE" term="%22Enterovirus%22">Enterovirus</searchLink><br /><searchLink fieldCode="DE" term="%22Basic+reproduction+number%22">Basic reproduction number</searchLink><br /><searchLink fieldCode="DE" term="%22Next+generation+matrix+method%22">Next generation matrix method</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+functions%22">Lyapunov functions</searchLink><br /><searchLink fieldCode="DE" term="%22Volterra-Lyapunov+matrices%22">Volterra-Lyapunov matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Optimal+control%22">Optimal control</searchLink><br /><searchLink fieldCode="DE" term="%22Pontrayagin's+Maximum+principle%22">Pontrayagin's Maximum principle</searchLink><br /><searchLink fieldCode="DE" term="%22616%2E9180015118%22">616.9180015118</searchLink><br /><searchLink fieldCode="DE" term="%22Enterovirus+diseases+--+Transmission+--+Mathematical+models%22">Enterovirus diseases -- Transmission -- Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+analytic+methods%22">Matrix analytic methods</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+principles+%28Mathematics%29%22">Maximum principles (Mathematics)</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: We propose a mathematical model for the transmission dynamics of enterovirus. We prove that if the basic reproduction number R0 1, a suitable Lyapunov function is used to establish the global stability of the disease free equilibrium, in which case the infection will die out over time. Our analysis further establish the global stability of the endemic equilibrium based on the approach of Volterra-Lyapunov matrices if R0 > 1. Our ndings show that when R0 > 1, the endemic equilibrium is globally asymptotically stable. In this case, the enterovirus will invade the population. It is shown that by reducing direct transmission rate by 80%, the basic reproduction number can be reduced below one and thus controlling the infection. Using optimal control with hygiene and sanitation campaigns as control measures, it is shown that the disease can be controlled within a shorter period of time as compared to minimizing the direct contact rate by 80%. Numerical simulations are provided to illustrate the results. ; M. Sc. (Applied Mathematics) ; Mathematical Sciences
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  Label: Document Type
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  Data: doctoral or postdoctoral thesis
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  Group: SrcInfo
  Data: 1 online resource (60 leaves) : black and white illustration, color graphs; application/pdf
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  Data: English
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  Data: https://hdl.handle.net/10500/28986
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  Data: https://hdl.handle.net/10500/28986
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  Data: edsbas.4465FECB
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Mathematical modelling
        Type: general
      – SubjectFull: Enterovirus
        Type: general
      – SubjectFull: Basic reproduction number
        Type: general
      – SubjectFull: Next generation matrix method
        Type: general
      – SubjectFull: Lyapunov functions
        Type: general
      – SubjectFull: Volterra-Lyapunov matrices
        Type: general
      – SubjectFull: Optimal control
        Type: general
      – SubjectFull: Pontrayagin's Maximum principle
        Type: general
      – SubjectFull: 616.9180015118
        Type: general
      – SubjectFull: Enterovirus diseases -- Transmission -- Mathematical models
        Type: general
      – SubjectFull: Matrix analytic methods
        Type: general
      – SubjectFull: Maximum principles (Mathematics)
        Type: general
    Titles:
      – TitleFull: Mathematical modelling and optimal control strategies of the transmission of enterovirus
        Type: main
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          Name:
            NameFull: Mabotsa, Malebese
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            NameFull: Munganga, J. M. W.
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            NameFull: Hassan, Adamu Shitu
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2022
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