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JOURNAL OF MECHANICAL ENGINEERING  > 2023  > Accepted Manuscript
Witbooi Peter Joseph, Vyambwera Sibaliwe Maku, Nsuami Mozart Umba. Control and elimination in an SEIR model for the disease dynamics of COVID-19 with vaccination[J]. JOURNAL OF MECHANICAL ENGINEERING. doi: 10.3934/math.2023411
Citation: Witbooi Peter Joseph, Vyambwera Sibaliwe Maku, Nsuami Mozart Umba. Control and elimination in an SEIR model for the disease dynamics of COVID-19 with vaccination[J]. JOURNAL OF MECHANICAL ENGINEERING. doi: 10.3934/math.2023411
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Control and elimination in an SEIR model for the disease dynamics of COVID-19 with vaccination

doi: 10.3934/math.2023411

  • Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South Africa

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  • Corresponding author: Witbooi Peter Joseph, Email: pwitbooi@uwc.ac.za; Tel: +27(0)219593027; Fax: +27(0)219591241
  • Received Date: 04 Sep 2022
  • Rev Recd Date: 16 Nov 2022
  • Accepted Date: 22 Nov 2022
    • Available Online: 02 Feb 2023
    Abstract
  • COVID-19 has become a serious pandemic affecting many countries around the world since it was discovered in 2019. In this research, we present a compartmental model in ordinary differential equations for COVID-19 with vaccination, inflow of infected and a generalized contact rate. Existence of a unique global positive solution of the model is proved, followed by stability analysis of the equilibrium points. A control problem is presented, with vaccination as well as reduction of the contact rate by way of education, law enforcement or lockdown. In the last section, we use numerical simulations with data applicable to South Africa, for supporting our theoretical results. The model and application illustrate the interesting manner in which a diseased population can be perturbed from within itself.

     

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