Control and elimination in an SEIR model for the disease dynamics of COVID-19 with vaccination

Peter Joseph Witbooi; Sibaliwe Maku Vyambwera; Mozart Umba Nsuami; Peter Joseph Witbooi; Sibaliwe Maku Vyambwera; Mozart Umba Nsuami

doi:10.3934/math.2023411

AIMS Mathematics

2023, Volume 8, Issue 4: 8144-8161. doi: 10.3934/math.2023411

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Research article

Control and elimination in an SEIR model for the disease dynamics of COVID-19 with vaccination

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

Received: 04 September 2022 Revised: 16 November 2022 Accepted: 22 November 2022 Published: 31 January 2023
MSC : 92D30, 34K20

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.
- basic reproduction number,
- generalized contact rate,
- infected immigrants,
- awareness,
- alertness
Citation: Peter Joseph Witbooi, Sibaliwe Maku Vyambwera, Mozart Umba Nsuami. Control and elimination in an SEIR model for the disease dynamics of COVID-19 with vaccination[J]. AIMS Mathematics, 2023, 8(4): 8144-8161. doi: 10.3934/math.2023411

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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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