Dynamics and analysis of COVID-19 disease transmission: The effect of vaccination and quarantine

Mlyashimbi Helikumi; Paride O. Lolika; Mlyashimbi Helikumi; Paride O. Lolika

doi:10.3934/mmc.2023017

Mathematical Modelling and Control

2023, Volume 3, Issue 3: 192-209. doi: 10.3934/mmc.2023017

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Dynamics and analysis of COVID-19 disease transmission: The effect of vaccination and quarantine

Mlyashimbi Helikumi ¹,
Paride O. Lolika ^{2
,
,}

1.
Mbeya University of Science and Technology, Department of Mathematics and Statistics, College of Science and Technical Education, P.O. Box 131, Mbeya, Tanzania
2.
University of Juba, Department of Mathematics, P.O. Box 82 Juba, Central Equatoria, South Sudan

Received: 03 January 2023 Revised: 09 April 2023 Accepted: 25 April 2023 Published: 01 September 2023

In this study, a fractional-order model for COVID-19 disease transmission is proposed and studied. First, the disease-free equilibrium and the basic reproduction number, $ {\cal R}_0 $ of the model has been communicated. The local and global stability of the disease-free equilibrium have been proved using well-constructed Lyapunov functions. Moreover, a normalized sensitivity analysis for the model parameters has been performed to identify their influence on $ {\cal R}_0 $. Real data on COVID-19 disease from Wuhan in China has been used to validate the proposed model. Finally, a simulation of the model has been performed to determine the effects of memory and control strategies. Overall, one can note that vaccination and quarantine have the potential to minimize the spread of COVID-19 in the population.
- COVID-19,
- mathematical model,
- disease-free equilibrium,
- stability analysis,
- simulations
Citation: Mlyashimbi Helikumi, Paride O. Lolika. Dynamics and analysis of COVID-19 disease transmission: The effect of vaccination and quarantine[J]. Mathematical Modelling and Control, 2023, 3(3): 192-209. doi: 10.3934/mmc.2023017

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Abstract

In this study, a fractional-order model for COVID-19 disease transmission is proposed and studied. First, the disease-free equilibrium and the basic reproduction number, $ {\cal R}_0 $ of the model has been communicated. The local and global stability of the disease-free equilibrium have been proved using well-constructed Lyapunov functions. Moreover, a normalized sensitivity analysis for the model parameters has been performed to identify their influence on $ {\cal R}_0 $. Real data on COVID-19 disease from Wuhan in China has been used to validate the proposed model. Finally, a simulation of the model has been performed to determine the effects of memory and control strategies. Overall, one can note that vaccination and quarantine have the potential to minimize the spread of COVID-19 in the population.

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