Global stability analysis of a COVID-19 epidemic model with incubation delay

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

doi:10.3934/mmc.2023003

Mathematical Modelling and Control

2023, Volume 3, Issue 1: 23-38. doi: 10.3934/mmc.2023003

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Global stability analysis of a COVID-19 epidemic model with incubation delay

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

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

Received: 01 October 2022 Revised: 27 December 2022 Accepted: 03 January 2023 Published: 14 February 2023

In this paper, we propose, analyze and simulate a time delay differential equation to investigate the transmission and spread of Coronavirus disease (COVID-19). The basic reproduction number of the model is determined and qualitatively used to investigate the global stability of the model's steady states. We use numerical simulations to support the analytical results in the study. From the simulation results, we note that whenever the basic reproduction number is greater than unity, the model solutions will be associated with periodic oscillations for a considerable time scale from the start before attaining stability. This suggests that the inclusion of the time delay factor destabilizes the endemic equilibrium point leading to periodic solutions that arise due to Hopf bifurcations for a certain time frame.
- global stability,
- time delay,
- epidemic model,
- Hopf bifurcation
Citation: Paride O. Lolika, Mlyashimbi Helikumi. Global stability analysis of a COVID-19 epidemic model with incubation delay[J]. Mathematical Modelling and Control, 2023, 3(1): 23-38. doi: 10.3934/mmc.2023003

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Abstract

In this paper, we propose, analyze and simulate a time delay differential equation to investigate the transmission and spread of Coronavirus disease (COVID-19). The basic reproduction number of the model is determined and qualitatively used to investigate the global stability of the model's steady states. We use numerical simulations to support the analytical results in the study. From the simulation results, we note that whenever the basic reproduction number is greater than unity, the model solutions will be associated with periodic oscillations for a considerable time scale from the start before attaining stability. This suggests that the inclusion of the time delay factor destabilizes the endemic equilibrium point leading to periodic solutions that arise due to Hopf bifurcations for a certain time frame.

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