Global stability analysis of a COVID-19 epidemic model with incubation delay
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 ste...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | Mathematical Modelling and Control |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2023003?viewType=HTML |
| _version_ | 1797826896092725248 |
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| author | Paride O. Lolika Mlyashimbi Helikumi |
| author_facet | Paride O. Lolika Mlyashimbi Helikumi |
| author_sort | Paride O. Lolika |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T12:39:37Z |
| format | Article |
| id | doaj.art-499e244f33564585b16ea9df526d0927 |
| institution | Directory Open Access Journal |
| issn | 2767-8946 |
| language | English |
| last_indexed | 2024-04-09T12:39:37Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj.art-499e244f33564585b16ea9df526d09272023-05-15T01:11:10ZengAIMS PressMathematical Modelling and Control2767-89462023-02-0131233810.3934/mmc.2023003Global stability analysis of a COVID-19 epidemic model with incubation delayParide O. Lolika 0Mlyashimbi Helikumi 11. University of Juba, Department of Mathematics, P.O. Box 82 Juba, Central Equatoria, South Sudan2. Mbeya University of Science and Technology, Department of Mathematics and Statistics, College of Science and Technical Education, P.O. Box 131, Mbeya, TanzaniaIn 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.https://www.aimspress.com/article/doi/10.3934/mmc.2023003?viewType=HTMLglobal stabilitytime delayepidemic modelhopf bifurcation |
| spellingShingle | Paride O. Lolika Mlyashimbi Helikumi Global stability analysis of a COVID-19 epidemic model with incubation delay Mathematical Modelling and Control global stability time delay epidemic model hopf bifurcation |
| title | Global stability analysis of a COVID-19 epidemic model with incubation delay |
| title_full | Global stability analysis of a COVID-19 epidemic model with incubation delay |
| title_fullStr | Global stability analysis of a COVID-19 epidemic model with incubation delay |
| title_full_unstemmed | Global stability analysis of a COVID-19 epidemic model with incubation delay |
| title_short | Global stability analysis of a COVID-19 epidemic model with incubation delay |
| title_sort | global stability analysis of a covid 19 epidemic model with incubation delay |
| topic | global stability time delay epidemic model hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2023003?viewType=HTML |
| work_keys_str_mv | AT parideololika globalstabilityanalysisofacovid19epidemicmodelwithincubationdelay AT mlyashimbihelikumi globalstabilityanalysisofacovid19epidemicmodelwithincubationdelay |