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Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate()
COVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for u...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Author(s). Published by Elsevier Ltd.
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9652120/ https://www.ncbi.nlm.nih.gov/pubmed/36406926 http://dx.doi.org/10.1016/j.imu.2022.101124 |
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author | Babasola, Oluwatosin Kayode, Oshinubi Peter, Olumuyiwa James Onwuegbuche, Faithful Chiagoziem Oguntolu, Festus Abiodun |
author_facet | Babasola, Oluwatosin Kayode, Oshinubi Peter, Olumuyiwa James Onwuegbuche, Faithful Chiagoziem Oguntolu, Festus Abiodun |
author_sort | Babasola, Oluwatosin |
collection | PubMed |
description | COVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for understanding the COVID-19 transmission dynamics and the way of mitigating its effect. The implementation of a mathematical model has proven helpful in further understanding the behaviour which has helped the policymaker in adopting the best policy necessary for reducing the spread. Most models are based on a system of equations which assume an instantaneous change in the transmission dynamics. However, it is believed that SARS-COV-2 have an incubation period before the tendency of transmission. Therefore, to capture the dynamics adequately, there would be a need for the inclusion of delay parameters which will account for the delay before an exposed individual could become infected. Hence, in this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a periodic solution and it further helps us to gain more insight into the transmission dynamics of the disease and strategy to reduce the risk of infection. |
format | Online Article Text |
id | pubmed-9652120 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | The Author(s). Published by Elsevier Ltd. |
record_format | MEDLINE/PubMed |
spelling | pubmed-96521202022-11-14 Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate() Babasola, Oluwatosin Kayode, Oshinubi Peter, Olumuyiwa James Onwuegbuche, Faithful Chiagoziem Oguntolu, Festus Abiodun Inform Med Unlocked Article COVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for understanding the COVID-19 transmission dynamics and the way of mitigating its effect. The implementation of a mathematical model has proven helpful in further understanding the behaviour which has helped the policymaker in adopting the best policy necessary for reducing the spread. Most models are based on a system of equations which assume an instantaneous change in the transmission dynamics. However, it is believed that SARS-COV-2 have an incubation period before the tendency of transmission. Therefore, to capture the dynamics adequately, there would be a need for the inclusion of delay parameters which will account for the delay before an exposed individual could become infected. Hence, in this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a periodic solution and it further helps us to gain more insight into the transmission dynamics of the disease and strategy to reduce the risk of infection. The Author(s). Published by Elsevier Ltd. 2022 2022-11-08 /pmc/articles/PMC9652120/ /pubmed/36406926 http://dx.doi.org/10.1016/j.imu.2022.101124 Text en © 2022 The Author(s) Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active. |
spellingShingle | Article Babasola, Oluwatosin Kayode, Oshinubi Peter, Olumuyiwa James Onwuegbuche, Faithful Chiagoziem Oguntolu, Festus Abiodun Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate() |
title | Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate() |
title_full | Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate() |
title_fullStr | Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate() |
title_full_unstemmed | Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate() |
title_short | Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate() |
title_sort | time-delayed modelling of the covid-19 dynamics with a convex incidence rate() |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9652120/ https://www.ncbi.nlm.nih.gov/pubmed/36406926 http://dx.doi.org/10.1016/j.imu.2022.101124 |
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