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Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo

This paper deals with modeling and simulation of the novel coronavirus in which the infectious individuals are divided into three subgroups representing three forms of infection. The rigorous analysis of the mathematical model is provided. We provide also a rigorous derivation of the basic reproduct...

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Autores principales: Ndondo, A.M., Kasereka, S.K., Bisuta, S.F., Kyamakya, K., Doungmo, E.F.G., Ngoie, R-B.M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Author(s). Published by Elsevier B.V. 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7999905/
https://www.ncbi.nlm.nih.gov/pubmed/33816092
http://dx.doi.org/10.1016/j.rinp.2021.104096
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author Ndondo, A.M.
Kasereka, S.K.
Bisuta, S.F.
Kyamakya, K.
Doungmo, E.F.G.
Ngoie, R-B.M.
author_facet Ndondo, A.M.
Kasereka, S.K.
Bisuta, S.F.
Kyamakya, K.
Doungmo, E.F.G.
Ngoie, R-B.M.
author_sort Ndondo, A.M.
collection PubMed
description This paper deals with modeling and simulation of the novel coronavirus in which the infectious individuals are divided into three subgroups representing three forms of infection. The rigorous analysis of the mathematical model is provided. We provide also a rigorous derivation of the basic reproduction number [Formula: see text]. For [Formula: see text] , we prove that the Disease Free Equilibium (DFE) is Globally Asymptotically Stable (GAS), thus COVID-19 extincts; whereas for [Formula: see text] , we found the co-existing phenomena under some assumptions and parametric values. Elasticity indices for [Formula: see text] with respect to different parameters are calculated with baseline parameter values estimated. We also prove that a transcritical bifurcation occurs at [Formula: see text]. Taking into account the control strategies like screening, treatment and isolation (social distancing measures), we present the optimal control problem of minimizing the cost due to the application of these measures. By reducing the values of some parameters, such as death rates (representing a management effort for all categories of people) and recovered rates (representing the action of reduction in transmission, improved screening, treatment for individuals diagnosed positive to COVID-19 and the implementation of barrier measures limiting contamination for undiagnosed individuals), it appears that after [Formula: see text] days, the peak of the pandemic is reached and shows that by continuing with this strategy, COVID-19 could be eliminated in the population.
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spelling pubmed-79999052021-03-29 Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo Ndondo, A.M. Kasereka, S.K. Bisuta, S.F. Kyamakya, K. Doungmo, E.F.G. Ngoie, R-B.M. Results Phys Article This paper deals with modeling and simulation of the novel coronavirus in which the infectious individuals are divided into three subgroups representing three forms of infection. The rigorous analysis of the mathematical model is provided. We provide also a rigorous derivation of the basic reproduction number [Formula: see text]. For [Formula: see text] , we prove that the Disease Free Equilibium (DFE) is Globally Asymptotically Stable (GAS), thus COVID-19 extincts; whereas for [Formula: see text] , we found the co-existing phenomena under some assumptions and parametric values. Elasticity indices for [Formula: see text] with respect to different parameters are calculated with baseline parameter values estimated. We also prove that a transcritical bifurcation occurs at [Formula: see text]. Taking into account the control strategies like screening, treatment and isolation (social distancing measures), we present the optimal control problem of minimizing the cost due to the application of these measures. By reducing the values of some parameters, such as death rates (representing a management effort for all categories of people) and recovered rates (representing the action of reduction in transmission, improved screening, treatment for individuals diagnosed positive to COVID-19 and the implementation of barrier measures limiting contamination for undiagnosed individuals), it appears that after [Formula: see text] days, the peak of the pandemic is reached and shows that by continuing with this strategy, COVID-19 could be eliminated in the population. The Author(s). Published by Elsevier B.V. 2021-05 2021-03-27 /pmc/articles/PMC7999905/ /pubmed/33816092 http://dx.doi.org/10.1016/j.rinp.2021.104096 Text en © 2021 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
Ndondo, A.M.
Kasereka, S.K.
Bisuta, S.F.
Kyamakya, K.
Doungmo, E.F.G.
Ngoie, R-B.M.
Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo
title Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo
title_full Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo
title_fullStr Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo
title_full_unstemmed Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo
title_short Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo
title_sort analysis, modeling and optimal control of covid-19 outbreak with three forms of infection in democratic republic of the congo
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7999905/
https://www.ncbi.nlm.nih.gov/pubmed/33816092
http://dx.doi.org/10.1016/j.rinp.2021.104096
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