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Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C

The role of humoral immune delay on the dynamics of HCV infection incorporating both the modes of infection transmission, namely, viral and cellular transmissions with a non-cytolytic cure of infected hepatocytes is studied. The local and global asymptotic stability of the boundary equilibria, namel...

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Detalles Bibliográficos
Autores principales: Pan, Sonjoy, Chakrabarty, Siddhartha P.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Indian National Science Academy 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7782052/
http://dx.doi.org/10.1007/s13226-020-0489-2
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author Pan, Sonjoy
Chakrabarty, Siddhartha P.
author_facet Pan, Sonjoy
Chakrabarty, Siddhartha P.
author_sort Pan, Sonjoy
collection PubMed
description The role of humoral immune delay on the dynamics of HCV infection incorporating both the modes of infection transmission, namely, viral and cellular transmissions with a non-cytolytic cure of infected hepatocytes is studied. The local and global asymptotic stability of the boundary equilibria, namely, infection-free and immune-free equilibrium are analyzed theoretically as well as numerically under the conditions on the basic reproduction number and the humoral immune reproduction number. The existence of Hopf bifurcation and consequent occurrence of bifurcating periodic orbits around the humoral immune activated equilibrium are illustrated. The findings show that Hopf bifurcation and stability switches occur under certain conditions as the bifurcation parameter crosses the critical values. Furthermore, the dynamical effect of the development rate of B cells is investigated numerically. The results obtained show that the system becomes unstable from stable and regains stability from instability depending on the development rate of B cells for a fixed delay value. Further, the results suggest that a high antigenic stimulation in humoral immunity is beneficial for uninfected hepatocytes with a significant reduction in virions density.
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spelling pubmed-77820522021-01-05 Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C Pan, Sonjoy Chakrabarty, Siddhartha P. Indian J Pure Appl Math Article The role of humoral immune delay on the dynamics of HCV infection incorporating both the modes of infection transmission, namely, viral and cellular transmissions with a non-cytolytic cure of infected hepatocytes is studied. The local and global asymptotic stability of the boundary equilibria, namely, infection-free and immune-free equilibrium are analyzed theoretically as well as numerically under the conditions on the basic reproduction number and the humoral immune reproduction number. The existence of Hopf bifurcation and consequent occurrence of bifurcating periodic orbits around the humoral immune activated equilibrium are illustrated. The findings show that Hopf bifurcation and stability switches occur under certain conditions as the bifurcation parameter crosses the critical values. Furthermore, the dynamical effect of the development rate of B cells is investigated numerically. The results obtained show that the system becomes unstable from stable and regains stability from instability depending on the development rate of B cells for a fixed delay value. Further, the results suggest that a high antigenic stimulation in humoral immunity is beneficial for uninfected hepatocytes with a significant reduction in virions density. Indian National Science Academy 2021-01-05 2020 /pmc/articles/PMC7782052/ http://dx.doi.org/10.1007/s13226-020-0489-2 Text en © Indian National Science Academy 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Pan, Sonjoy
Chakrabarty, Siddhartha P.
Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C
title Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C
title_full Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C
title_fullStr Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C
title_full_unstemmed Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C
title_short Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C
title_sort hopf bifurcation and stability switches induced by humoral immune delay in hepatitis c
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7782052/
http://dx.doi.org/10.1007/s13226-020-0489-2
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