Abstract
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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The first author is grateful to Indian Institute of Technology Guwahati for the financial support provided to pursue his Ph.D.
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Pan, S., Chakrabarty, S.P. Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C. Indian J Pure Appl Math 51, 1673–1695 (2020). https://doi.org/10.1007/s13226-020-0489-2
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DOI: https://doi.org/10.1007/s13226-020-0489-2