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Modeling the effect of non-cytolytic immune response on viral infection dynamics in the presence of humoral immunity

  • Mausumi Dhar
  • Shilpa Samaddar
  • Paritosh BhattacharyaEmail author
Original paper
  • 33 Downloads

Abstract

In this paper, a mathematical model describing the viral infection dynamics with non-cytolytic effect of humoral immune response is presented and analyzed. The effect of non-cytolytic immune response on the process of viral infectivity has been basically described by the non-cytolytic cure of infected cells and inhibition of viral replication, i.e., the non-lytic immune response. The sufficient criteria for the local and global stability of the equilibria, namely disease-free equilibrium, immune-free equilibrium and chronic equilibrium with humoral response, have been determined in terms of two threshold parameters, viz., the basic reproduction number, \(R_0\), and the humoral immune response reproduction number, \(R_1\). The condition governing the occurrence of Hopf bifurcation around the chronic equilibrium with humoral response has been obtained using the rate of infection as a bifurcation parameter. The obtained results indicate that the infection gets eradicated for \(R_0 \le 1\) and persists in the body for \(R_0 > 1\). Numerical simulations are presented to support our analytical findings. The comparison of various viral dynamic models suggests that the incorporation of the non-cytolytic immune response increases the concentration of uninfected cells, but causes a depletion of humoral immune response. Further, the effect of non-cytolytic immune response on the dynamical behavior of the system has been demonstrated.

Keywords

Humoral immune response Non-cytolytic immune response Global stability Hopf bifurcation 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of Technology AgartalaTripuraIndia

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