Modeling the effect of non-cytolytic immune response on viral infection dynamics in the presence of humoral immunity
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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.
KeywordsHumoral immune response Non-cytolytic immune response Global stability Hopf bifurcation
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Conflict of interest
The authors declare that they have no conflict of interest.
- 3.Douam, F., Lavillette, D., Cosset, F.L.: The mechanism of HCV entry into host cells. In: Progress in Molecular Biology and Translational Science, vol. 129, pp. 63–107. Elsevier (2015)Google Scholar
- 8.Zhou, X., Shi, X., Zhang, Z., Song, X.: Dynamical behavior of a virus dynamics model with CTL immune response. Appl. Math. Comput. 213(2), 329–347 (2009)Google Scholar
- 9.Kajiwara, T., Sasaki, T.: Global stability of pathogen-immune dynamics with absorption. J. Biol. Dyn. 4(3), 258–269 (2010)Google Scholar
- 13.Montefiori, D.C.: Role of complement and Fc receptors in the pathogenesis of HIV-1 infection. In: Fauci, A.S., Pantaleo, G. (eds.) Immunopathogenesis of HIV Infection, pp. 119–138. Springer-Verlag, Berlin, Heidelberg (1997) Google Scholar
- 17.Obaid, M.A., Elaiw, A.: Stability of virus infection models with antibodies and chronically infected cells. In: Abstract and Applied Analysis, vol. 2014. Hindawi (2014)Google Scholar
- 35.Wang, Z., Xu, R.: Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response. Commun. Nonlinear Sci. Numer. Simul. 17(2), 964–978 (2012)Google Scholar