Abstract
ABSTRACTIn this paper, the dynamical behaviours for a five-dimensional virus infection model with three delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses and Beddington–DeAngelis incidence are investigated. The reproduction numbers for virus infection, antibody immune response, CTL immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By using the Lyapunov functionals and linearization method, the threshold conditions on the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response and interior, respectively, are established. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is investigated by using the bifurcation theory. Numerical simulations are presented to justify the analytical results.
Highlights
In recent years, the virus infection models provide comprehensive views for our understanding of diseases, such as HIV, influenza, HBV, Ebola, HTLV and HCV
We have investigated a virus infection model (1) with intracellular delay τ1, virus replication delay τ2 and immune response delay τ3
We assume that the production of cytotoxic T-lymphocyte (CTL) immune response depends on the infected cells and CTL cells based above important biological meaning
Summary
The virus infection models provide comprehensive views for our understanding of diseases, such as HIV, influenza, HBV, Ebola, HTLV and HCV (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24]). In this paper we consider a five-dimensional virus infection model with three time delays which describes the interactions of antibody, CTL immune responses and Beddington–DeAngelis incidence rate dx(t) = dt.
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