Stability of delayed virus infection model with a general incidence rate and adaptive immune response

Authors

Zhimin Chen, South China Normal University
Xiuxiang Liu, South China Normal University
Zhongzhong Xie, South China Normal University

Abstract

We present the dynamical behaviors of a virus infection model with general infection rate, immune responses and two intracellular delays which describe the interactions of the HIV virus, target cells, CTL cells and antibodies within host. Three factors are incorporated in this model: (1) the intrinsic growth rate of uninfected cells, (2) a nonlinear incidence rate function considering both virus-tocell infection and cell-to-cell transmission, and (3) a nonlinear productivity and removal function. By the method of Lyapunov functionals and LaSalle’s invariance principle, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection R0, for antibody immune response R1, for CTL immune response R2, for CTL immune competition R3 and for antibody immune competition R4. The numerical simulations are given to illustrate our theoretical results.

Recommended Citation

Chen, Zhimin; Liu, Xiuxiang; and Xie, Zhongzhong (2018). Stability of delayed virus infection model with a general incidence rate and adaptive immune response, Applications and Applied Mathematics: An International Journal (AAM), Vol. 13, Iss. 2, Article 7.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss2/7