一类具有细胞内时滞和免疫反应的病毒动力学模型

A VIRUS DYNAMICS MODEL WITH AN INTRACELLULAR DELAY AND IMMUNE RESPONSE

研究一类具有细胞内时滞和免疫反应的病毒感染模型,利用Lasalle不变集原理和构造Lyapunov函数方法证明:当基本再生数R_0<1时,未感染平衡点E_0全局渐近稳定,也即病毒消失;给出了边界平衡点E^0,E_1,E_2局部稳定性的充分条件和τ=0时正平衡点E_3的存在和全局渐近稳定性条件;最后,通过数值模拟验证了理论结果.

A mathematical model on the control of viral infections with an intra- cellular delay and lytic and non-lytic immune responses is studied in this paper. By using the Lyapunov-LaSalle method, it is shown that the uninfected equilibrium Eo is globMly asymptoticMly stable if the basic reproduction number Ro 〈 1, in this case, the virus disappears; Some sufficient conditions for the local stability of the three boundary equilibria E0, El, E2, as well as the existence and globally asymptotic stability of the positive equilibrium E3 are given; Finally, some numerical simulations are provided to support the theoretical results.