Wang Yan, Lu Minmin, Jiang Daqing
College of Science, China University of Petroleum (East China), Qingdao 266580, China.
Key Laboratory of Unconventional Oil & Gas Development, China University of Petroleum (East China), Qingdao 266580, China.
Math Biosci Eng. 2020 Nov 27;18(1):274-299. doi: 10.3934/mbe.2021014.
In this paper, an HIV infection model with latent infection, Beddington-DeAngelis infection function, B-cell immune response and four time delays is formulated. The well-posedness of the model solution is rigorously derived, and the basic reproduction number $\mathcal{R}_0$ and the B-cell immune response reproduction number $\mathcal{R}_1$ are also obtained. By analyzing the modulus of the characteristic equation and constructing suitable Lyapunov functions, we establish the global asymptotic stability of the uninfected and the B-cell-inactivated equilibria for the four time delays, respectively. Hopf bifurcation occurs at the B-cell-activated equilibrium when the model includes the immune delay, and the B-cell-activated equilibrium is globally asymptotically stable if the model does not include it. Numerical simulations indicate that the increase of the latency delay, the cell infection delay and the virus maturation delay can cause the B-cell-activated equilibrium stabilize, while the increase of the immune delay can cause it destabilize.
本文建立了一个具有潜伏感染、Beddington-DeAngelis感染函数、B细胞免疫反应和四个时滞的HIV感染模型。严格推导了模型解的适定性，并得到了基本再生数$\mathcal{R}_0$和B细胞免疫反应再生数$\mathcal{R}_1$。通过分析特征方程的模并构造合适的Lyapunov函数，我们分别建立了四个时滞下未感染平衡点和B细胞失活平衡点的全局渐近稳定性。当模型包含免疫时滞时，B细胞激活平衡点处发生Hopf分岔，而当模型不包含免疫时滞时，B细胞激活平衡点全局渐近稳定。数值模拟表明，潜伏期时滞、细胞感染时滞和病毒成熟时滞的增加会导致B细胞激活平衡点稳定，而免疫时滞的增加会导致其不稳定。
