The role of humoral immune delay on the dynamics of HCV infection incorporating both the modes of infection transmission, namely, viral and cellular transmissions with a non-cytolytic cure of infected hepatocytes is studied. The local and global asymptotic stability of the boundary equilibria, namely, infection-free and immune-free equilibrium are analyzed theoretically as well as numerically under the conditions on the basic reproduction number and the humoral immune reproduction number. The existence of Hopf bifurcation and consequent occurrence of bifurcating periodic orbits around the humoral immune activated equilibrium are illustrated. The findings show that Hopf bifurcation and stability switches occur under certain conditions as the bifurcation parameter crosses the critical values. Furthermore, the dynamical effect of the development rate of B cells is investigated numerically. The results obtained show that the system becomes unstable from stable and regains stability from instability depending on the development rate of B cells for a fixed delay value. Further, the results suggest that a high antigenic stimulation in humoral immunity is beneficial for uninfected hepatocytes with a significant reduction in virions density.

研究了体液免疫延迟在HCV感染动力学中的作用，该感染结合了两种感染传播方式，即病毒和细胞传播以及感染肝细胞的非细胞溶解治疗。在基本复制数和体液免疫复制数的条件下，从理论上和数值上分析了边界平衡的局部和全局渐近稳定性，即无感染和无免疫平衡。说明了霍夫夫分叉的存在以及随之而来的围绕体液免疫激活平衡的分叉周期性轨道的发生。研究结果表明，Hopf分叉和稳定性开关在某些条件下会发生，因为分叉参数越过临界值。此外，对B细胞进行了数值研究。获得的结果表明，对于固定的延迟值，取决于B细胞的发育速度，系统会从稳定状态变得不稳定，并从不稳定状态恢复到稳定状态。此外，结果表明，体液免疫中的高抗原刺激对未感染的肝细胞有益，并且病毒体密度显着降低。