Viral infections remain a major cause of deaths globally. Here, we focus on Hepatitis B and C viruses (HBV and HCV) infection dynamics in the liver and blood cells, taking into account non-cytotoxic and cytotoxic mediated immune response as well as antiviral therapy. The analysis of the model is presented in terms of the reproduction number, ${\mathcal{R}}_0$. The system has a globally stable disease-free equilibrium when ${\mathcal{R}}_0$ is below unit. It exhibits forward bifurcation when ${\mathcal{R}}_0$ is greater than one, with a locally asymptotically stable endemic equilibrium point. By carrying out sensitivity analysis using the Latin Hypercube Sampling scheme (LHS), we determine the key processes that are essential in containing the infection. Our results suggest that, the production of virions from blood and liver cells as well as degeneration of Cytotoxic T-Lymphocytes (CTLs) can greatly aggravate HBV and HCV infections. Moreover, CTL-mediated immune response alone cannot effectively contain the infection. Although virion production from the liver and blood as well as per-capita loss of CTLs were observed to greatly aggravate the infection, their effects imposed on the infection dynamics were not significantly different. We recommend based on the results that, use of highly effective antiviral/combination therapy to block production of new virions is an ideal approach to containing the infections.

病毒感染仍然是全球范围内死亡的主要原因。在这里，我们将重点放在乙肝和丙肝病毒（HBV和HCV）在肝脏和血细胞中的感染动态，同时考虑到非细胞毒性和细胞毒性介导的免疫反应以及抗病毒治疗。对模型的分析是根据复制数表示的，${\mathcal{[R}}_0$。该系统在以下情况下具有全局稳定的无病平衡${\mathcal{[R}}_0$低于单位。当出现${\mathcal{[R}}_0$大于1，具有局部渐近稳定的地方平衡点。通过使用拉丁文超立方体抽样方案（LHS）进行敏感性分析，我们确定了控制感染的关键过程。我们的结果表明，血液和肝细胞中病毒粒子的产生以及细胞毒性T淋巴细胞（CTL）的变性会大大加重HBV和HCV感染。而且，仅CTL介导的免疫反应不能有效地遏制感染。尽管观察到肝脏和血液中毒粒的产生以及人均CTL的丧失大大加剧了感染，但它们对感染动态的影响没有显着差异。我们建议根据结果，