The long and binding treatment of tuberculosis (TB) at least 6–8 months for the new cases, the partial immunity given by BCG vaccine, the loss of immunity after a few years doing that strategy of TB control via vaccination and treatment of infectious are not sufficient to eradicate TB. TB is an infectious disease caused by the bacillus Mycobacterium tuberculosis. Adults are principally attacked. In this work, we assess the impact of vaccination in the spread of TB via a deterministic epidemic model (SV ELI) (Susceptible, Vaccinated, Early latent, Late latent, Infectious). Using the Lyapunov–Lasalle method, we analyse the stability of epidemic system (SV ELI) around the equilibriums (disease-free and endemic). The global asymptotic stability of the unique endemic equilibrium whenever ${\mathcal{R}}_0>1$ is proved, where ${\mathcal{R}}_0$ is the reproduction number. We prove also that when ${\mathcal{R}}_0$ is less than 1, TB can be eradicated. Numerical simulations, using some TB data found in the literature in relation with Cameroon, are conducted to approve analytic results, and to show that vaccination coverage is not sufficient to control TB, effective contact rate has a high impact in the spread of TB.

对于新病例，至少需要6-8个月的长期结核病结合治疗，BCG疫苗给予部分免疫，几年后通过疫苗接种和传染病控制结核的策略后丧失免疫力。还不足以根除结核病。结核是由结核分枝杆菌引起的传染病。成人主要受到攻击。在这项工作中，我们通过确定性流行病模型（SV ELI）（易感，疫苗接种，早期潜伏，晚期潜伏，传染性）评估疫苗接种对结核病传播的影响。使用Lyapunov–Lasalle方法，我们分析了流行系统的稳定性（SV ELI）围绕平衡（无疾病和地方病）。每当地方唯一平衡的全局渐近稳定性${\mathcal{[R}}_0>\mathrm{1个}$ 被证明，在哪里 ${\mathcal{[R}}_0$是复制编号。我们还证明${\mathcal{[R}}_0$小于1，可以消除TB。使用与喀麦隆有关的文献中发现的一些结核病数据进行了数值模拟，以验证分析结果，并表明疫苗接种覆盖率不足以控制结核病，有效接触率对结核病的传播有很大影响。