The aim of this work is to study global dynamics of target-mediated drug disposition (TMDD) models and their solutions by nonstandard finite difference (NSFD) schemes. Firstly, we use comparison principles and the Lyapunov stability theory for ODEs to establish positivity, boundedness, local and global asymptotic stability of the TMDD models. Secondly, positivity-preserving NSFD schemes are proposed and their dynamical properties are analysed rigorously. Lastly, we perform a set of numerical simulations to support and illustrate the theoretical results and to show advantages of the NSFD schemes over standard ones. The results show that there is a good agreement between the numerical results and theoretical ones. In addition, the numerical simulations indicate that the constructed NSFD schemes are dynamically stable and efficient in replicating the complex dynamical properties of the continuous models.

这项工作的目的是通过非标准有限差分（NSFD）方案研究靶标介导的药物处置（TMDD）模型及其解决方案的全局动力学。首先，我们使用比较原理和Lyapunov稳定性理论对ODE进行建模，建立了TMDD模型的正性，有界性，局部和全局渐近稳定性。其次，提出了保正性NSFD方案，并对其动力学特性进行了严格分析。最后，我们执行了一组数值模拟，以支持和说明理论结果，并展示了NSFD方案相对于标准方案的优势。结果表明，数值结果与理论值吻合良好。此外，