人工抗体治疗 COVID-19 的病毒动力学模型

A Virus Dynamica Model for COVID-19Therapy with Artificial Antibody

摘要: 在本文中，我们建立了常量注射 ACE2 受体药物治疗 COVID-19 的动力学模型。首先，我们在生物学意义下定义了基本再生数 R₀，并且得出了系统的两个平衡点：无病平衡点 E₀ 和地方病平衡点 E₁。其次，利用 Lyapunov 函数和 Routh-Hurwitz 判据证明了无病平衡点和地方病平衡点的存在性和稳定性条件，即当 R₀ < 1 时，E₀ 局部渐近稳定；更进一步可证存在一个常数 R₁。 当 R₁ < 1 时，E₀ 全局渐近稳定；当 R₀ > 1 时，E₁ 局部渐近稳定。最后，通过数值模拟验证了所得结论。

Abstract: In this paper, we formulate a dynamic model for COVID-19 therapy with the constsnt injection of ACE2. First, the basic reproduction number R₀ is given. We get two possible biologically meaningful equilibria: disease-free equilibrium E₀ and infection equilibrium E₁ . When R₀ < 1, disease-free equilibrium E0 is locally asymptotically stable; further, we can prove that there exists an R₁, when R₁ < 1, disease-free equilibrium E₀ is globally asymptotically stable; when R₀ > 1, E₁ is locally asymptotically stable. Finally, numerical simulation is also presented to demonstrate the applicability of the theoretical predictions.