本篇論文主要探討具有急性與慢性階段和雙線性傳染率的非線性微分方程系統，將感染者分為急性感染者及慢性感染者，建立了SEI傳染病模型的分支：SEIV模型。透過微分方程相關理論證明了無病均衡點及疾病均衡點的局部與整體穩定性，並且在數學上以及公衛領域上，皆獲得影響傳染疾病是否滅絕或持續蔓延的關鍵條件：基本再生數。 In this thesis, we mainly analyze the stability of an SEI epidemic system with acute and chronic stages and bilinear incidence rate. We use the technique of Hurwitz criterion and Lyapunov function to analyze the stability of free-disease equilibrium point P_{0} and endemic equilibrium point P^{*}. Furthermore, both in Mathematics and Public Health, we obtain the basic reproduction number R_{0} which determines whether the disease extinguishes or spreads.
