论文标题
具有地方性平衡的新易感感染（SI）模型
A New Susceptible-Infectious (SI) Model With Endemic Equilibrium
论文作者
论文摘要
本文的重点是新的易感感染模型的动态，该模型由一个易感组（$ s $）和两个不同的传染性组（$ i_1 $和$ i_2 $）组成。感染后，一个人将成为这些感染形式不同的传染性群体之一。此外，在疾病进展过程中，I_1组中受感染的个人可能会传递给具有较高死亡率的传染性$ I_2 $。在这项研究中，证明了该模型解决方案的积极性。研究物种灭绝的稳定性分析，$ I_1 $ - 无均衡平衡和地方性平衡以及无病平衡。检查了疾病的基本繁殖数与每个感染阶段的基本繁殖数之间的关系。在特定条件下研究了该模型，并获得了精确的解决方案。
The focus of this article is on the dynamics of a new susceptible-infected model which consists of a susceptible group ($S$) and two different infectious groups ($I_1$ and $I_2$). Once infected, an individual becomes a member of one of these infectious groups which have different clinical forms of infection. In addition, during the progress of the illness, an infected individual in group $I_1$ may pass to the infectious group $I_2$ which has a higher mortality rate. In this study, positiveness of the solutions for the model is proved. Stability analysis of species extinction, $I_1$-free equilibrium and endemic equilibrium as well as disease-free equilibrium is studied. Relation between the basic reproduction number of the disease and the basic reproduction number of each infectious stage is examined. The model is investigated under a specific condition and its exact solution is obtained.
