论文标题
向后分叉，基本的再感染数量和SEIRE流行模型的鲁棒性，并得到恢复
Backward bifurcation, basic reinfection number and robustness of a SEIRE epidemic model with reinfection
论文作者
论文摘要
最近的证据表明，从COVID-19恢复的个人可以重新感染。但是，这种现象很少使用数学模型研究。在本文中，我们提出了一个SEIRE流行模型，以通过再感染来描述流行病的传播。我们获得了重要的阈值$ R_0 $（基本复制号）和RC（小于一个阈值）。我们的调查表明，当$ r_0> 1 $时，该系统具有地方性平衡，在全球渐近稳定。当$ r_c <r_0 <1 $时，流行系统将表现出双态动力学。也就是说，该系统具有向后分叉，无法消除该疾病。为了消除这种疾病，我们必须确保基本的繁殖数$ r_0 $小于$ r_c $。获得了基本的再感染数来测量再感染力，这是疾病动力学的新临界点。我们还给出了鲁棒性的定义，这是一个新概念，以衡量完全消除双态流行系统疾病的难度。进行数值模拟以验证结论。
Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose a SEIRE epidemic model to describe the spread of the epidemic with reinfection. We obtain the important thresholds $R_0$ (the basic reproduction number) and Rc (a threshold less than one). Our investigations show that when $R_0 > 1$, the system has an endemic equilibrium, which is globally asymptotically stable. When $R_c < R_0 < 1$, the epidemic system exhibits bistable dynamics. That is, the system has backward bifurcation and the disease cannot be eradicated. In order to eradicate the disease, we must ensure that the basic reproduction number $R_0$ is less than $R_c$. The basic reinfection number is obtained to measure the reinfection force, which turns out to be a new tipping point for disease dynamics. We also give definition of robustness, a new concept to measure the difficulty of completely eliminating the disease for a bistable epidemic system. Numerical simulations are carried out to verify the conclusions.
