论文标题
微观马尔可夫链方法的分叉分析在网络中基于接触的流行病扩散
Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks
论文作者
论文摘要
传播在单个宿主种群中传播的许多流行病室模型的动力学表现出二阶相变。从缺乏感染个体到流行状态，这种转变是感染性参数的函数。在这里，我们从动力学系统的角度研究了这种转变，用于一个被称为微观马尔可夫链方法的离散时间隔室流行模型，该模型的适用性被证明在预测未来的流行病扩散场景中非常有用。我们表明，存在一个稳定和全球吸引子的地方性状态，其存在是跨临界分叉的结果。该数学分析以实用应用中的模型为基础。
The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications.
