论文标题
关于离散时间网络流行模型的流行平衡的稳定性
On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model
论文作者
论文摘要
网络流行模型已被广泛采用以描述传播现象。这些模型的地方性均衡在病毒营销，创新传播和信息扩散领域具有重要意义。但是，尚未完全探索其稳定性条件。在本文中，我们以离散时间的方式研究了具有异质过渡速率的网络易感感染感染感染（SIS）流行模型的地方性平衡的稳定性。我们表明，对于任何非平凡初始条件，流行平衡（如果存在）在渐近稳定。在初始条件下的轻度假设下，我们进一步证明，在扩散过程中，相对于地方性平衡没有过度冲击。最后，我们在现实世界网络上进行数值实验以证明我们的结果。
Networked epidemic models have been widely adopted to describe propagation phenomena. The endemic equilibrium of these models is of great significance in the field of viral marketing, innovation dissemination, and information diffusion. However, its stability conditions have not been fully explored. In this paper we study the stability of the endemic equilibrium of a networked Susceptible-Infected-Susceptible (SIS) epidemic model with heterogeneous transition rates in a discrete-time manner. We show that the endemic equilibrium, if it exists, is asymptotically stable for any nontrivial initial condition. Under mild assumptions on initial conditions, we further prove that during the spreading process there exists no overshoot with respect to the endemic equilibrium. Finally, we conduct numerical experiments on real-world networks to demonstrate our results.
