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.

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关于离散时间网络流行病模型流行平衡的稳定性

网络流行病模型已被广泛用于描述传播现象。这些模型的地方性均衡在病毒式营销、创新传播和信息传播领域具有重要意义。然而，其稳定性条件尚未得到充分探索。在本文中，我们以离散时间的方式研究具有异质转变率的网络化易感-感染-易感 (SIS) 流行病模型的流行平衡的稳定性。我们证明了地方性平衡（如果存在）对于任何非平凡的初始条件都是渐近稳定的。在对初始条件的温和假设下，我们进一步证明在传播过程中不存在相对于地方性平衡的超调。最后，