论文标题
马尔可夫开关下网络上网络上的随机微分方程SIS模型
A stochastic differential equation SIS model on network under Markovian switching
论文作者
论文摘要
我们在马尔可夫政权转换的效果下研究网络上的随机SI（易感感染感染）流行动力学。我们首先证明存在独特的全球积极解决方案，并为系统找到一个积极的不变设置。然后，我们发现A.S.的足够条件灭绝和随机持久性，还显示了它们与控制开关和网络拓扑结构的马尔可夫链的固定概率分布的关系。我们为在确保随机持久性的条件下的样品路径溶液的时间平均值提供了渐近下限。通过这种结合，如果随机持久性的条件成立，我们能够证明存在不变概率度量的存在。在不同的条件下，我们证明了政权开关扩散的积极复发和成长性。
We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant set for the system. Then, we find sufficient conditions for a.s. extinction and stochastic permanence, showing also their relation with the stationary probability distribution of the Markov chain that governs the switching and with the network topology. We provide an asymptotic lower bound for the time average of the sample-path solution under the conditions ensuring stochastic permanence. From this bound, we are able to prove the existence of an invariant probability measure if the condition of stochastic permanence holds. Under a different condition, we prove the positive recurrence and the ergodicity of the regime-switching diffusion.
