论文标题
具有流行病学应用的图形上的局部密度依赖于马尔可夫的过程
Local-density dependent Markov processes on graphons with epidemiological applications
论文作者
论文摘要
我们研究了从Graphon采样的一类大图上的局部密度依赖性Markov过程，其中顶点的过渡速率受其邻居状态的影响。我们表明，随着平均程度收敛到无穷大，瞬态状态中该过程的演变会收敛到一组非局部内部派对微分方程的溶液。如果在此类图形上易感感染感染敏感（SIS）过程，我们还为流行阈值提供了严格的衍生。
We investigate local-density dependent Markov processes on a class of large graphs sampled from a graphon, where the transition rates of the vertices are influenced by the states of their neighbors. We show that as the average degree converges to infinity, the evolution of the process in the transient regime converges to the solution of a set of non-local integro-partial differential equations. We also provide rigorous derivation for the epidemic threshold in the case of the Susceptible-Infected-Susceptible (SIS) process on such graphons.
