2022/04/28 by Xue, Xiaofeng
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2204.13234
In this paper we are concerned with N-urn susceptible-infected-removed epidemics, where each urn is in one of three states, namely `susceptible', `infected' and `removed'. We assume that recovery rates of infected urns and infection rates between infected and susceptible urns are all coordinate-dependent. We show that the hydrodynamic limit of our model is driven by a deterministic (C[0, 1])^′-valued process with density which is the solution to a nonlinear C[0, 1]-valued ordinary differential equation consistent with a mean-field analysis. We further show that the fluctuation of our process is driven by a generalized Ornstein-Uhlenbeck process. A key step in proofs of above main results is to show that sates of different urns are approximately independent as N→+∞.