Large and Moderate Deviations for Empirical Density Fields of Stochastic Seir Epidemics with Vertex-Dependent Transition Rates

In this paper, we are concerned with stochastic susceptible-exposed-infected-removed epidemics on complete graphs with vertex-dependent transition rates. Large and moderate deviations of empirical density fields of our models are given. Proofs of our main results utilize exponential martingale strategies. In the proof of the moderate deviation principle, we introduce an iteration approach to check the exponential tightness of scaled density fields of our processes. As an application of our main results, moderate deviations of a family of hitting times of our processes are also given.