A Robust Moment Closure for General Continuous-time Epidemic Processes

Abstract

We develop a robust moment closure for a general class of continuous-time epidemic spreading processes, the elements of which are prevalent in the literature. Our moment closure method takes as input a general stochastic compartmental spreading process defined for $n$ agents and $m$ compartments, and produces a system of 2nm differential equations whose solutions provide nontrivial approximations to the marginal compartmental membership probabilities for each agent. This is an improvement over the commonly used mean-field type approximation, which provides no such guarantee. We demonstrate that our results provide useful predictions with examples performed on two models of competitive spreading processes, and find the developed closure to be more informative than mean-field approximations.