Modeling stochastic processes in disease spread across a heterogeneous social system.

Diffusion processes are governed by external triggers and internal dynamics in complex systems. Timely and cost-effective control of infectious disease spread critically relies on uncovering underlying diffusion mechanisms, which is challenging due to invisible infection pathways and time-evolving intensity of infection cases. Here, we propose a new diffusion framework for stochastic processes, which models disease spread across metapopulations by incorporating human mobility as topological pathways in a heterogeneous social system. We apply Bayesian inference with the stochastic Expectation-Maximization algorithm to quantify underlying diffusion dynamics in terms of exogeneity and endogeneity and estimate cross-regional infection flow based on Granger causality. The effectiveness of our proposed model is shown by using comprehensive simulation procedures (robustness tests with noisy data considering missing or delayed human case reporting in real situations) and by applying the model to real data from 15-y dengue outbreaks in Australia.