This paper is concerned with the modeling of infectious disease spread in a composite space-time domain under conditions of uncertainty. We focus on stochastic modeling that accounts for basic mechanisms of disease distribution and multi-sourced in situ uncertainties. Starting from the general formulation of population migration dynamics and the specification of transmission and recovery rates, the model studies the functional formulation of the evolution of the fractions of susceptible-infected-recovered individuals. The suggested approach is capable of: a) modeling population dynamics within and across localities, b) integrating the disease representation (i.e. susceptible-infected-recovered individuals) with observation time series at different geographical locations and other sources of information (e.g. hard and soft data, empirical relationships, secondary information), and c) generating predictions of disease spread and associated parameters in real time, while considering model and observation uncertainties. Key aspects of the proposed approach are illustrated by means of simulations (i.e. synthetic studies), and a real-world application using hand-foot-mouth disease (HFMD) data from China.