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The occurrence of arsenic in drinking water is an issue of considerable interest. In the case of Bangladesh, arsenic concentrations have been closely monitored since the early 1990s through an extensive sampling network. The focus of the present work is methodological. In particular, we propose the application of a holistochastic framework of human exposure to study lifetime population damage due to arsenic exposure across Bangladesh. The Bayesian Maximum Entropy theory is an important component of this framework, which possesses solid theoretical foundations and offers powerful tools to assimilate a variety of knowledge bases (physical, epidemiologic, toxicokinetic, demographic, etc.) and uncertainty sources (soft data, measurement errors, etc.). The holistochastic exposure approach leads to physically meaningful and informative spatial maps of arsenic distribution in Bangladesh drinking water. Global indicators of the adverse health effects on the population are generated, and valuable insight is gained by blending information from different scientific disciplines. The numerical results indicate an increased lifetime bladder cancer probability for the Bangladesh population due to arsenic. The health effect estimates obtained and the associated uncertainty assessments are valuable tools for a broad spectrum of end-users.

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This paper describes the spatiotemporal epistematics knowledge synthesis and graphical user interface (SEKS-GUI) framework and its application in medical geography problems. Based on sound theoretical reasoning, the interactive software library of SEKS-GUI explores heterogeneous (spatially non-homogeneous and temporally non-stationary) health attribute distributions (disease incidence, mortality, human exposure, epidemic propagation etc.); expresses the health system's dependence structure using (ordinary and generalized) spatiotemporal covariance models; synthesizes core knowledge bases, empirical evidence and multi-sourced system uncertainty; and generates a meaningful picture of the real-world system using spacetime dependent probability functions and associated maps of health attributes. The implementation stages of the SEKS-GUI library are described in considerable detail using appropriate screens. The wide applicability of SEKS-GUI is demonstrated by reviewing a selection of real-world case studies.

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.

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[1] This work presents a computational formulation of the Bayesian maximum entropy (BME) approach to solve a stochastic partial differential equation (PDE) representing the advection-reaction process across space and time. The solution approach provided by BME has some important features that distinguish it from most standard stochastic PDE techniques. In addition to the physical law, the BME solution can assimilate other sources of general and site-specific knowledge, including multiple-point nonlinear space/time statistics, hard measurements, and various forms of uncertain (soft) information. There is no need to explicitly solve the moment equations of the advection-reaction law since BME allows the information contained in them to consolidate within the general knowledge base at the structural (prior) stage of the analysis. No restrictions are posed on the shape of the underlying probability distributions or the space/time pattern of the contaminant process. Solutions of nonlinear systems of equations are obtained in four space/time dimensions and efficient computational schemes are introduced to cope with complexity. The BME solution at the prior stage is in excellent agreement with the exact analytical solution obtained in a controlled environment for comparison purposes. The prior solution is further improved at the integration (posterior) BME stage by assimilating uncertain information at the data points as well as at the solution grid nodes themselves, thus leading to the final solution of the advection-reaction law in the form of the probability distribution of possible concentration values at each space/time grid node. This is the most complete way of describing a stochastic solution and provides considerable flexibility concerning the choice of the concentration realization that is more representative of the physical situation. Numerical experiments demonstrated a high solution accuracy of the computational BME approach. The BME approach can benefit from the use of parallel processing (the relevant systems of equations can be processed simultaneously at each grid node and multiple integrals calculations can be accelerated significantly, etc.).