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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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 multisourced 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.

SUMMARYDue to both the complexity of real systems and the technical difficulties inherent to extremal analysis, the statistics of extremes in spatio-temporal processes has become one of the most challenging research areas in relation to the increasingly demanding interest on risk assessment tools in many fields of application. Recent advances in spatio-temporal statistical analysis are focused, in particular, on the formulation and study of new model families, flexible to represent such real complexities and, at the same time, suitable for technical treatment and interpretation, as well as on related system dynamics problems.In this paper, significant characteristics of threshold exceedances with reference to structural properties of the processes generating such events, particularly in the context of input/output systems, are analyzed. Specifically, the effect of spatial deformation and blurring transformations on the second order structure and the geometrical properties of excursion sets is studied and illustrated through some simulated cases. A spatio-temporal model based on spatial deformation and blurring, which provides a suitable representation for a variety of environmental applications, is formulated, and further aspects regarding the temporal structure of threshold exceedances are explored and discussed.