Susceptibles-infectives-removals (SIR) and its derivatives are the classic mathematical models for the study of infectious diseases in epidemiology. In order to model and simulate epidemics of an infectious disease, we use cellular automata (CA). The simplifying assumptions of SIR and naive CA limit their applicability to the real world characteristics. A global stochastic cellular automata paradigm (GSCA) is proposed, which incorporates geographic and demographic based interactions. The interaction measure between the cells is a function of population density and Euclidean distance, and has been extended to include geographic, demographic and migratory constraints. The progression of diseases using traditional CA and classic SIR are analyzed, and similar behavior to the SIR model is exhibited by GSCA, using the geographic information systems (GIS) gravity model for interactions. The limitations of the SIR and naive CA models of homogeneous population with uniform mixing are addressed by the GSCA model. The GSCA model is oriented to heterogeneous population, and can incorporate interactions based on geography, demography, environment and migration patterns. The progression of diseases can be modeled at higher levels of fidelity using the GSCA model, and facilitates optimal deployment of public health resources for prevention, control and surveillance of infectious diseases.

Emerging infectious diseases continue to place a strain on the welfare of the population by decreasing the population's general health and increasing the burden on public health infrastructure. This paper addresses these issues through the development of a computational framework for modeling and simulating infectious disease outbreaks in a specific geographic region facilitating the quantification of public health policy decisions. Effectively modeling and simulating past epidemics to project current or future disease outbreaks will lead to improved control and intervention policies and disaster preparedness. In this paper, we introduce a computational framework that brings together spatio-temporal geography and population demographics with specific disease pathology in a novel simulation paradigm termed, global stochastic field simulation (GSFS). The primary aim of this simulation paradigm is to facilitate intelligent what-if-analysis in the event of health crisis, such as an influenza pandemic. The dynamics of any epidemic are intrinsically related to a region's spatio-temporal characteristics and demographic composition and as such, must be considered when developing infectious disease control and intervention strategies. Similarly, comparison of past and current epidemics must include demographic changes into any effective public health policy for control and intervention strategies. GSFS is a hybrid approach to modeling, implicitly combining agent-based modeling with the cellular automata paradigm. Specifically, GSFS is a computational framework that will facilitate the effective identification of risk groups in the population and determine adequate points of control, leading to more effective surveillance and control of infectious diseases epidemics. The analysis of past disease outbreaks in a given population and the projection of current or future epidemics constitutes a significant challenge to Public Health. The corresponding design of computational models and the simulation that facilitates epidemiologists' understanding of the manifestation of diseases represents a challenge to computer and mathematical sciences.

In this paper, we propose the use of Cellular Automata paradigm to simulate an infectious disease outbreak. The simulator facilitates the study of dynamics of epidemics of different infectious diseases, and has been applied to study the effects of spread vaccination and ring vaccination strategies. Fundamentally the simulator loosely simulates SIR (Susceptible Infected Removed) and SEIR (Susceptible Exposed Infected Removed). The Geo-spatial model with global interaction and our approach of global stochastic cellular automata are also discussed. The global stochastic cellular automata takes into account the demography, culture of a region. The simulator can be used to study the dynamics of disease epidemics over large geographic regions. We analyze the effects of distances and interaction on the spread of various diseases.

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