Modeling Infectious Diseases Using Global Stochastic Cellular Automata

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.