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Cellular automaton modeling of epidemics. (English) Zbl 0709.92018

Summary: This study investigates random cellular automaton models with emphasis on their application to epidemiology. We conjecture that there may be a spatial factor involved in contagious disease. Random cellular automata would seem a natural mode for statistical exploration of this conjecture. We examine a random cellular automaton measle model proposed by D. Mollison [J. R. Stat. Soc., Ser. B 39, 283-326 (1977; Zbl 0374.60110)]; a homogeneous version of this model is shown to coincide with the macroscopic spatially invariant “basic stochastic” epidemic model discussed by N. T. J. Bailey [The mathematical theory of infectious diseases and its applications. (1975; Zbl 0334.92024)].
Some theory and proposed statistical methodology are suggested. Our experimental findings indicate that the course of an epidemic depends strongly on initial configuration of the infectives, all other parameters remaining fixed. This is consistent with our conjecture that the spatial distribution of the carriers contains significant information. Whether the random cellular automata are valid models for actual epidemis awaits statistical resolution.

MSC:

92D30 Epidemiology
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
68Q45 Formal languages and automata
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