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Coexistence results for a spatial stochastic epidemic model. (English) Zbl 1071.60079

A continuous time Markov spatial stochastic model of epidemic on \(\mathbf{Z}^d\) is considered in which healthy individuals give birth to healthy individuals on empty nearest neighbor sites and infected individuals infect their healthy nearest neighbors. Individuals also can die at certain rates and infected individual can recover. Coexistence means that there exists an epidemic state of the model, i.e. a stationary measure for the process with nonzero numbers of infected and healthy individuals. It is shown that for any strictly positive value of the recover rate an epidemic state in any dimension is possible for appropriate values of the other parameters. This model is compared to the deterministic dynamic non-spatial model for the means of healthy and infected persons numbers.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
92D30 Epidemiology
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