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An epidemic model with births and deaths is considered on a two dimensionalLxL lattice. Each individual can have global infective contacts according tothe standard SIR model rules or local infective contacts with its nearestneighbors. We propose a deterministic approach to this model and verified thatthere is a good agreement with the stochastic simulations for differentsituations of the disease transmission and parameters corresponding topertussis and rubella in the prevaccine era.

SIR model with local and global infective contacts: A deterministic approach and applications