On global and local critical points of extended contact process on homogeneous trees. (English) Zbl 1135.92323
Summary: We study spatial stochastic epidemic models called household models. The household models have more than two states at each vertex of a graph in contrast to the contact process. We show that in the household models on trees, two thresholds of infection rates characterize epidemics. The global critical infection rate is defined by epidemic occurrence. However, some households may be eventually disease-free even for infection rates above the global critical infection rate, in as far as they are smaller than the local critical point. Whether the global one is smaller than the local one depends on the graph and the model. We show that, in the household models, the global one is smaller than the local one on homogeneous trees.
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