Automata network SIR models for the spread of infectious diseases
are studied. The local rule consists of two subrules. The first one,
applied sequentially, describes the motion of the individuals, the
second is synchronous and models infection and removal (or recovery).
The spatial correlations created by the application of the second
subrule are partially destroyed according to the degree of mixing
of the population which follows from the application of the first
subrule. One- and two-population models are considered. In the second
case, individuals belonging to one population may be infected only
by individuals belonging to the other population as is the case,
for example, for the heterosexual propagation of a venereal disease.
It is shown that the occurrence of the epidemic in one population
may be triggered by the occurrence of the epidemic in the other population.
The emphasis is on the influence of the degree of mixing of the individuals
which follows from their diffusive motion. In particular, the asymptotic
behaviours for very small and very large mixing are determined. When
the degree of mixing tends to infinity the correlations are completely
destroyed and the time evolution of the epidemic is then correctly
predicted by the mean-field approximation.
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