  Viruses constantly undergo mutations with genomic changes. The propagation of
variants of viruses is an interesting problem. We perform numerical simulations
of the microscopic epidemic model based on network theory for the spread of
variants. Assume that a small number of individuals infected with the variant
are added to widespread infection with the original virus. When a highly
infectious variant that is more transmissible than the original lineage is
added, the variant spreads quickly to the wide space. On the other hand, if the
infectivity is about the same as that of the original virus, the infection will
not spread. The rate of spread is not linear as a function of the infection
strength but increases non-linearly. This cannot be explained by the
compartmental model of epidemiology but can be understood in terms of the
dynamic absorbing state known from the contact process.
