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.
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