  In this paper, we investigate the asymptotic behavior of nearly unstable
Hawkes processes whose regression kernel has $L^1$ norm strictly greater than
one and close to one as time goes to infinity. We find that,the scaling size
determines the scaling behavior of the processes like in \cite{MR3313750}.
Specifically,after suitable rescaling, the limit of the sequence of Hawkes
processes is deterministic.And also with another appropriate rescaling, the
sequence converges in law to an integrated Cox Ingersoll Ross like process.
This theoretical result may apply to model the recent COVID19 in epidemiology
and in social network.
