  We proposed a new generalized model based on the classical Hawkes process
with environmental multipliers, which is called an environmentally-adaptive
Hawkes (EAH) model. Compared to the classical self-exciting Hawkes process, the
EAH model exhibits more flexibility in a macro environmentally temporal sense,
and can model more complex processes by using dynamic branching matrix. We
demonstrate the well-definedness of this EAH model. A more specified version of
this new model is applied to model COVID-19 pandemic data through an efficient
EM-like algorithm. Consequently, the proposed model consistently outperforms
the classical Hawkes process.
