Alternative 1
The system described in equation (5) of the
Mathematical Analysis can be used as input to the
odepack routines LSODI and LSODIS. However neither of them provides root finding, i.e., events and fast reactions can not be part of the same model. To achieve this we need to develop our own root finding extension.
Alternative 2
The system described in equation (5) of the
Mathematical Analysis can be used as input to IDA, which is part of the
SUNDIALS package. IDA provides a root finder and thus events and fast reactions can be mixed.