  In [Aziz-Alaoui, 2002] a three species ODE model, based on a modified
Leslie-Gower scheme is investigated. It is shown that under certain
restrictions on the parameter space, the model has bounded solutions for all
positive initial conditions, which eventually enter an invariant attracting
set. We show that this is not true. To the contrary, solutions to the model can
blow up in finite time, even under the restrictions derived in [Aziz-Alaoui,
2002], if the initial data is large enough. We also prove similar results for
the spatially extended system. We validate all of our results via numerical
simulations.
