  In the present study, we have modified the traditional May-Holling-Tanner
predator-prey model used to represent the interaction between least weasel and
field-vole population by adding an Allee effect (strong and weak) on the
field-vole population and alternative food source for the weasel population. It
is shown that the dynamic is different from the original May-Holling-Tanner
predator-prey interaction since new equilibrium points have appeared in the
first quadrant. Moreover, the modified model allows the extinction of both
species when the Allee effect (strong and weak) on the prey is included, while
the inclusion of the alternative food source for the predator shows that the
system can support the coexistence of the populations, extinction of the prey
and coexistence and oscillation of the populations at the same time.
Furthermore, we use numerical simulations to illustrate the impact that
changing the predation rate and the predator intrinsic growth rate have on the
basin of attraction of the stable equilibrium point or stable limit cycle in
the first quadrant. These simulations show the stabilisation of predator and
prey populations and/or the oscillation of these two species over time.
