In this paper, we consider a reaction–difusion model in population dynamics and
study the impact of diferent types of Allee efects with logistic growth in the heterogeneous closed region. For strong Allee efects, usually, species unconditionally die out
and an extinction-survival situation occurs when the efect is weak according to the
resource and sparse functions. In particular, we study the impact of the multiplicative
Allee efect in classical difusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee efect, and the population survives in some domain
and diverges otherwise. Positive sparsity gives a strong Allee efect, and the population extinct without any condition. The infuence of Allee efects on the existence and
persistence of positive steady states as well as global bifurcation diagrams is presented.
The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented.
When the difusion is absent, we consider the model with and without harvesting,
which are initial value problems (IVPs) and study the local stability analysis and present
bifurcation analysis. We present a number of numerical examples to verify analytical
results.