In this paper, considering the aggregation effect and Allee effect of
cyanobacteria population and the harvesting of both cyanobacteria and
fish by human beings, we put forward a new cyanobacteria-fish model with
two harvesting terms and a modified Holling type IV functional response
function. The main purpose of this paper is to further understand the
influence of harvesting terms on the dynamic behavior of
cyanobacteria-fish model. Critical conditions for the existence and
stability of several interior equilibria are given. The economic
equilibria and the maximum sustainable total yield problem are also
studied. The model exhibits several bifurcations, such as transcritical
bifurcation, saddle-node bifurcation, Hopf bifurcation and
Bogdanov-Takens bifurcation. From the perspective of biology, we
conclude that the harvesting terms can determine the survival mode of
cyanobacteria and fish. Finally, concrete examples of our model are
given through numerical simulation to verify and enrich the theoretical
results.