In this paper, we analyze a predator-predator-parasite model, which considers prey subjected to predator fear effect and two modes of harvesting (cooperation hunting by predators and artificial harvesting of prey). Firstly, mathematical analysis of the model with regard to the non-negativity, boundedness of solutions, stability of equilibria, permanence, backward bifurcation and Hopf-bifurcation of the model are analyzed. Secondly, we obtain some numerical simulation results: we conduct extensive numerical simulations to explore the roles of fear effect and other biologically related parameters (e.g. disease transmission rate of prey, hunting cooperation and artificial harvesting), we find that low levels fear and hunting cooperation can stabilize the eco-epidemiological system, and low level artificial harvesting will produce chaotic oscillations, but high level artificial harvesting will stabilize the eco-epidemiological system. In reality, we should protect vulnerable species from fear and cooperation hunting by predators, because decrease in the number of vulnerable species may lead to decrease in species diversity. Moreover, artificial harvesting of species with certain economic value is generally carried out (such as fish populations). However, if the species density is too low, the chaotic oscillation of the population is dangerous to the survival of the population, increasing the probability of population extinction, and it is impossible to obtain a constant yield from the fluctuating population. Therefore, it is desirable to promote the overall stable equilibrium state of the system by artificial harvesting. In addition, it is also observed the presence of disease in an ecosystem can promote stable coexistence of species.