Intra-specific competition in predator can promote the coexistence of an eco-epidemiological model with strong Allee effects in prey

• We study dynamics of eco-epidemiological system with disease and Allee effect in prey and Hydra effect in predator.
• Disease transmission follows the standard incidence.
• Perform local and global dynamics of the model equations.
• Competition in the predator can promote the coexistence of all the three populations.

An eco-epidemiological model with Allee effects and disease in prey has been proposed and analyzed. The proposed model incorporates intra-specific competition in predator due to the limited food source, and assumes standard incidence disease transmission. We analyzed the corresponding submodels with and without the Allee effects to obtain the complete dynamics of the full model. Our results show that our full model shows multi-stability between the planner equilibriums (where the susceptible prey co-exists with infected prey or predator); both the full model and its submodels exhibit the hydra effects caused by the intra-specific competition in predator. We determined the existence of multiple interior attractors and their stability. Our analysis shows that our system has at most two interior equilibria whose stability is either both saddle or one stable with another one saddle. One of the most interesting findings is that the competition in the predator can promote the coexistence of all the three populations. In addition, we discussed how the frequency-dependent transmission differs from the model with the density-dependent transmission and compare the hydra effects observed in our model to other existing models in literature.