Bifurcation analysis of a fractional-order eco-epidemiological system with two delays

This article investigates a fractional-order eco-epidemiological system with digestion and latency delays incorporating pathogens as pest biocontrol agents. The pest species in question feeds on the crop and a wild host species. Choosing two distinct time delays as bifurcation parameters, explicit sufficient conditions for Hopf bifurcation of the system are derived at the positive interior equilibrium point. To simplify calculations, the implicit array and cross-curve methods are employed to determine the critical values of bifurcation points. Numerical simulations validate the theoretical results and further examine the effects of disease transmission rate, crop density, and memory effect on the bifurcation points. The results demonstrate that the fractional order plays a crucial role in determining the occurrence of Hopf bifurcation, either hastening or delaying its onset.