An eco-epidemiological model with general functional response of predator to prey

We consider a generalization of the nonautonomous model in [Xingge Niu, Tailei Zhang, Zhidong Teng, The asymptotic behavior of a nonautonomous eco-epidemic model with disease in the prey, Applied Mathematical Modelling 35, 457-470 (2011)] by adding a general function corresponding to predation on uninfected preys as well as general functions associated to the vital dynamics of the susceptible prey and predator populations. We obtain persistence and extinction results for the infected prey based on some assumptions on the bidimensional predator-prey subsystem that describes the dynamics in the absence of infected preys. We apply our results to eco-epidemiological models constructed from several predator-prey models existent in the literature. Some illustrative simulation is undertaken.