In ecosystem , the interaction of the species such as competition among species , cooperation , predator-prey interaction , etc is a natural phenomena . Predator-prey interaction is a basic mechanism for two species dynamics and its mathematical models that explain many phenomena in nature . On the other hand , the spread of infectious disease among biotic population plays an underlying role in evolution of species , not only growth of species population , but also interaction of species . As usual , the resources necessary for individuals to survive in the habitat environment are distributed spatially heterogeneously , which influences the evolution of interacting species as well as the spread of infectious disease . This iires us to take into account the spatial-temporal movement of individuals living spatially heterogeneous in our ecoepidemic models . Therefore in this thesis by considering these factors , first we considered a model that is devoted to incorporate the spatial heterogeneity , conversion lag from prey biomass to predator biomass into a predator-prey model with disease in predators , which is governed by a delayed reaction-diffusion system . In this proposed model , we obtained required conditions for the coexistence of the populations exposed to disease , the appearance of limit cycles and existence of complex dynamics such as Takens-Bogdanov and Hopf-Zero bifurcations. In the real world , many species have a life history that takes them through two stages , juvenile and adult stage or immature and mature stage . Individuals in each stage are identical in their biological characteristics , and some vital rates (rates of survival , development , and reproduction) of individuals in a population almost always depend on stage structure . When dividing one population species into two groups including mature and immature individuals , the age for maturity is represented by a time delay , which leads to systems of retarded functional differential equations . In prey-predator models , usually it is assumed that predator feeds on prey , but in the real world , anti-predator behavior of prey population exists and many experiments have shown that this behavior is achieved in two ways . One way is morphological changes or through changes in behavior . Another way is that the prey attack their predators . Some authors have studied these cases and suggested that more efficient anti-predator behavior is beneficial to the prey population , and can reduce the predator density , also they introduced the various rates for anti-predator behavior of prey into the predator population . Keeping this behavior in mind , we built an eco-epidemiological model with an age structure in the predator population , two time delays due to gestation time of the mature predator and the maturation age. In the second model , we obtained required conditions for the coexistence of the populations exposed to disease , the appearance of limit cycles and existence of complex dynamics such as Bogdanov-Takens bifurcation .