The Land-use change emerges as a fundamental factor in the increase in zoonotic diseases, affecting both ecosystems and human populations. The edge effect between forested areas and their surrounding environments, modifies species distribution, and consequently the dynamics zoonotic wildlife. Patches with high perimeter-to-area ratios may experience a more pronounced edge effect, justifying the relevance of studying patch shape in a disease dynamics. In addition, competition between species, especially between those that act as reservoirs and those that do not, plays a crucial role in eco-epidemiological dynamics. In this context, our study addresses competition dynamics between two species employ the Lotka-Volterra model. We introduce an internal classification in the host species with two compartments, susceptible and infected, and model the disease transmission rate using a function linked to parameters associated with the edge effect. Specifically, the transmission rate differentiates interactions between susceptible and infected individuals in the core area and the edge of the patch, being a function dependent on the shape index of the patch, and is of the edge effect and host density. We predicted that, although competition can decrease the spread of the disease among hosts, the edge effect can paradoxically increase it.