Chagas disease is an important neglected tropical disease which causes on average about 7000 deaths per year, and an estimated 25 million people risk of acquiring it. This illness is often found in rural areas, which are usually characterized by poverty and presence of animals which act as reservoirs of the disease. Our main objective is to study the effect of animal grazing on the disease levels of the human population. For this purpose, we consider two environments (domestic and wild) where each one has permanent residents, and there is a proportion of animals that move between both environments due to grazing. This movement is modeled through the residence time in each environment. We analyze the proposed model and finally, we discuss the influence of domestic animals residence time on the disease level of human population.