Yaws is a chronic infection caused by the bacterium Treponema pallidum susp. pertenue (TPE) that was thought to be an exclusive human pathogen but was recently found and confirmed in nonhuman primates. In this paper, we develop the first compartmental ODE model for TPE infection with treatment of wild olive baboons. We solve for disease-free and endemic equilibria and give conditions on local and global stability of the disease-free equilibrium. We calibrate the model based on the data from Lake Manyara National Park in Tanzania. We use the model to help the park managers devise an effective strategy for treatment. We show that an increasing treatment rate yields a decrease in disease prevalence. This indicates that TPE can be eliminated through intense management in closed population. Specifically, we show that if the whole population is treated at least once every 5-6 years, a disease-free equilibrium can be reached. Furthermore, we demonstrate that to see a substantial decrease of TPE infection to near-elimination levels within 15 years, the whole population needs to be treated every 2-3 years.