Trachoma, a neglected tropical disease (NTDs) caused by bacteriumChlamydia trachomatis, is a leading cause of infectious blindness. Efforts are underway to eliminate trachoma as a public health problem by using the “SAFE” strategy. While mathematical models are now standard tools used to support elimination efforts and there are a variety of models studying different aspects of trachoma transmission dynamics, the “F” component of the strategy corresponding to facial cleanliness has received very little attention so far. In this paper, we incorporate human behavior into a standard epidemiological model and develop a dynamical game during which individuals practice facial cleanliness based on their epidemiological status and perceived benefits and costs. We found that the number of infectious individuals generally increases with the difficulty to access a water source. However, this increase happens only during three transition periods and the prevalence stays constant otherwise. Consequently, improving access to water can help eliminate trachoma, but the improvement needs to be significant enough to cross at least one of the three transition thresholds; otherwise the improved access will have no noticeable effect.