We establish and study an \(\mathit {SIRS}\) epidemic model for a zoonotic disease only transmitted from animals to humans but not the opposite way, with a general nonlinear incidence rate assuming that the animal population has already reached an endemic equilibrium. Due to the zoonotic transmission, there is no disease-free equilibrium, and unlike in most epidemic models, no threshold dynamics can be observed. Using a transformation of variables, we derive a Lyapunov function for the global asymptotic stability of the unique endemic equilibrium, independently of model parameters.