Impact of Predation-Mediated Transmission and Vector Pathogenicity on Trypanosoma rangeli Epidemiology: A Bifurcative Model Study

Although Trypanosoma rangeli (T. rangeli) is non-pathogenic to humans, it is pathogenic to triatomines, the vectors of Chagas disease, and thus indirectly influences the disease’s transmission dynamics. Recent observations reveal that susceptible non-human hosts can become infected by preying on infected triatomines, establishing a significant transmission route for T. rangeli known as predation transmission. This study presents a mathematical model that integrates host predation and vector pathogenicity, examining how these factors jointly affect T. rangeli transmission. We derive two key thresholds: [Formula: see text], representing the basic reproduction number of triatomine vectors, and [Formula: see text], denoting the basic reproduction number of T. rangeli. The predation rate m is used as a parameter to characterize vector population dynamics. The model shows that the vector-free equilibrium is globally stable when [Formula: see text], while the parasite-free equilibrium is globally stable for [Formula: see text] . A forward bifurcation occurs at [Formula: see text], marking a qualitative shift in system behavior. For [Formula: see text], the system admits a parasite-positive equilibrium, which may lose stability via a Hopf bifurcation, resulting in oscillatory dynamics. We also prove uniform persistence of the model solutions, ensuring long-term survival of T. rangeli whenever [Formula: see text] . Numerical simulations reveal that host predation significantly reduces the transmission risk of T. rangeli, and pathogenic effects play a crucial role in driving oscillatory patterns. These analytical and numerical results provide valuable insights for developing effective prevention and control strategies against Chagas disease.