MATHEMATICAL MODELING AND ANALYSIS OF RABIES TRANSMISSION DYNAMICS WITH VACCINATION - Isiyaku, M.; Abdullahi, Musa; Husseini, A.; Song, I. M.; Bade, S. H.; Abubakar, A.; Gidado, Umar (FUDMA JOURNAL OF SCIENCES, 2025)
Rabies remains a fatal zoonotic disease that poses a significant public health challenge, particularly in low- and middle-income countries. In this study, we develop and analyze a deterministic compartmental model based on ordinary differential equations to investigate the transmission dynamics of rabies between humans and dogs.  Basic properties of the model such as positivity, boundedness, and the existence of equilibria are established, and the model is well-posed mathematically and biologically. The basic reproduction number, ​, is derived using the next-generation matrix method, and stability analysis reveals that the rabies-free equilibrium is locally and globally asymptotically stable when . The model exhibits a unique endemic equilibrium, when , which is also globally stable whenever . Sensitivity analysis using both normalized forward sensitivity indices and partial rank correlation coefficients (PRCC) identifies the most influential parameters on ​. Numerical simulations demonstrate that vaccination, particularly in the dog population is the most effective control strategy in reducing the spread of rabies. The results emphasize the importance of prioritizing control interventions in the dog population to effectively manage and reduce the burden of rabies.
Keywords: Rabies; Reproduction Number; Vaccination; Stability; Sensitivity