Local Stability Analysis and Numerical Simulation of A Rabies Transmission Model with Vaccination and Culling

Abstract

Rabies remains a serious zoonotic disease requiring effective control strategies in both human and dog populations. This study analyzes the local stability of an SVEIR–SVEIR rabies transmission model incorporating vaccination and culling interventions. The model is analyzed analytically and numerically using parameter values obtained from relevant literature. The study involves identifying equilibrium states, deriving the basic reproduction number through the Next Generation Matrix approach, and analyzing the eigenvalues of the Jacobian matrix. The analysis indicates that the disease-free equilibrium remains locally asymptotically stable for , whereas instability occurs when . Numerical simulations confirm that increasing vaccination and culling rates reduces the infected populations, with dog vaccination having a stronger effect than culling in suppressing rabies transmission. This study is limited to local stability analysis and may be extended through global stability and optimal control analysis in future research.