A next-generation matrix approach using Routh–Hurwitz criterion and quadratic Lyapunov function for modeling animal rabies with infective immigrants

Abstract

Rabies remains a major public health concern in many regions of the world, particularly in poorer nations. This study proposes a mathematical model for the animal rabies transmission dynamics, considering infective immigrants and vaccination as potential control measures to address this issue. The effective reproduction number (Re) was calculated by using the next-generation matrix approach. By using Routh–Hurwitz Criterion, a disease-free equilibrium point (DFE) was obtained and proved to be locally asymptotically stable if Re<1 and unstable otherwise, and also, by using the quadratic Lyapunov function DFE was determined to be globally asymptotically stable. Moreover, sensitivity analysis of the model parameters on the (Re) was performed using the normalized forward sensitivity index method. For simulation analysis, the numerical analysis was performed with the help of the MATLAB software. The simulated data results revealed that the increase in vaccination rate and decreasing infective immigrants will reduce the spread of the decrease, which was depicted graphically.

Keywords

• Next-generation matrix approach
• Routh–Hurwitz criterion
• Quadratic Lyapunov function
• Rabies
• Infective immigrants
• Stability analysis