A comprehensive mathematical model of Nipah virus transmission dynamics: Stability analysis and numerical simulations

The Nipah virus (NiV) is a zoonotic pathogen known for causing severe illnesses in both animals and humans, including encephalitis and respiratory issues. In this study, we present a nonlinear system of ordinary differential equations to model the transmission dynamics of the Nipah virus. The total population is divided into ten distinct compartments: susceptible, infected, and recovered groups for humans, fruit bats, and pigs, along with a vaccination compartment for humans. The model was shown to be positive and bounded, and the corresponding equilibrium points were determined. The basic reproduction number, R0 was derived using the next-generation matrix approach. Local and global stability properties were then examined through Jacobian matrix analysis and the construction of an appropriate Lyapunov function. The analysis indicates that the disease-free equilibrium is asymptotically stable for R0<1, whereas endemic equilibria arise and remain stable when R0>1. Numerical simulations are consistent with the analytical results and suggest that higher vaccination and recovery rates contribute to a reduction in infection levels and support long-term disease control.