Mathematical Modeling and Analysis of Human-to-Human Transmitted Viral Encephalitis

Encephalitis, a severe neurological condition caused by human-to-human (H2H) transmitted viruses, such as herpes simplex virus (HSV), requires a rigorous mathematical framework to understand its transmission dynamics. This study develops a nonlinear compartmental model, SEITR (Susceptible–Exposed–Infected–Treated–Recovered), to characterize the progression of viral encephalitis. The basic reproduction number (R 0 ) is derived using the next-generation matrix method, serving as a threshold parameter determining disease persistence. The local and global stability of the disease-free and endemic equilibria are established through a rigorous mathematical analysis. Additionally, a sensitivity analysis quantifies the impact of key parameters on R 0 , offering more profound insights into their mathematical significance. Numerical simulations validate the theoretical results, demonstrating the system’s dynamical behavior under varying epidemiological conditions. This study provides a mathematically rigorous approach to modeling viral encephalitis transmission, filling a gap in the literature and offering a foundation for future research in infectious disease dynamics.