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

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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 (R0) 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 R0, 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.