Adaptive Neuro-Fuzzy Inference System for Transmission Dynamics of HIV with an SEIRS Epidemic Model

This study presents a mathematical model aiming to analyze the transmission dynamics of a Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) epidemic model for HIV, with a particular focus on the impact of media. The choice of an Adaptive Neuro-Fuzzy Inference System (ANFIS) for modeling HIV transmission dynamics is driven by its adeptness in capturing complex nonlinear interactions within disease models. The research involves formulating a system of differential equations for each population group, including the susceptible, exposed, infected, and recovered classes. The study provides a comprehensive understanding of the dynamics of disease spread through rigorous mathematical analysis. The calculation of the basic reproduction number is performed, and examining two equilibria, namely the disease-free and endemic states, reveals important insights. Significantly, it is established that the disease-free equilibrium is both locally and globally asymptotically stable. Numerical simulations are conducted using an innovative hybrid soft computing approach called the ANFIS to validate the findings. This study can be replicated in similar endemic/pandemic diseases of these categories and can help provide insights for effective control strategies.