Bifurcation and chaos design of radial basis neural network for predictive modeling of fractional double-strain HIV co-infection model with intercellular delays and stochastic effects.

The aim of the present study is to obtain the numerical solutions of the fractional double-strain HIV co-infection model with intercellular delays and stochastic effects (FDS-HIV-IDS) by employing a novel radial basis neural network with Levenberg-Marquardt backpropagation (RBNN-LMB). The nonlinear model accounts for multiple interacting populations, and logistic growth is introduced to describe the interaction between wild-type and drug-resistant HIV strains. The analysis of the model considers threshold criteria for both local and global stability of infection-free, dominant, and coexistence equilibria. The nonlinear model incorporates multiple interacting groups, and its numerical solutions are approximated through the stochastic RBNN-LMB framework. Consequently, double-strain dynamics transition from stability to instability (periodic oscillations to chaos) more frequently and at earlier stages. This also leads to a higher total viral load compared to single-strain scenarios, highlighting the greater risk of treatment failure when resistance emerges. A dataset is generated using the numerical predictor-corrector method, where the data are split into 75% for training and 10% for validation and 15% for testing, in order to minimize the mean square error (MSE). The solver architecture consists of fifteen hidden neurons, a single input structure, and a radial basis activation function to approximate the system dynamics effectively. The accuracy of the method is demonstrated through the overlapping of predicted and reference outputs, while the very small absolute error (AE) values confirm its precision. Furthermore, statistical evaluations using different operators support the reliability and robustness of the proposed approach.