Hepatitis B virus spreading via Beddington–DeAngelis incidence function and feed-forward neural network with optimal control

Using an appropriate mathematical model, this study aims to examine the transmission dynamics and optimal control of hepatitis B virus spreading, employing the Beddington-DeAngelis incidence function, a hybrid method of 4th order Runge-Kutta method (RK4) and feed-forward neural network (FFNN), as the integration of epidemiological models with neural network is particularly important for representing disease propagation. The well-posedness, local and global stability conditions are obtained using the threshold parameter. Some sensitive epidemic parameters and their relative impacts are quantified. Based on the local and global properties of the model and sensitivity analysis, a control problem is formulated to control the infection by minimizing the HBV-infected population and maximizing the recovered population using three control measures. Finally, a hybrid method of supervised FFNN and RK4 with two hidden layers is used to effectively approximate the temporal dynamics of HBV transmission and verify the theoretical results, as well as the effects of controls.