The dynamics of hepatitis B virus transmission using a stochastic differential model and feed forward neural network approach.

Hepatitis B transmission is influenced by environmental variability, immune response and vaccination, making its spread inherently stochastic, while the integration of stochastic modeling with machine learning is particularly important for representing disease uncertainty in varied surroundings. We present a hybrid innovative framework that combines a stochastic epidemiological model with a feed-forward neural network to study hepatitis B virus (HBV) dynamics. We show the well-posedness by establishing the existence of solutions with uniqueness, and analyze extinction and persistence of the disease. In addition, a supervised approach of feed-forward neural network (FFNN) having two hidden layers, each consist of 20 neurons will be used to effectively approximate the dynamics of the model. To evaluate robustness of the network while handling the stochastic model, we evaluate the performance by regression and mean squared error (MSE), and to show a strong alliance among the stochastic trajectories and predicted simulations obtained by the neural network.