Machine learning-enhanced stochastic modeling of Marburg virus transmission in human–bat populations

A serious threat to global health is the Marburg virus, which affects human beings as well as non-human primates. This study develops a comprehensive stochastic mathematical model to examine Marburg virus transmission dynamics in human and bat populations, incorporating vaccination effects and random environmental factors including immigration, climate change, and behavioral variations. In this work, we employ stochastic differential equations coupled with neural network analysis to capture the complex disease dynamics. First, we prove that the solution exists globally and is positive. Next, we establish the fundamental stochastic reproduction number, which serves as a threshold parameter determining disease extinction ( R 0 s < 1 ) or persistence ( R 0 s > 1 ) in the population. Numerical simulation is performed to investigate the dynamics of Marburg virus disease in the population. Numerical simulation shows that as value of vaccination increases, it leads to decreases in the spread of Marburg virus. This shows that vaccination is very important to control the spread of Marburg virus in the community. A feedforward neural network (FFNN) is employed as a surrogate model and trained using the numerical solution generated by the Euler–Maruyama scheme. The network learns a continuous nonlinear mapping from simulation time to the corresponding compartmental states, thereby providing a smooth approximation of the realized stochastic trajectory. The simulated dataset is randomly divided into training (70%), validation (15%), and testing (15%) subsets. The accuracy of Neural Networks in prediction and modeling is demonstrated by dividing the data into 70% for training, 15% for testing, and 15% for validation. Validating its accuracy, the model attains a mean squared error of 2.39 × 10⁻⁴ averaged over the eight compartments and a regression coefficient close to one (R = 0.999). The results of this study offer public health strategists effective tools for reducing or eliminating Marburg virus.