Impact of supervise neural network on a stochastic epidemic model with Levy noise

This paper primarily focused on analyzing a stochastic $ \mathcal{SVIR} $ epidemic model that incorporates Levy noises. The population may be divided into four distinct compartments: vulnerable class ($ \mathcal{S} $), vaccinated individuals ($ \mathcal{V} $), infected individuals ($ \mathcal{I} $), and recovered individuals ($ \mathcal{R} $). To achieve this, we chose existing and unique techniques as the most feasible solution. In the nexus, the stochastic model was theoretically analyzed using a suitable Lyapunov function. This analysis broadly covered the existence and uniqueness of the non-negative solution, as well as the dynamic properties related to both the disease-free equilibrium and the endemic equilibrium. In order to eradicate diseases, a stochastic threshold value denoted as "$\textbf{R}_0$" was used to determine if they may be eradicated. If $ \textbf{R}_0 < 1, $ it means that the illnesses have the potential to become extinct. Moreover, we provided numerical performance results of the proposed model using the artificial neural networks technique combined with the Bayesian regularization method. We firmly believe that this study will establish a solid theoretical foundation for comprehending the spread of an epidemic, the implementation of effective control strategies, and addressing real-world issues across various academic disciplines.