In this study, we explore the concept of symmetry as it applies to the dynamics of the Hepatitis B Virus (HBV) epidemic model. By incorporating symmetric principles in the stochastic model, we ensure that the control strategies derived are not only effective but also consistent across varying conditions, and ensure the reliability of our predictions. This paper presents a stochastic optimal control analysis of an HBV epidemic model, incorporating vaccination as a pivotal control measure. We formulate a stochastic model to capture the complex dynamics of HBV transmission and its progression to acute and chronic stages. By leveraging stochastic differential equations, we examine the model’s stationary distribution and asymptotic behavior, elucidating the impact of random perturbations on disease dynamics. Optimal control theory is employed to derive control strategies aimed at minimizing the disease burden and vaccination costs. Through rigorous numerical simulations using the fourth-order Runge–Kutta method, we demonstrate the efficacy of the proposed control measures. Our findings highlight the critical role of vaccination in controlling HBV spread and provide insights into the optimization of vaccination strategies under stochastic conditions. The symmetry within the proposed model equations allows for a balanced approach to analyzing both acute and chronic stages of HBV.

This paper investigates a spatially heterogeneous stochastic reaction–diffusion SVIR epidemic model incorporating vaccination, waning immunity, and environmental fluctuations. The proposed system extends the classical deterministic epidemic framework by introducing diffusion effects, spatially dependent transmission rates, and multiplicative Gaussian white noise perturbations. The model is formulated as a system of stochastic partial differential equations subject to homogeneous Neumann boundary conditions. First, the well‐posedness of the model is established by proving the existence, uniqueness, positivity, and global boundedness of strong solutions through semigroup theory, Itô calculus, and comparison techniques. The stochastic transformation approach is employed to convert the original system into an equivalent random partial differential system, enabling rigorous analytical treatment. Furthermore, the qualitative behavior of the model is analyzed in terms of disease extinction and persistence under the combined influence of spatial diffusion and stochastic perturbations. The effects of vaccination, immunity loss, and environmental noise intensities on epidemic propagation are investigated theoretically and numerically. Numerical simulations, including two‐dimensional and three‐dimensional surface plots, heat maps, stochastic time‐series profiles, and phase portraits, are presented to validate the theoretical findings. The results demonstrate that diffusion and stochasticity significantly affect disease transmission patterns, whereas vaccination plays an essential role in suppressing infection spread. The proposed framework provides a more realistic and comprehensive description of epidemic dynamics in heterogeneous environments and may contribute to the development of effective disease control strategies.