This study examines a stochastic susceptible-exposed-infected-recovered-vaccinated $(\mathbf{S}{\mathbf{E}}_1{\mathbf{E}}_2\mathbf{I}\mathbf{R}\mathbf{V})$ model exhibiting the dynamics of the computer virus within the wireless sensor networks (WSNs) while considering the unpredictability of nodes and the impact of anti-virus measures. The model is formulated with reasonable assumptions, and the stochastic stability is performed with a derivation of a six-dimensional Fokker-Planck equation. To obtain an analytical representation of the probability density functions, a scheme is developed and subsequently implemented in MATLAB. The behavior of the model around the quasi-endemic state is numerically investigated, which reflects the main objective and unique novelty of the present work. On the basis of various parameter settings, graphical illustrations of the model are presented showing the authenticity of the analytical results and complex aspects of the phenomenon. The paper concludes with a brief summary of the study and important insights for future research.