Researchers and practitioners in the fields of science and engineering encounter significant challenges when it comes to mitigating the proliferation of computer worms, owing to their rapid spread within computer and communication networks. This study delves into a comprehensive analysis of the mathematical model governing the hazard of worm propagation in such networks. Specifically, the mathematical framework employed herein encompasses a system of ordinary differential equations. In numerous instances, mathematical models have been employed to quantitatively investigate the propagation patterns of worms across computer networks. In this scholarly article, we present an enhanced Susceptible-Exposed-Infected-Quarantined-Vaccinated (SEIQV) model, denoted as Susceptible-Exposed-Infected-Quarantined-Patched (SEIQP), which effectively captures the dissemination dynamics of an insider threat within a network featuring air gaps. To facilitate the study, we leverage the power of feedforward neural networks that are trained using the backpropagated Levenberg-Marquardt optimization algorithm. These neural networks serve as surrogate tools, providing solutions to the SEIQP model. To evaluate the efficacy of our approach, we meticulously assess their performance across three distinct scenarios. Additionally, the stability of the mathematical model is examined by manipulating the probability of an insider threat removing a patch from the host, denoted as . Our empirical findings conclusively establish the effectiveness of the proposed approach in addressing the intricate challenges associated with insider threats within network environments.