This research work presents a novel approach to combat propaganda and misinformation in the context of information warfare through the integration of a modified logistic differential equation, a Physics-Informed Neural Network (PINN), and a comprehensive parameter sensitivity analysis. The study leverages the LIAR dataset, which offers a diverse range of labelled statements reflecting real-world political discourse, making it an ideal foundation for capturing the complexities of propaganda dynamics. The modified logistic equation, incorporating parameters such as spread rate (α), decay rate (β), and growth rate (γ), is employed to capture the intricate dynamics of information spread and adoption. The PINN model uses domain knowledge and data to estimate the underlying dynamics and unknown parameters of the logistic equation. This allows for highly accurate classification and analysis of propaganda spread. Thereafter, a parameter sensitivity analysis is conducted under different attacker intensities, categorized as aggressive, neutral, and non-aggressive. Varying population sizes are considered to assess the implications of different parameter combinations. The results reveal the significant influence of the spread rate parameter (α), highlighting the aggressiveness of the attacker’s propaganda dissemination in information warfare scenarios. Furthermore, the proposed PINN-based model’s performance is evaluated against two benchmark models: a Term Frequency-Inverse Document Frequency (TF- IDF) model and the random forest classifier. The PINN model achieved an impressive accuracy rate of 97.32% on the LIAR dataset, outperforming both the TF-IDF model (93.87%) and the random forest classifier (95%). This demonstrates the superior predictive power and effectiveness of the PINN model in capturing the complexities of information spread in the realm of propaganda and misinformation. This research lays down a robust groundwork for research aimed at combating propaganda and pushing the boundaries of information warfare. It achieves this by validating the efficacy of the proposed model and showcasing its superiority when compared to existing benchmark models. The comprehensive parameter sensitivity analysis further enhances the understanding of the system’s behavior and offers insights into the impact of varying parameter values.