In epidemiological research, key factors such as \(R_0\) and the epidemic threshold \(\tau\) over a contact network critically shape control strategies. Predicting \(\tau\) through structural network properties remains challenging, though network-based models offer improved accuracy. Various structural approaches exist for predicting \(\tau\) . The widely used QMF approach uses the spectral radius as a single parameter. However, prediction can be improved globally using only the number of nodes n and the energy of graph E(G). This paper designed and experimented KSES (K Spectral Energy Smooth) as a new structural and spectral prediction approach of \(\tau\) . KSES is evaluated both theoretically, through mathematical foundations, and empirically, using qualitative, quantitative, and comparative analysis supported by descriptive statistics, data analytics, and visualisations derived from a large and heterogeneous dataset. Results lead to a theorem for a new lower bound of E(G) for pragmatic applications related to some network types and ranges of n. KSES offers better computational and memory efficiency, as well as robust performance to predict \(\tau\) , making it particularly attractive and simple without sacrificing precision for large-scale, real-time (or resource-limited) network analyses. Moreover, results show that the KSES approach effectively predicts \(\tau\) . It captures the full network structure, including its connectivity and diffusion properties. KSES is superior, shares a common rolling trend, and performs well compared to earlier structural prediction approaches, including the most commonly used QMF, KSEL. Therefore, the new approach KSES, extends the structural and spectral areas to analyse and control spreading processes over a network. These results are practically relevant to advising an effective epidemiological control policy.
