Epidemic threshold : a Laplacian spectral and structural approach of prediction

In epidemiology studies, control processes are driven by key parameters, such as $R_0$ , the epidemic threshold $\tau$ over a contact network. By network-based models, the knowledge of network structures improves the prediction of $\tau$ , which is a challenge using structural features of a contact network. There are several structural approaches to predict $\tau$ . The common QMF (Quenched Mean-Field) approach uses the spectral radius as a single parameter. However, prediction can be improved using the node number, spectral radius, and Laplacian energy of graph. In this paper, at different levels, we design and experiment a new structural and spectral prediction approach of $\tau$ called KSEL (K Spectral Energy of Laplacian). Theoretical and formal levels establish mathematical foundations, while qualitative, quantitative, and comparative levels compute a descriptive statistics summary, some data analytics, and visualisation through a large and heterogeneous dataset. Results show that the new approach effectively predicts $\tau$ . It captures the full network structure, connectivity, and network diffusion features. KSEL is similar, shares a common rolling trend, and performs really good compared to the previous structural prediction approaches, including the most commonly used QMF. There is a strong positive correlation and similar value distribution between KSEL and the previous structural prediction approaches that accepted the null hypothesis by ANOVA analysis. Therefore, the new approach is structurally enriched; it extends the structural and spectral area to analyse and control spreading processes over a network. The results can have practical interests to advise an effective epidemiological control policy.