Identifying how pain transitions from acute to chronic is critical in designing effective prevention and management techniques for patients’ well-being, physically, psychosocially, and financially. There is an increasingly pressing need for a quantitative and predictive method to evaluate how low back pain trajectories are classified and, subsequently, how we can more effectively intervene during these progression stages. In order to better understand pain mechanisms, we investigated, using computational modeling, how best to describe pain trajectories by developing a platform by which we studied the transition of acute chronic pain. The present study uses a computational neuroscience-based method to conduct such trajectory research, motivated by the use of hypothalamic–pituitary–adrenal (HPA) axis activity-history over a time-period as a way to mimic pain trajectories. A numerical simulation study is presented as a “proof of concept” for this modeling approach. This model and its simulation results have highlighted the feasibility and the potential of developing such a broader model for patient evaluations.

Quantitative analysis of internet memes—digital cultural phenomena that propagate through online networks—remains an understudied domain in computational social science. Building upon established research that modeled meme popularity through ordinary differential equations, this study presents a novel machine learning approach to classify and predict meme popularity trajectories. Previous work identified four distinct post-peak patterns: smooth decay, oscillatory decay, plateau, and sustained growth. We significantly expanded the empirical foundation by constructing a comprehensive dataset of 2000+ memes, leveraging Google Trends time-series data. Our methodological framework employed a two-stage machine learning pipeline: first, implementing k-means clustering ($ k = 4 $) for unsupervised pattern discovery, followed by support vector classification for supervised learning. This approach enabled both validation of previously identified trajectory patterns and development of a predictive model for meme popularity evolution. Additionally, we conducted a systematic analysis of the relationship between meme taxonomic categories (e.g., catchphrases, viral videos) and their temporal popularity patterns. Our findings contribute to the emerging field of computational memetics and offer insights into the quantitative dynamics of online cultural transmission. The resulting classification model demonstrates robust predictive capabilities, with implications for understanding viral content dynamics in digital ecosystems.

We develop a two-age smoking-dynamics model for youth and adult groups that incorporates education acquisition, aging, cessation and relapse, disease progression, age-dependent social mixing, and a weak Allee effect in smoking initiation. Education is modeled as a protective status acquired through schooling and aging transitions, while initiation depends on both education status and prevalence-dependent social reinforcement. We establish the well-posedness of the system, derive the smoking-free equilibrium in closed form, and obtain the compact age-structured threshold ${\mathcal{R}}_0^{\mathrm{age}}=\rho \left(\mathrm{diag}(g_Y,g_A)C\right)$, where C is the age-mixing matrix and $g_a$ summarizes the within-age smoking-invasion potential. Using center-manifold analysis, we derive conditions under which Allee-type social reinforcement can generate a backward bifurcation, implying that reducing ${\mathcal{R}}_0^{\mathrm{age}}$ below one may not always be sufficient for elimination when endemic prevalence is high. We also analyze the impact of cross-age mixing on the threshold and use a quasi-steady-state approximation to characterize the quitting–relapse loop while preserving the threshold structure. Numerical simulations illustrate baseline youth and adult prevalence trends, identify youth initiation, relapse, cessation, and education protection as dominant drivers of threshold sensitivity, and show that education-based interventions are most effective when they directly reduce the susceptibility of educated youths to smoking initiation.