Obesity is a chronic, multifactorial disease and a major global public health challenge. Defined by excessive fat accumulation, obesity significantly increases the risk of numerous diseases, including type 2 diabetes mellitus (T2DM), cardiovascular disease, heart failure, and metabolic dysfunction-associated steatotic liver disease, contributing to rising morbidity and mortality rates worldwide. Although several pharmacological treatments have demonstrated notable efficacy in weight management, concerns regarding drug safety remain a significant challenge. Metabolic bariatric surgery (MBS) has emerged as the most effective intervention for achieving long-term and sustained weight loss; however, it is typically reserved for advanced stages of the disease. Moreover, the role of MBS in managing obesity-related comorbidities remains a topic of ongoing debate. In this review, we provide a comprehensive analysis of the epidemiology of obesity and its associated comorbidities, along with the latest insights into the mechanisms underlying obesity-induced chronic complications. Growing evidence highlights the crucial role of imbalances between white and brown adipose tissues, alterations in gut microbiota, genetic and epigenetic modifications, and immune system dysregulation in driving obesity and its related conditions. These emerging insights have unveiled numerous potential therapeutic targets with promising weight-reducing effects. Furthermore, advancements in our understanding of signal transduction pathways may pave the way for future multimodal therapeutic strategies in obesity management, ushering in a new era of precision medicine.

This paper investigates the strong convergence of a fully discrete scheme for the stochastic Allen–Cahn equation with multiplicative noise, combining a tamed Milstein method for the temporal discretization with the finite element method in space. The proposed method is shown to be unconditionally stable in spatial dimensions $$d\in \{1,2,3\}$$ d ∈ { 1 , 2 , 3 } . Beyond the inherent challenges caused by, see, e.g., [1], the cubic non-globally Lipschitz drift term and multiplicative driving noise in the convergence analysis, the Milstein scheme further complicates the error estimation of the noise term compared to the Euler-Maruyama discretization. By introducing a novel auxiliary process, we rigorously establish strong convergence rates in both space and time under mild assumptions for $$d\in \{1,2\}$$ d ∈ { 1 , 2 } . Our analysis shows that the temporal convergence order is doubled compared to that of tamed Euler-Maruyama scheme. Numerical experiments are provided to confirm the theoretical results and to demonstrate that the proposed scheme exhibits improved robustness over the pure semi-implicit Milstein method.