数学最新文献

Intestinal crypts are test tube-like structures lined with an epithelial monolayer. Under homeostasis, mitotic forces drive epithelial cells to migrate up the crypt, from the stem cell niche. As the cells migrate up the crypt, they differentiate into specialised cells. This process is regulated by morphogen gradients established by distinct populations of subepithelial fibroblasts, and recent studies suggest fibroblasts and epithelial cells have co-evolved to maintain crypt structure and function via complementary morphogen expression. We present a mathematical model of fibroblast-epithelial cross-talk, in which fibroblast and epithelial phenotypes emerge from morphogen binding to cell surface receptors. The model predicts the formation of distinct zones of mutually supporting phenotypes at different crypt heights. These findings support the idea that fibroblast and epithelial cell phenotypes are an emergent property of the crypt microenvironment. We use the model to investigate how mutations in the fibroblasts may disrupt these phenotypic zones. Our results suggest that such mutations may lead to uncontrolled epithelial cell growth and, as such, indicate how dysfunctional fibroblasts may contribute to the emergence of colorectal cancer.

The 2009 influenza A (H1N1) epidemic in China provided a unique natural experiment to evaluate school closures, as it overlapped with two school vacations. Utilizing the epidemiological data from this outbreak, our study specifically assesses the impact of holidays and systematically evaluates the efficacy of school-specific prevention measures in curbing influenza transmission. By using the enhanced piecewise linear representation model and calculating the effective reproduction number R_t, we divided the entire pandemic period into six stages. We employed the Susceptible-Exposed-Infective-Removed model with quarantine compartments to align with the prevention and control policy. We quantified the effectiveness of holidays and school-specific prevention strategies using parameter estimation results. Moreover, we explored several comparative scenarios, including holiday cancellations or extensions, to further demonstrate the impact of school closure and policies. The comparison of different transmission phases revealed a 14.0% and 16.5% reduction in the mean of R_t during the summer vacation and the National Day holiday, respectively. Furthermore, the relaxation of school-specific preventive measures could potentially lead to a doubling of the accumulated case count within several months. In contrast, the extension of holiday periods demonstrated a notable mitigating impact on the epidemic curve. School-specific prevention strategies and school holidays exert a beneficial and significant influence on mitigating the spread of the influenza A (H1N1) epidemic. Our research findings and methods can provide insights for implementing school closure strategies to mitigate similar emerging infectious diseases.

The time-to-first-event analysis is often used for studies involving multiple event times, where each component is treated equally, regardless of their clinical importance. Alternative summaries such as Win Ratio, Net Benefit, and Win Odds (WO) have drawn attention lately because they can handle different types of outcomes and allow for a hierarchical ordering in component outcomes. In this paper, we focus on WO and propose proportional WO regression models to evaluate the treatment effect on multiple outcomes while controlling for other risk factors. The models are easily interpretable as a standard logistic regression model. However, the proposed WO regression is more advanced; multiple outcomes of different types can be modeled together, and the estimating equation is constructed based on all possible and potentially dependent pairings of a treated individual with a control one under the functional response modeling framework. In addition, informative ties are carefully distinguished from those inconclusive comparisons due to censoring, and the latter is handled via the inverse probability of censoring weighting method. We establish the asymptotic properties of the estimated regression coefficients using the U-statistic theory and demonstrate the finite sample performance through numerical studies.