A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally as...A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.展开更多
Statistical two-group comparisons are widely used to identify the significant differentially expressed (DE) signatures against a therapy response for microarray data analysis. We applied a rank order statistics based ...Statistical two-group comparisons are widely used to identify the significant differentially expressed (DE) signatures against a therapy response for microarray data analysis. We applied a rank order statistics based on an Autoregressive Conditional Heteroskedasticity (ARCH) residual empirical process to DE analysis. This approach was considered for simulation data and publicly available datasets, and was compared with two-group comparison by original data and Auto-regressive (AR) residual. The significant DE genes by the ARCH and AR residuals were reduced by about 20% - 30% to these genes by the original data. Almost 100% of the genes by ARCH are covered by the genes by the original data unlike the genes by AR residuals. GO enrichment and Pathway analyses indicate the consistent biological characteristics between genes by ARCH residuals and original data. ARCH residuals array data might contribute to refining the number of significant DE genes to detect the biological feature as well as ordinal microarray data.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10971021)the Ministry of Education of China (Grant No. 109051)+1 种基金the Ph.D. Programs Foundation of Ministry of China (Grant No. 200918)the Graduate Innovative Research Project of NENU (Grant No. 09SSXT117)
文摘A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.
文摘Statistical two-group comparisons are widely used to identify the significant differentially expressed (DE) signatures against a therapy response for microarray data analysis. We applied a rank order statistics based on an Autoregressive Conditional Heteroskedasticity (ARCH) residual empirical process to DE analysis. This approach was considered for simulation data and publicly available datasets, and was compared with two-group comparison by original data and Auto-regressive (AR) residual. The significant DE genes by the ARCH and AR residuals were reduced by about 20% - 30% to these genes by the original data. Almost 100% of the genes by ARCH are covered by the genes by the original data unlike the genes by AR residuals. GO enrichment and Pathway analyses indicate the consistent biological characteristics between genes by ARCH residuals and original data. ARCH residuals array data might contribute to refining the number of significant DE genes to detect the biological feature as well as ordinal microarray data.
