A stochastic epidemic model with two age groups is established in this study,in which the susceptible(S),the exposed(E),the infected(I),the hospitalized(H)and the recovered(R)are involved within the total population,t...A stochastic epidemic model with two age groups is established in this study,in which the susceptible(S),the exposed(E),the infected(I),the hospitalized(H)and the recovered(R)are involved within the total population,the aging rates between two age groups are set to be constant.The existence-and-uniqueness of global positive solution is firstly showed.Then,by constructing several appropriate Lyapunov functions and using the high-dimensional Itô’s formula,the sufficient conditions for the stochastic extinction and stochastic persistence of the exposed individuals and the infected individuals are obtained.The stochastic extinction indicator and the stochastic persistence indicator are less-valued expressions compared with the basic reproduction number.Meanwhile,the main results of this study are modified into multi-age groups.Furthermore,by using the surveillance data for Fujian Provincial Center for Disease Control and Prevention,Fuzhou COVID-19 epidemic is chosen to carry out the numerical simulations,which show that the age group of the population plays the vital role when studying infectious diseases.展开更多
We consider the task of binary classification in the high-dimensional setting where the number of features of the given data is larger than the number of observations.To accomplish this task,we propose an adherently p...We consider the task of binary classification in the high-dimensional setting where the number of features of the given data is larger than the number of observations.To accomplish this task,we propose an adherently penalized optimal scoring(APOS)model for simultaneously performing discriminant analysis and feature selection.In this paper,an efficient algorithm based on the block coordinate descent(BCD)method and the SSNAL algorithm is developed to solve the APOS approximately.The convergence results of our method are also established.Numerical experiments conducted on simulated and real datasets demonstrate that the proposed model is more efficient than several sparse discriminant analysis methods.展开更多
基金Supported by National Natural Science Foundation of China(61911530398,12231012)Consultancy Project by the Chinese Academy of Engineering(2022-JB-06,2023-JB-12)+3 种基金the Natural Science Foundation of Fujian Province of China(2021J01621)Special Projects of the Central Government Guiding Local Science and Technology Development(2021L3018)Royal Society of Edinburgh(RSE1832)Engineering and Physical Sciences Research Council(EP/W522521/1).
文摘A stochastic epidemic model with two age groups is established in this study,in which the susceptible(S),the exposed(E),the infected(I),the hospitalized(H)and the recovered(R)are involved within the total population,the aging rates between two age groups are set to be constant.The existence-and-uniqueness of global positive solution is firstly showed.Then,by constructing several appropriate Lyapunov functions and using the high-dimensional Itô’s formula,the sufficient conditions for the stochastic extinction and stochastic persistence of the exposed individuals and the infected individuals are obtained.The stochastic extinction indicator and the stochastic persistence indicator are less-valued expressions compared with the basic reproduction number.Meanwhile,the main results of this study are modified into multi-age groups.Furthermore,by using the surveillance data for Fujian Provincial Center for Disease Control and Prevention,Fuzhou COVID-19 epidemic is chosen to carry out the numerical simulations,which show that the age group of the population plays the vital role when studying infectious diseases.
基金supported by the National Natural Science Foundation of China(No.12271097)the Key Program of National Science Foundation of Fujian Province of China(No.2023J02007)+1 种基金the Central Guidance on Local Science and Technology Development Fund of Fujian Province(No.2023L3003)the Fujian Alliance of Mathematics(No.2023SXLMMS01)。
文摘We consider the task of binary classification in the high-dimensional setting where the number of features of the given data is larger than the number of observations.To accomplish this task,we propose an adherently penalized optimal scoring(APOS)model for simultaneously performing discriminant analysis and feature selection.In this paper,an efficient algorithm based on the block coordinate descent(BCD)method and the SSNAL algorithm is developed to solve the APOS approximately.The convergence results of our method are also established.Numerical experiments conducted on simulated and real datasets demonstrate that the proposed model is more efficient than several sparse discriminant analysis methods.
