A generalized competitive system with stochastic perturbations is proposed in this paper,in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process.By theories of stochastic different...A generalized competitive system with stochastic perturbations is proposed in this paper,in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process.By theories of stochastic differential equations,such as comparison theorem,Ito’s integration formula,Chebyshev’s inequality,martingale’s properties,etc.,the existence and the uniqueness of global positive solution of the system are obtained.Then sufficient conditions for the extinction of the species almost surely,persistence in the mean and the stochastic permanence for the system are derived,respectively.Finally,by a series of numerical examples,the feasibility and correctness of the theoretical analysis results are verified intuitively.Moreover,the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.展开更多
This paper analyzes the spread of the COVID-19 epidemic in China,establishes a SEIR^(+CAQ)epidemiologic model that classifies the diagnosed population into asymptomatic,mild,and severe,and considers the condition of a...This paper analyzes the spread of the COVID-19 epidemic in China,establishes a SEIR^(+CAQ)epidemiologic model that classifies the diagnosed population into asymptomatic,mild,and severe,and considers the condition of an isolated population.First of all,we theoretically analyzed the key problems of the disease-free equilibrium,stability,and basic reproduction number of the model.Then,combined with the actual data,the development trend of the epidemic situation is simulated and compared,and the influence of some important parameters is discussed in the model evaluation part.Finally,based on the theoretical analysis and numerical simulation results,we forecast the future development of the COVID-19 epidemic and put forward some reasonable scientific suggestions for the government to formulate a future epidemic prevention policy.展开更多
基金Acknowledgments The authors would like to thank the editors and the anonymous referees for their helpful suggestions and comments which led to the improvement of our original manuscript. This work is supported by the National Natural Science Foundation of China （11372294 and 11261017）, Scientific Research Fund of Sichuan Provincial Education Department （14ZB0115 and 15ZB0113）, Zhejiang Provincial Natural Science Foundation （LQ13A010023） and Doctorial Research Fund of Southwest University of Science and Technology （15zx7138）.
基金Acknowledgments The authors thank the editor and referees for their valuable comments and suggestions. This work is supported by the National Basic Research Program of China （2010CB732501） and the National Natural Science Foundation of China （61273015）, the NSFC Tianyuan Foundation （Grant No. 11226256） and the Zhejiang Provincial Natural Science Foundation of China （Grant No. LY13A010010）, Zhejiang Provincial Natural Science Foundation of China LQ13A010023）.
基金This work is supported by the Sichuan Science and Technology Program under Grant 2017JY0336 and Hunan Science and Technology Program under Grant 2019JJ50399National College Students,Innovation and Entrepreneurship Training Program under Grant S202010619021Longshan Talent Research Fund of Southwest University of Science and Technology under Grants 17LZX670 and 18LZX622.
文摘A generalized competitive system with stochastic perturbations is proposed in this paper,in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process.By theories of stochastic differential equations,such as comparison theorem,Ito’s integration formula,Chebyshev’s inequality,martingale’s properties,etc.,the existence and the uniqueness of global positive solution of the system are obtained.Then sufficient conditions for the extinction of the species almost surely,persistence in the mean and the stochastic permanence for the system are derived,respectively.Finally,by a series of numerical examples,the feasibility and correctness of the theoretical analysis results are verified intuitively.Moreover,the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.
基金This work is supported by the National College Students’s Innovation and Entrepreneurship Training Program(S202010619021)School of Science College Student Innovation Fund Project of Southwest University of Science and Tech-nology+1 种基金Application Basic Project of Sichuan Science and Technology Department(2017JY0336)Longshan Academic Talent Research Support Program of Southwest University of Science and Technology(17LZX670,18LZX622).
文摘This paper analyzes the spread of the COVID-19 epidemic in China,establishes a SEIR^(+CAQ)epidemiologic model that classifies the diagnosed population into asymptomatic,mild,and severe,and considers the condition of an isolated population.First of all,we theoretically analyzed the key problems of the disease-free equilibrium,stability,and basic reproduction number of the model.Then,combined with the actual data,the development trend of the epidemic situation is simulated and compared,and the influence of some important parameters is discussed in the model evaluation part.Finally,based on the theoretical analysis and numerical simulation results,we forecast the future development of the COVID-19 epidemic and put forward some reasonable scientific suggestions for the government to formulate a future epidemic prevention policy.
