In this paper,a stochastic multi-group AIDS model with saturated incidence rate is studied.We prove that the system is persistent in the mean under some parametric restrictions.We also obtain the sufficient condition ...In this paper,a stochastic multi-group AIDS model with saturated incidence rate is studied.We prove that the system is persistent in the mean under some parametric restrictions.We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function.Our results indicate that the existence of ergodic stationary distribution does not rely on the interior equilibrium of the corresponding deterministic system,which greatly improves upon previous results.展开更多
In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, a...In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.展开更多
This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing...This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing a series of appropriate stochastic Lyapunov functions,the asymptotic behaviors around the equilibria of deterministic model are obtained,and we demonstrate that the stochastic system exists a stationary Markov process.Third,the conditions for persistence in the mean and extinction of the stochastic system are established.Finally,we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results.The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.展开更多
In this paper,a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures is proposed.Firstly,the existence and uniqueness of the global positive solution is obtained.Secondly,threshold ...In this paper,a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures is proposed.Firstly,the existence and uniqueness of the global positive solution is obtained.Secondly,threshold criteria for the stochastic extinction and persistence in the mean with probability one are established.Moreover,a sufficient condition for the existence of unique ergodic stationary distribution for any positive solution is also established.Finally,numerical simulations are carried out in combination with real COVID-19 data from Urumqi,China and the theoretical results are verified.展开更多
A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively...A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively, the thresholds between the weak persistence in the mean and extinction of populations are established.展开更多
Considering the impact of environmental white noise on the quantity and behavior ofvector of disease,a stochastic differential model describing the transmission of Denguefever between mosquitoes and humans,in this pap...Considering the impact of environmental white noise on the quantity and behavior ofvector of disease,a stochastic differential model describing the transmission of Denguefever between mosquitoes and humans,in this paper,is proposed.By using Lyapunovmethods and Ito's formula,we first prove the existence and uniqueness of a globalpositive solution for this model.Further,some sufficient conditions for the extinction andpersistence in the mean of this stochastic model are obtained by using the techniquesof a series of stochastic inequalities.In addition,we also discuss the existence of aunique stationary distribution which leads to the stochastic persistence of this disease.Finally,several numerical simulations are carried to illustrate the main results of thiscontribution.展开更多
This paper is concerned with a three-species competitive model with both white noises and Levy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between ...This paper is concerned with a three-species competitive model with both white noises and Levy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between persistence in the mean and extinction for each species. The sufficient criteria for stability in distribution of solutions are obtained. Finally, numerical simulations are carried out to verify the theoretical results.展开更多
基金The work was supported by NSF of China(11801041,11871473)Foudation of Jilin Province Science and Technology Development(20190201130JC)+1 种基金Scientific Rsearch Foundation of Jilin Provincial Education Department(JJKH20181172KJ,JJKH20190503KJ)Natural Science Foundation of Changchun Normal University.
文摘In this paper,a stochastic multi-group AIDS model with saturated incidence rate is studied.We prove that the system is persistent in the mean under some parametric restrictions.We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function.Our results indicate that the existence of ergodic stationary distribution does not rely on the interior equilibrium of the corresponding deterministic system,which greatly improves upon previous results.
文摘In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.
基金supported by the Research Fund for the Taishan Scholar Project of Shandong Province of China,Shandong Provincial Natural Science Foundation of China(ZR2019MA003)。
文摘This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing a series of appropriate stochastic Lyapunov functions,the asymptotic behaviors around the equilibria of deterministic model are obtained,and we demonstrate that the stochastic system exists a stationary Markov process.Third,the conditions for persistence in the mean and extinction of the stochastic system are established.Finally,we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results.The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.
基金approved by the institutional ethics committee of Xinjiang Medical University.(IRB No.:XJYKDXR20221001001)supported by the Natural Science Foundation of XinJiang(Grant Nos.2021D01C268).
文摘In this paper,a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures is proposed.Firstly,the existence and uniqueness of the global positive solution is obtained.Secondly,threshold criteria for the stochastic extinction and persistence in the mean with probability one are established.Moreover,a sufficient condition for the existence of unique ergodic stationary distribution for any positive solution is also established.Finally,numerical simulations are carried out in combination with real COVID-19 data from Urumqi,China and the theoretical results are verified.
文摘A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively, the thresholds between the weak persistence in the mean and extinction of populations are established.
基金This research is partially supported by the National Natural Science Foundation of China(Grant nos.11961066 and 11771373)the Scientific Research Program of Colleges in Xinjiang(Grant no.X.JEDU2018I001).
文摘Considering the impact of environmental white noise on the quantity and behavior ofvector of disease,a stochastic differential model describing the transmission of Denguefever between mosquitoes and humans,in this paper,is proposed.By using Lyapunovmethods and Ito's formula,we first prove the existence and uniqueness of a globalpositive solution for this model.Further,some sufficient conditions for the extinction andpersistence in the mean of this stochastic model are obtained by using the techniquesof a series of stochastic inequalities.In addition,we also discuss the existence of aunique stationary distribution which leads to the stochastic persistence of this disease.Finally,several numerical simulations are carried to illustrate the main results of thiscontribution.
基金The work is supported by National Science Foundation of China （No. 11472298）, the Fundamental Research Funds for the Central Universities （No. ZXH2012K004）, the National Science Foundation of Tianjin City （No. 13JCQNJC04400） and the NNSF of P. R. China （No. 11401574）.
文摘This paper is concerned with a three-species competitive model with both white noises and Levy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between persistence in the mean and extinction for each species. The sufficient criteria for stability in distribution of solutions are obtained. Finally, numerical simulations are carried out to verify the theoretical results.
