A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The ...A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.展开更多
In this paper, we consider a nonautonomous competitive model with dispersion and a finite number of discrete delays. The system, which consists of two Lotka-Volterra patches, has two competitors: one can disperse betw...In this paper, we consider a nonautonomous competitive model with dispersion and a finite number of discrete delays. The system, which consists of two Lotka-Volterra patches, has two competitors: one can disperse between the two patches, but the other is confined to one patch and cannot disperse. Our purpose is to demonstrate that the dispersion rates have no effect on the uniform persistence of the solutions of the system. Furthermore, we establish the conditions under which the system admits a positive periodic solution which attracts all solutions.展开更多
Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for fi...Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)<1 and linearly stable if R_(c)=1;while V^(0)is unstable if R_(c)>1.展开更多
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obta...A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.展开更多
A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and...A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.展开更多
In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using ...In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using the method of the next generation matrix.It shows that disease-free equilibrium is globally asymptotically stable when R0<1;the disease is uniformly persistent when R_(0)>1.Secondly,we select dengue fever case data from Guangdong Province from 2006 to 2019 for numerical simulations and predict its development trend.Finally,we conduct parameter sensitivity analysis,and the results show that increasing media publicity can to some extent reduce the number of patients.展开更多
In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of th...In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of the solution to the model under initial conditions are proven.Secondly,it is proven that when R_(0)<1,the disease-free equilibrium is locally and globally asymptotically stable;and when R_(0)>1,the disease is uniformly persistent and there is at least a positive equilibrium.Finally,the effectiveness of the theoretical results is demonstrated by numerical simulation,and the impact of vaccination on disease transmission is predicted.展开更多
Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and glob...Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.展开更多
In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only...In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only obtain necessary as well as sufficient and necessary conditions for the oscillation of ail eventually positive solutions about the positive equilibrium, but also obtain some sufficient conditions for the convergence of eventually positive solutions. Furthermore, authors also show that such model is uniformly persistent, and that all its eventually positive solutions are bounded.展开更多
In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilib...In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed, and then uniformly persistent sufficient conditions of populations were found.展开更多
This paper is concerned with interactional models for adults of two species delayed by their mature periods. The existence and local stability of equilibria are discussed thoroughly for competitive systems, cooperativ...This paper is concerned with interactional models for adults of two species delayed by their mature periods. The existence and local stability of equilibria are discussed thoroughly for competitive systems, cooperative systems and predator-prey systems, respectively. For systems with interaction of competition and cooperation, it is found that the two populations are uniformly persistent if the positive equilibrium is stable. For predator-prey interaction, however, some further conditions are needed to guarantee the persistence of the systems.展开更多
In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-de...In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.展开更多
We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positi...We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.展开更多
The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By m...The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.展开更多
In this paper,we proposed and analyzed a five-dimensional system of ordinary differential equations modeling the competition of two competing bacteria in a chemostat under the influence of the leachate recirculation a...In this paper,we proposed and analyzed a five-dimensional system of ordinary differential equations modeling the competition of two competing bacteria in a chemostat under the influence of the leachate recirculation and in the presence of a pathogen associated only with the bacteria 1.We suppose that the nutriment is present into two forms,soluble and insoluble nutriment,and both two forms are continuously added to the chemostat.The proposed model takes the form of an"SI"epidemic model and uses general increasing growth functions and general increasing incidence rate.It admits multiple equilibria that we give the conditions under which we assure both the existence and the local stability of each equilibrium point.The possibility of periodic trajectory was excluded,and the uniform persistence of both types of bacteria was proved.Finally,several numerical examples confirming the theoretical findings are given.展开更多
In this paper,we propose a Zika transmission model which considers human-to-human sexual transmission,the extrinsic incubation period of mosquitoes,and the vector-bias effect.Firstly,the explicit expression of the bas...In this paper,we propose a Zika transmission model which considers human-to-human sexual transmission,the extrinsic incubation period of mosquitoes,and the vector-bias effect.Firstly,the explicit expression of the basic reproduction number R_(0) is given by using the next-generation operator method,and the global dynamics of the model are established by taking R_(0) as the threshold condition,that is,if R_(0)≤1,the disease-free equilibrium is globally asymptotically stable,if R_(0)>1,the model has a unique endemic equilibrium that is locally asymptotically stable and the disease persists.And when we ignore the vector-bias effect,the global asymptotic stability of the endemic equilibrium is proved by constructing a Lyapunov function.Then,we select the reported epidemic data from Brazil for fitting,which verifies the obtained theoretical results.Meanwhile,we study the impact of human-to-human sexual transmission rate and mosquito-tohuman transmission rate on the spread and prevalence of Zika.In addition,we calculate the sensitivity indices of R_(0) to the model parameters and provide effective measures to control Zika transmission.The simulation results indicate that extending the extrinsic incubation period of mosquitoes is beneficial for disease control while ignoring the vectorbias effect will underestimate the risk of Zika transmission.展开更多
Seasonality is repetitive in the ecological,biological and human systems.Seasonal factors affect both pathogen survival in the environment and host behavior.In this study,we considered a five-dimensional system of ord...Seasonality is repetitive in the ecological,biological and human systems.Seasonal factors affect both pathogen survival in the environment and host behavior.In this study,we considered a five-dimensional system of ordinary differential equations modeling an epidemic in a seasonal environment with a general incidence rate.We started by studying the autonomous system by investigating the global stability of steady states.Later,we proved the existence,uniqueness,positivity and boundedness of a periodic orbit in a non-autonomous system.We demonstrate that the global dynamics are determined using the basic reproduction number R_(o) which is defined by the spectral radius of a linear integral operator.We showed that if R_(o)<1,then the disease-free periodic solution is globally asymptotically stable and if R_(o)>1,then the trajectories converge to a limit cycle reflecting the persistence of the disease.Finally,we present a numerical investigation that support our results.展开更多
In this paper, a nonautonomous predator-prey dispersion model is studied, where all parameters are time-dependent. The system, which is consisted of n-patches, the prey specics can disperse among n-patches, but the pr...In this paper, a nonautonomous predator-prey dispersion model is studied, where all parameters are time-dependent. The system, which is consisted of n-patches, the prey specics can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved the system is uniformly persistent under any dispersion rates effect. Furthermore, sufficient conditions are established for global stability of the system.展开更多
This paper devotes to study the N species competition system with time delays in a periodic environment. some verifiable sufficient conditions which are easy to be verified for dissipation, the existence of period...This paper devotes to study the N species competition system with time delays in a periodic environment. some verifiable sufficient conditions which are easy to be verified for dissipation, the existence of periodic solution and global asymptotic stability of periodic solution are obtained.展开更多
文摘A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.
基金This research is supported by the National Natural Science Foundation of China the Natural Science Foundation of Henan Province.
文摘In this paper, we consider a nonautonomous competitive model with dispersion and a finite number of discrete delays. The system, which consists of two Lotka-Volterra patches, has two competitors: one can disperse between the two patches, but the other is confined to one patch and cannot disperse. Our purpose is to demonstrate that the dispersion rates have no effect on the uniform persistence of the solutions of the system. Furthermore, we establish the conditions under which the system admits a positive periodic solution which attracts all solutions.
基金partially supported by the National Natural Science Foundation of China(Nos.11901027,11971273and 12126426)the Major Program of the National Natural Science Foundation of China(No.12090014)+4 种基金the State Key Program of the National Natural Science Foundation of China(No.12031020)the Natural Science Foundation of Shandong Province(No.ZR2018MA004)the China Postdoctoral Science Foundation(No.2021M703426)the Pyramid Talent Training Project of BUCEA(No.JDYC20200327)the BUCEA Post Graduate Innovation Project(No.PG2022143)。
文摘Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)<1 and linearly stable if R_(c)=1;while V^(0)is unstable if R_(c)>1.
文摘A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.
文摘A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.
基金Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2022JM-023)。
文摘In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using the method of the next generation matrix.It shows that disease-free equilibrium is globally asymptotically stable when R0<1;the disease is uniformly persistent when R_(0)>1.Secondly,we select dengue fever case data from Guangdong Province from 2006 to 2019 for numerical simulations and predict its development trend.Finally,we conduct parameter sensitivity analysis,and the results show that increasing media publicity can to some extent reduce the number of patients.
基金supported by the Natural Science Foundation of Xinjiang(No.2022D01E41)the National Natural Science Foundation of China(No.12261087)the Open Project of Key Laboratory of Applied Mathematics of Xinjiang Autonomous Region(No.2021D04014)。
文摘In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of the solution to the model under initial conditions are proven.Secondly,it is proven that when R_(0)<1,the disease-free equilibrium is locally and globally asymptotically stable;and when R_(0)>1,the disease is uniformly persistent and there is at least a positive equilibrium.Finally,the effectiveness of the theoretical results is demonstrated by numerical simulation,and the impact of vaccination on disease transmission is predicted.
基金Supported by the NNSF of China(10671021)the SRF of Hunan Provincial Education Department(09C388)
文摘Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.
文摘In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only obtain necessary as well as sufficient and necessary conditions for the oscillation of ail eventually positive solutions about the positive equilibrium, but also obtain some sufficient conditions for the convergence of eventually positive solutions. Furthermore, authors also show that such model is uniformly persistent, and that all its eventually positive solutions are bounded.
文摘In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed, and then uniformly persistent sufficient conditions of populations were found.
基金National Natural science Foundation of China(10771048,10671209).
文摘This paper is concerned with interactional models for adults of two species delayed by their mature periods. The existence and local stability of equilibria are discussed thoroughly for competitive systems, cooperative systems and predator-prey systems, respectively. For systems with interaction of competition and cooperation, it is found that the two populations are uniformly persistent if the positive equilibrium is stable. For predator-prey interaction, however, some further conditions are needed to guarantee the persistence of the systems.
文摘In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.
文摘We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.
基金The research is supported by the Scientific Research Foundation of the Doctor Department of Hubei University of Technology.
文摘The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.
文摘In this paper,we proposed and analyzed a five-dimensional system of ordinary differential equations modeling the competition of two competing bacteria in a chemostat under the influence of the leachate recirculation and in the presence of a pathogen associated only with the bacteria 1.We suppose that the nutriment is present into two forms,soluble and insoluble nutriment,and both two forms are continuously added to the chemostat.The proposed model takes the form of an"SI"epidemic model and uses general increasing growth functions and general increasing incidence rate.It admits multiple equilibria that we give the conditions under which we assure both the existence and the local stability of each equilibrium point.The possibility of periodic trajectory was excluded,and the uniform persistence of both types of bacteria was proved.Finally,several numerical examples confirming the theoretical findings are given.
基金supported by the National Natural Science Foundation of China(11801431)the Natural Science Basic Research Plan in Shaanxi Province of China(2021JM-445,2022JM-023).
文摘In this paper,we propose a Zika transmission model which considers human-to-human sexual transmission,the extrinsic incubation period of mosquitoes,and the vector-bias effect.Firstly,the explicit expression of the basic reproduction number R_(0) is given by using the next-generation operator method,and the global dynamics of the model are established by taking R_(0) as the threshold condition,that is,if R_(0)≤1,the disease-free equilibrium is globally asymptotically stable,if R_(0)>1,the model has a unique endemic equilibrium that is locally asymptotically stable and the disease persists.And when we ignore the vector-bias effect,the global asymptotic stability of the endemic equilibrium is proved by constructing a Lyapunov function.Then,we select the reported epidemic data from Brazil for fitting,which verifies the obtained theoretical results.Meanwhile,we study the impact of human-to-human sexual transmission rate and mosquito-tohuman transmission rate on the spread and prevalence of Zika.In addition,we calculate the sensitivity indices of R_(0) to the model parameters and provide effective measures to control Zika transmission.The simulation results indicate that extending the extrinsic incubation period of mosquitoes is beneficial for disease control while ignoring the vectorbias effect will underestimate the risk of Zika transmission.
基金funded by the University of Jeddah,Jeddah,Saudi Arabia,under Grant No.(UJ-23-DR-279)。
文摘Seasonality is repetitive in the ecological,biological and human systems.Seasonal factors affect both pathogen survival in the environment and host behavior.In this study,we considered a five-dimensional system of ordinary differential equations modeling an epidemic in a seasonal environment with a general incidence rate.We started by studying the autonomous system by investigating the global stability of steady states.Later,we proved the existence,uniqueness,positivity and boundedness of a periodic orbit in a non-autonomous system.We demonstrate that the global dynamics are determined using the basic reproduction number R_(o) which is defined by the spectral radius of a linear integral operator.We showed that if R_(o)<1,then the disease-free periodic solution is globally asymptotically stable and if R_(o)>1,then the trajectories converge to a limit cycle reflecting the persistence of the disease.Finally,we present a numerical investigation that support our results.
基金Supported by the Natural Science Foundatioll of Henan province (994051600)
文摘In this paper, a nonautonomous predator-prey dispersion model is studied, where all parameters are time-dependent. The system, which is consisted of n-patches, the prey specics can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved the system is uniformly persistent under any dispersion rates effect. Furthermore, sufficient conditions are established for global stability of the system.
文摘This paper devotes to study the N species competition system with time delays in a periodic environment. some verifiable sufficient conditions which are easy to be verified for dissipation, the existence of periodic solution and global asymptotic stability of periodic solution are obtained.
