A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global ...A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.展开更多
A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are in...A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.展开更多
Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural birth...Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.展开更多
In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction rat...In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.展开更多
In this paper, an epidemic SIS model with nonlinear infectivity on heterogeneous networks and time delays is investigated. The oscillatory behavior of the solutions is studied. Two sufficient conditions are provided t...In this paper, an epidemic SIS model with nonlinear infectivity on heterogeneous networks and time delays is investigated. The oscillatory behavior of the solutions is studied. Two sufficient conditions are provided to guarantee the oscillatory behavior for the solutions. Some computer simulations are demonstrated.展开更多
A mesoscale coupled atmosphere–ocean model has been developed based on the GRAPES（Global and Regional Assimilation and Prediction System） regional typhoon model（GRAPES_TYM） and ECOM-si（estuary, coast and ocean m...A mesoscale coupled atmosphere–ocean model has been developed based on the GRAPES（Global and Regional Assimilation and Prediction System） regional typhoon model（GRAPES_TYM） and ECOM-si（estuary, coast and ocean model（semi-implicit））. Coupling between the typhoon and ocean models was conducted by exchanging wind stress, heat, moisture fluxes, and sea surface temperatures（SSTs） using the coupler OASIS3.0. Numerical prediction experiments were run with and without coupling for the case of Typhoon Muifa in the western North Pacific. To investigate the impact of using more accurate SST information on the simulation of the track and the intensity of Typhoon Muifa, experiments were also conducted using increased SST resolution in the initial condition field of the control test. The results indicate that increasing SST resolution in the initial condition field somewhat improved the intensity forecast, and use of the coupled model improved the intensity forecast significantly, with mean absolute errors in maximum wind speed within 48 and 72 h reduced by 32% and 20%, respectively. Use of the coupled model also resulted in less pronounced over-prediction of the intensity of Typhoon Muifa by the GRAPES_TYM. Moreover, the effects of using the coupled model on the intensity varied throughout the different stages of the development of Muifa owing to changes in the oceanic mixed layer depth. The coupled model had pronounced effects during the later stage of Muifa but had no obvious effects during the earlier stage. The SSTs predicted by the coupled model decreased by about 5–6℃ at most after the typhoon passed, in agreement with satellite data. Furthermore, based on analysis on the sea surface heat flux, wet static energy of the boundary layer, atmospheric temperature, and precipitation forecasted by the coupled model and the control test, the simulation results of this coupled atmosphere–ocean model can be considered to reasonably reflect the primary mechanisms underlying the interactions between tropical cyclones and oceans.展开更多
The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov functi...The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions con- necting the disease-free equilibrium and the endemic equilibrium when R0 〉 1 and c 〉 c^＊. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R0 〉 1 and c ∈（0, c^＊）.展开更多
Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often je...Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.展开更多
We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma(2004), for which...We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma(2004), for which some sufficient conditions for the global stability of the endemic equilibrium were given in some earlier works. In this paper, we first prove by Lyapunov function method that the endemic equilibrium of the deterministic model is globally asymptotically stable whenever the basic reproduction number is larger than one. For the stochastic version, we obtain some sufficient conditions for the global stability of the endemic equilibrium by constructing a class of different Lyapunov functions.展开更多
基金Supported by the NSF of China（10371105） Supported by the Youth Science Foundation of Xinyang Normal University（20060202）
文摘A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.
基金This work is supported by National Natural Science Foundation of China (10171106)the Special Fund for Major State Basic Research Projects (G1999032805)
文摘A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.
文摘Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.
文摘In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.
文摘In this paper, an epidemic SIS model with nonlinear infectivity on heterogeneous networks and time delays is investigated. The oscillatory behavior of the solutions is studied. Two sufficient conditions are provided to guarantee the oscillatory behavior for the solutions. Some computer simulations are demonstrated.
基金The National Basic Research and Development Program(973 Program)of China under contract No.2009CB421506the National Natural Science Foundation of China under contract No.40975035China Meteorological Administration GRAPES Research Fund
文摘A mesoscale coupled atmosphere–ocean model has been developed based on the GRAPES（Global and Regional Assimilation and Prediction System） regional typhoon model（GRAPES_TYM） and ECOM-si（estuary, coast and ocean model（semi-implicit））. Coupling between the typhoon and ocean models was conducted by exchanging wind stress, heat, moisture fluxes, and sea surface temperatures（SSTs） using the coupler OASIS3.0. Numerical prediction experiments were run with and without coupling for the case of Typhoon Muifa in the western North Pacific. To investigate the impact of using more accurate SST information on the simulation of the track and the intensity of Typhoon Muifa, experiments were also conducted using increased SST resolution in the initial condition field of the control test. The results indicate that increasing SST resolution in the initial condition field somewhat improved the intensity forecast, and use of the coupled model improved the intensity forecast significantly, with mean absolute errors in maximum wind speed within 48 and 72 h reduced by 32% and 20%, respectively. Use of the coupled model also resulted in less pronounced over-prediction of the intensity of Typhoon Muifa by the GRAPES_TYM. Moreover, the effects of using the coupled model on the intensity varied throughout the different stages of the development of Muifa owing to changes in the oceanic mixed layer depth. The coupled model had pronounced effects during the later stage of Muifa but had no obvious effects during the earlier stage. The SSTs predicted by the coupled model decreased by about 5–6℃ at most after the typhoon passed, in agreement with satellite data. Furthermore, based on analysis on the sea surface heat flux, wet static energy of the boundary layer, atmospheric temperature, and precipitation forecasted by the coupled model and the control test, the simulation results of this coupled atmosphere–ocean model can be considered to reasonably reflect the primary mechanisms underlying the interactions between tropical cyclones and oceans.
基金Partially supported by the NSF of Guangdong Province(2016A030313426)the HLUCF of South China Normal University(2016YN30)
文摘The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions con- necting the disease-free equilibrium and the endemic equilibrium when R0 〉 1 and c 〉 c^＊. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R0 〉 1 and c ∈（0, c^＊）.
文摘Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.
基金Supported by the National Natural Science Foundation of China (Grant No. 12071058)。
文摘We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma(2004), for which some sufficient conditions for the global stability of the endemic equilibrium were given in some earlier works. In this paper, we first prove by Lyapunov function method that the endemic equilibrium of the deterministic model is globally asymptotically stable whenever the basic reproduction number is larger than one. For the stochastic version, we obtain some sufficient conditions for the global stability of the endemic equilibrium by constructing a class of different Lyapunov functions.
