A periodic pulse differential equation model of tumor immunotherapy is established by considering the periodic and transient behavior of infusing immune cells. Using comparison theorem and Floquet multiplier theory of...A periodic pulse differential equation model of tumor immunotherapy is established by considering the periodic and transient behavior of infusing immune cells. Using comparison theorem and Floquet multiplier theory of the impulsive differential equation, the boundedness of the model solution, the existence and stability of the free-tumor periodic solution are given. Furthermore, the persistence of the system is analyzed. Numerical simulations are carried to confirm the main theorems.展开更多
A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be appl...A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be applied to one with other periodic impulse coefficients.展开更多
This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are s...This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age, while infected individuals are structured by infection age （duration since infection）. The time dependent disease-free equilibrium is determined, for which an explicit expression exists. The analytical results show that there exists a globally stable infectiomfree situation if the impulsive period T and proportion p satisfy Ro（p,T） 〈 1. Optimal problem is discussed： Pulse vaccination strategy with minimal costs at given R0（p, T） 〈 1.展开更多
How to prevent and control the outbreak of mosquito-borne diseases,such as malaria,dengue fever and Zika,is an urgent worldwide public health problem.The most conventional method for the control of these diseases is t...How to prevent and control the outbreak of mosquito-borne diseases,such as malaria,dengue fever and Zika,is an urgent worldwide public health problem.The most conventional method for the control of these diseases is to directly kill mosquitoes by spraying insecticides or removing their breeding sites.However,the traditional method is not effective enough to keep the mosquito density below the epidemic risk threshold.With promising results international,the World Mosquito Program’s Wolbachia method is helping to reduce the occurrence of diseases transmitted by mosquitoes.In this paper,we introduce a generalized discrete model to study the dynamics of the Wolbachia infection frequency in mosquito populations where infected mosquitoes are impulsively released.This generalized model covers all the relevant existing models since 1959 as some special cases.After summarizing known results of discrete models deduced from the generalized one,we put forward some interesting open questions to be further investigated for the periodic impulsive releases.展开更多
In this paper, a non-smooth population model with impulsive effects is proposed by combining discontinuity and non-smoothness. According to the qualitative theory of differential equations, the global analysis of the ...In this paper, a non-smooth population model with impulsive effects is proposed by combining discontinuity and non-smoothness. According to the qualitative theory of differential equations, the global analysis of the model is discussed. Using the theory of impulsive differential equations, the existence conditions of order one periodic solution are obtained. And the impulsive controllers are designed to make the pest populations stay at the refuge level. Some simulations are carried out to prove the results.展开更多
基金Acknowledgments This project was supported by Hunan China （Nos. 14JJ2089, 13JJ9008） and （Nos. 14A128, 12C0361）. Provincial Natural Science Foundation of Hunan Provincial Education Department
文摘A periodic pulse differential equation model of tumor immunotherapy is established by considering the periodic and transient behavior of infusing immune cells. Using comparison theorem and Floquet multiplier theory of the impulsive differential equation, the boundedness of the model solution, the existence and stability of the free-tumor periodic solution are given. Furthermore, the persistence of the system is analyzed. Numerical simulations are carried to confirm the main theorems.
基金This work is supported by the National Science Fund of Peop1e's Republic of China
文摘A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be applied to one with other periodic impulse coefficients.
基金supported by Natural Science Foundation of Henan Province under Grant No.092300410206Science and Technology Program of Educational Department of Henan Province under Grant No. 2009A110015
文摘This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age, while infected individuals are structured by infection age （duration since infection）. The time dependent disease-free equilibrium is determined, for which an explicit expression exists. The analytical results show that there exists a globally stable infectiomfree situation if the impulsive period T and proportion p satisfy Ro（p,T） 〈 1. Optimal problem is discussed： Pulse vaccination strategy with minimal costs at given R0（p, T） 〈 1.
基金supported by National Natural Science Foundation of China(Grant Nos.11971127,12071095 and 11631005)the Changjiang Scholars Program and Program for Innovative Research Team in University(Grant No.IRT 16R16)。
文摘How to prevent and control the outbreak of mosquito-borne diseases,such as malaria,dengue fever and Zika,is an urgent worldwide public health problem.The most conventional method for the control of these diseases is to directly kill mosquitoes by spraying insecticides or removing their breeding sites.However,the traditional method is not effective enough to keep the mosquito density below the epidemic risk threshold.With promising results international,the World Mosquito Program’s Wolbachia method is helping to reduce the occurrence of diseases transmitted by mosquitoes.In this paper,we introduce a generalized discrete model to study the dynamics of the Wolbachia infection frequency in mosquito populations where infected mosquitoes are impulsively released.This generalized model covers all the relevant existing models since 1959 as some special cases.After summarizing known results of discrete models deduced from the generalized one,we put forward some interesting open questions to be further investigated for the periodic impulsive releases.
文摘In this paper, a non-smooth population model with impulsive effects is proposed by combining discontinuity and non-smoothness. According to the qualitative theory of differential equations, the global analysis of the model is discussed. Using the theory of impulsive differential equations, the existence conditions of order one periodic solution are obtained. And the impulsive controllers are designed to make the pest populations stay at the refuge level. Some simulations are carried out to prove the results.
