In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the...In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solutions to the展开更多
Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptib...Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.展开更多
A delayed mathematical model of Dengue dynamical transmission between vector mosquitoes and human, incorporating a control strategy of perfect pediatric vaccination is proposed in this paper. By some analytical skills...A delayed mathematical model of Dengue dynamical transmission between vector mosquitoes and human, incorporating a control strategy of perfect pediatric vaccination is proposed in this paper. By some analytical skills, we obtain the existence of disease-free equilibria and endemic equilibrium, the necessary conditions of global asymptotical stability about two disease-free equilibria. Further, by Pontryagin’s maximum principle, we obtain the optimal control of the disease. Finally, numerical simulations are carried out to verify the correctness of the theoretical results and feasibility of the control measure.展开更多
We propose,in this paper,a hybrid Cholera transmission model with phage to simulate the interaction between Vibrio cholerae and phages in the host population and environment,which is coupled with some reaction-diffusi...We propose,in this paper,a hybrid Cholera transmission model with phage to simulate the interaction between Vibrio cholerae and phages in the host population and environment,which is coupled with some reaction-diffusion equations and first-order partial differential equations.The precise formulation of basic reproduction number(Ro)is deduced,which characterizes the elimination or prevalence of this disease.Specifically,the disease-free steady state is globally asymptotically stable for R_(0)≤1 but unstable for R_(0)>1.Further,the phage invasion reproduction number Ri is also obtained,which portrays the impact of phages on Vibrio cholerae in the environment.That is,for R_(0)>1,the phage-free endemic steady state is globally asymptotically stable if R_(1)≤1,and the phage-present endemic steady state is globally asymptotically stable if R_(1)>1.Numerical simulations are introduced for the purpose of verifying the main results.展开更多
文摘In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solutions to the
文摘Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.
文摘A delayed mathematical model of Dengue dynamical transmission between vector mosquitoes and human, incorporating a control strategy of perfect pediatric vaccination is proposed in this paper. By some analytical skills, we obtain the existence of disease-free equilibria and endemic equilibrium, the necessary conditions of global asymptotical stability about two disease-free equilibria. Further, by Pontryagin’s maximum principle, we obtain the optimal control of the disease. Finally, numerical simulations are carried out to verify the correctness of the theoretical results and feasibility of the control measure.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant Nos.2022TSYCCX0015 and 2021D01E12)the National Natural Science Foundation of China(Grant No.12361103)the Scientific Research and Innovation Project of Outstanding Doctoral Students in Xinjiang University(Grant No.XJU2022BS022).
文摘We propose,in this paper,a hybrid Cholera transmission model with phage to simulate the interaction between Vibrio cholerae and phages in the host population and environment,which is coupled with some reaction-diffusion equations and first-order partial differential equations.The precise formulation of basic reproduction number(Ro)is deduced,which characterizes the elimination or prevalence of this disease.Specifically,the disease-free steady state is globally asymptotically stable for R_(0)≤1 but unstable for R_(0)>1.Further,the phage invasion reproduction number Ri is also obtained,which portrays the impact of phages on Vibrio cholerae in the environment.That is,for R_(0)>1,the phage-free endemic steady state is globally asymptotically stable if R_(1)≤1,and the phage-present endemic steady state is globally asymptotically stable if R_(1)>1.Numerical simulations are introduced for the purpose of verifying the main results.
