A stochastic SIRS epidemic model with nonlinear incidence rate and varying population size is for... more A stochastic SIRS epidemic model with nonlinear incidence rate and varying population size is formulated to investigate the effect of stochastic environmental variability on inter-pandemic transmission dynamics of influenza A. Sufficient conditions for extinction and persistence of the disease are established. In the case of persistence, the existence of endemic stationary distribution is proved and the distance between stochastic solutions and the endemic equilibrium of the corresponding deterministic system in the time mean sense is estimated. Based on realistic parameters of influenza A in humans, numerical simulations have been performed to verify/extend our analytical results. It is found that: (i) the deterministic threshold of the influenza A extinction [Formula: see text] may exist and the threshold parameter will be overestimated in case of neglecting the impaction of environmental noises; (ii) the presence of environmental noises is capable of supporting the irregular recu...
Discrete and Continuous Dynamical Systems - Series B, 2014
The environment of HIV-1 infection and treatment could be nonperiodically time-varying. The purpo... more The environment of HIV-1 infection and treatment could be nonperiodically time-varying. The purposes of this paper are to investigate the effects of time-dependent coefficients on the dynamics of a non-autonomous and non-periodic HIV-1 infection model with two delays, and to provide explicit estimates of the lower and upper bounds of the viral load. We established sufficient conditions for the permanence and extinction of the non-autonomous system based on two positive constants R * and R * (R * ≥ R * ) that could be precisely expressed by the coefficients of the system: (i) If R * < 1, then the infection-free steady state is globally attracting; (ii) if R * > 1, then the system is permanent. When the system is permanent, we further obtained detailed estimates of both the lower and upper bounds of the viral load. The results show that both R * and R * reduce to the basic reproduction ratio of the corresponding autonomous model when all the coefficients become constants. Numerical simulations have been performed to verify/extend our analytical results. We also provided some numerical results showing that both permanence and extinction are possible when R * < 1 < R * holds.
In this paper, we incorporate an extra logistic growth term for uninfected CD4+ T-cells into an H... more In this paper, we incorporate an extra logistic growth term for uninfected CD4+ T-cells into an HIV-1 infection model with both intracellular delay and immune response delay which was studied by Pawelek et al. in [26]. First, we proved that if the basic reproduction number R0 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; 1, then the infection-free steady state is globally asymptotically stable. Second, when R0 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; 1, then the system is uniformly persistent, suggesting that the clearance or the uniform persistence of the virus is completely determined by R0. Furthermore, given both the two delays are zero, then the infected steady state is asymptotically stable when the intrinsic growth rate of the extra logistic term is sufficiently small. When the two delays are not zero, we showed that both the immune response delay and the intracellular delay may destabilize the infected steady state by leading to Hopf bifurcation and stable periodic oscillations, on which we analyzed the direction of the Hopf bifurcation as well as the stability of the bifurcating periodic orbits by normal form and center manifold theory introduced by Hassard et al. Third, we engaged numerical simulations to explore the rich dynamics like chaotic oscillations, complicated bifurcation diagram of viral load due to the logistic term of target cells and the two time delays.
2010 International Conference on Intelligent Computation Technology and Automation, 2010
In this paper, various numerical calculation methods are rigorously combined to model and analyze... more In this paper, various numerical calculation methods are rigorously combined to model and analyze the acoustic characteristics of a heavy truck cab. Firstly a brief introduction of different numerical calculation methods is given, then the finite element structure model and cavity model of the cab are built. The statistical energy analysis models of the cab, including structural subsystems and cavity
An SEIR epidemic model with different distributed latencies and general nonlinear incidence is pr... more An SEIR epidemic model with different distributed latencies and general nonlinear incidence is presented and studied. By constructing suitable Lyapunov functionals, the biologically realistic sufficient conditions for threshold dynamics are established. It is shown that the infection-free equilibrium is globally attractive when the basic reproduction number is equal to or less than one, and that the disease becomes globally attractively endemic when the basic reproduction number is larger than one. The criteria in this paper generalize and improve some previous results in the literatures.
We formulate and study a predator-prey model with nonmonotonic functional response type and weak ... more We formulate and study a predator-prey model with nonmonotonic functional response type and weak Allee effects on the prey, which extends the system studied by Ruan and Xiao in [Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math. 61 (2001Math. 61 ( ), no. 4, 1445Math. 61 ( -1472 but containing an extra term describing weak Allee effects on the prey. We obtain the global dynamics of the model by combining the global qualitative and bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and the subcritical Hopf bifurcations, and the homoclinic bifurcation, as the values of parameters vary. In the generic case, the model has the bifurcation of cusp type of codimension 2 (i.e., Bogdanov-Takens bifurcation).
A stochastic SIRS epidemic model with nonlinear incidence rate and varying population size is for... more A stochastic SIRS epidemic model with nonlinear incidence rate and varying population size is formulated to investigate the effect of stochastic environmental variability on inter-pandemic transmission dynamics of influenza A. Sufficient conditions for extinction and persistence of the disease are established. In the case of persistence, the existence of endemic stationary distribution is proved and the distance between stochastic solutions and the endemic equilibrium of the corresponding deterministic system in the time mean sense is estimated. Based on realistic parameters of influenza A in humans, numerical simulations have been performed to verify/extend our analytical results. It is found that: (i) the deterministic threshold of the influenza A extinction [Formula: see text] may exist and the threshold parameter will be overestimated in case of neglecting the impaction of environmental noises; (ii) the presence of environmental noises is capable of supporting the irregular recu...
Discrete and Continuous Dynamical Systems - Series B, 2014
The environment of HIV-1 infection and treatment could be nonperiodically time-varying. The purpo... more The environment of HIV-1 infection and treatment could be nonperiodically time-varying. The purposes of this paper are to investigate the effects of time-dependent coefficients on the dynamics of a non-autonomous and non-periodic HIV-1 infection model with two delays, and to provide explicit estimates of the lower and upper bounds of the viral load. We established sufficient conditions for the permanence and extinction of the non-autonomous system based on two positive constants R * and R * (R * ≥ R * ) that could be precisely expressed by the coefficients of the system: (i) If R * < 1, then the infection-free steady state is globally attracting; (ii) if R * > 1, then the system is permanent. When the system is permanent, we further obtained detailed estimates of both the lower and upper bounds of the viral load. The results show that both R * and R * reduce to the basic reproduction ratio of the corresponding autonomous model when all the coefficients become constants. Numerical simulations have been performed to verify/extend our analytical results. We also provided some numerical results showing that both permanence and extinction are possible when R * < 1 < R * holds.
In this paper, we incorporate an extra logistic growth term for uninfected CD4+ T-cells into an H... more In this paper, we incorporate an extra logistic growth term for uninfected CD4+ T-cells into an HIV-1 infection model with both intracellular delay and immune response delay which was studied by Pawelek et al. in [26]. First, we proved that if the basic reproduction number R0 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; 1, then the infection-free steady state is globally asymptotically stable. Second, when R0 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; 1, then the system is uniformly persistent, suggesting that the clearance or the uniform persistence of the virus is completely determined by R0. Furthermore, given both the two delays are zero, then the infected steady state is asymptotically stable when the intrinsic growth rate of the extra logistic term is sufficiently small. When the two delays are not zero, we showed that both the immune response delay and the intracellular delay may destabilize the infected steady state by leading to Hopf bifurcation and stable periodic oscillations, on which we analyzed the direction of the Hopf bifurcation as well as the stability of the bifurcating periodic orbits by normal form and center manifold theory introduced by Hassard et al. Third, we engaged numerical simulations to explore the rich dynamics like chaotic oscillations, complicated bifurcation diagram of viral load due to the logistic term of target cells and the two time delays.
2010 International Conference on Intelligent Computation Technology and Automation, 2010
In this paper, various numerical calculation methods are rigorously combined to model and analyze... more In this paper, various numerical calculation methods are rigorously combined to model and analyze the acoustic characteristics of a heavy truck cab. Firstly a brief introduction of different numerical calculation methods is given, then the finite element structure model and cavity model of the cab are built. The statistical energy analysis models of the cab, including structural subsystems and cavity
An SEIR epidemic model with different distributed latencies and general nonlinear incidence is pr... more An SEIR epidemic model with different distributed latencies and general nonlinear incidence is presented and studied. By constructing suitable Lyapunov functionals, the biologically realistic sufficient conditions for threshold dynamics are established. It is shown that the infection-free equilibrium is globally attractive when the basic reproduction number is equal to or less than one, and that the disease becomes globally attractively endemic when the basic reproduction number is larger than one. The criteria in this paper generalize and improve some previous results in the literatures.
We formulate and study a predator-prey model with nonmonotonic functional response type and weak ... more We formulate and study a predator-prey model with nonmonotonic functional response type and weak Allee effects on the prey, which extends the system studied by Ruan and Xiao in [Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math. 61 (2001Math. 61 ( ), no. 4, 1445Math. 61 ( -1472 but containing an extra term describing weak Allee effects on the prey. We obtain the global dynamics of the model by combining the global qualitative and bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and the subcritical Hopf bifurcations, and the homoclinic bifurcation, as the values of parameters vary. In the generic case, the model has the bifurcation of cusp type of codimension 2 (i.e., Bogdanov-Takens bifurcation).
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