In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium ...In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. We derive that the global dynamics are completely determined by the values of the basic reproduction number： if the basic reproduction number is less than one, the uninfected equilibrium is globally asymptotically stable, and the virus is cleared; if the basic reproduction number is larger than one, then the infection persists, and the infected equilibrium is globally asymptotically stable.展开更多
In this paper, with the method of adaptive dynamics, we investigate the coevolution of phenotypic traits of predator and prey species. The evolutionary model is constructed from a deterministic approximation of the un...In this paper, with the method of adaptive dynamics, we investigate the coevolution of phenotypic traits of predator and prey species. The evolutionary model is constructed from a deterministic approximation of the underlying stochastic ecological processes. Firstly, we investigate the ecological and evolutionary conditions that allow for continu- ously stable strategy and evolutionary branching. We find that evolutionary branching in the prey phenotype will occur when the frequency dependence in the prey carrying capacity is not strong. Furthermore, it is found that if the two prey branches move far away enough, the evolutionary branching in the prey phenotype will induce the sec- ondary branching in the predator phenotype. The final evolutionary outcome contains two prey and two predator species. Secondly, we show that under symmetric interactions the evolutionary model admits a supercritical Hopf bifurcation if the frequency depen- dence in the prey carrying capa.city is very weak. Evolutionary cycle is a likely outcome of the nmtation-selection processes. Finally, we find that frequency-dependent selection can drive the predator population to extinction under asymmetric interactions.展开更多
There has been a global attack of A/H1N1 virus in 2009, which widely affected the world＇s normal stability and economic development. Since the emergence of the first diagnosed A/H1N1 influenza infected person in 11 M...There has been a global attack of A/H1N1 virus in 2009, which widely affected the world＇s normal stability and economic development. Since the emergence of the first diagnosed A/H1N1 influenza infected person in 11 May 2009 in China, very strict policy including quarantine and isolation measures were widely implemented to control the spread of this disease before the vaccine appeared. We propose a compartmental model that mimics the infection process of A/H1N1 under control strategies taken in China's Mainland. Apart from theoretical analysis, using the statistic data of Shaanxi Province, we estimated the unknown epidemiological parameters of this disease in Shaanxi via least-squares fitting method. The estimated control reproductive number of H1N1 for its first peak was Rc1 = 2.555 （95% CI： 2.362 2.748） and that for the second peak was Rc2 = 1.886 （95% CI： 1.765-2.001）. Our findings in this paper suggest that neither quarantine nor isolation measures could be relaxed, and the implementation of these interventions can reduce the pandemic outbreak of A/H1N1 pandemic significantly.展开更多
文摘In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. We derive that the global dynamics are completely determined by the values of the basic reproduction number： if the basic reproduction number is less than one, the uninfected equilibrium is globally asymptotically stable, and the virus is cleared; if the basic reproduction number is larger than one, then the infection persists, and the infected equilibrium is globally asymptotically stable.
文摘In this paper, with the method of adaptive dynamics, we investigate the coevolution of phenotypic traits of predator and prey species. The evolutionary model is constructed from a deterministic approximation of the underlying stochastic ecological processes. Firstly, we investigate the ecological and evolutionary conditions that allow for continu- ously stable strategy and evolutionary branching. We find that evolutionary branching in the prey phenotype will occur when the frequency dependence in the prey carrying capacity is not strong. Furthermore, it is found that if the two prey branches move far away enough, the evolutionary branching in the prey phenotype will induce the sec- ondary branching in the predator phenotype. The final evolutionary outcome contains two prey and two predator species. Secondly, we show that under symmetric interactions the evolutionary model admits a supercritical Hopf bifurcation if the frequency depen- dence in the prey carrying capa.city is very weak. Evolutionary cycle is a likely outcome of the nmtation-selection processes. Finally, we find that frequency-dependent selection can drive the predator population to extinction under asymmetric interactions.
文摘There has been a global attack of A/H1N1 virus in 2009, which widely affected the world＇s normal stability and economic development. Since the emergence of the first diagnosed A/H1N1 influenza infected person in 11 May 2009 in China, very strict policy including quarantine and isolation measures were widely implemented to control the spread of this disease before the vaccine appeared. We propose a compartmental model that mimics the infection process of A/H1N1 under control strategies taken in China's Mainland. Apart from theoretical analysis, using the statistic data of Shaanxi Province, we estimated the unknown epidemiological parameters of this disease in Shaanxi via least-squares fitting method. The estimated control reproductive number of H1N1 for its first peak was Rc1 = 2.555 （95% CI： 2.362 2.748） and that for the second peak was Rc2 = 1.886 （95% CI： 1.765-2.001）. Our findings in this paper suggest that neither quarantine nor isolation measures could be relaxed, and the implementation of these interventions can reduce the pandemic outbreak of A/H1N1 pandemic significantly.
