This contribution probes into ergodic stationary distribution for two stochastic SVELIT(susceptible-vaccinated-early latent-late latent-infective-treated)tuberculosis(TB)models to observe the impact of white noises an...This contribution probes into ergodic stationary distribution for two stochastic SVELIT(susceptible-vaccinated-early latent-late latent-infective-treated)tuberculosis(TB)models to observe the impact of white noises and color noises on TB control in random environments.We first investigate the existence and uniqueness of ergodic stationary distribution(EUESD)for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions,and suficient conditions on the extinction of disease are acquired.Next,sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established.Eventually,some numerical examples validate the theoretical findings.What's more,it has been observed that higher amplitude noises may lead to the eradication of TB,which is conducive to TB control.展开更多
It is beyond dispute that cytotoxic T-lymphocytes(CTLs)exert a vital function in the host's antiviral defense mechanism.With the idea of the above factor and the logistic proliferation of CD4+T-cells,we establish ...It is beyond dispute that cytotoxic T-lymphocytes(CTLs)exert a vital function in the host's antiviral defense mechanism.With the idea of the above factor and the logistic proliferation of CD4+T-cells,we establish a HTLV-I(human T-cell leukemia virus type-I)mathematical model.First,two threshold parameters Ro and Re(the basic reproduction numbers for viral infection and CTL immune response,respectively)are obtained.Second,sufficient criteria for local and global asymptotic stabilities of the feasible equilibria of the model are deduced,respectively.Third,the sensitivity analyses of Ro and Rc are performed to better understand the effective strategies for HTLV-I infection.Finally,not only numerical simulations are given to illustrate the stability conclusions,but also the biological significance is stated.展开更多
文摘This contribution probes into ergodic stationary distribution for two stochastic SVELIT(susceptible-vaccinated-early latent-late latent-infective-treated)tuberculosis(TB)models to observe the impact of white noises and color noises on TB control in random environments.We first investigate the existence and uniqueness of ergodic stationary distribution(EUESD)for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions,and suficient conditions on the extinction of disease are acquired.Next,sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established.Eventually,some numerical examples validate the theoretical findings.What's more,it has been observed that higher amplitude noises may lead to the eradication of TB,which is conducive to TB control.
基金supported by the National Natural Science Foundation(NNSF)of China(Nos.11871201,11871238 and 12001178)。
文摘It is beyond dispute that cytotoxic T-lymphocytes(CTLs)exert a vital function in the host's antiviral defense mechanism.With the idea of the above factor and the logistic proliferation of CD4+T-cells,we establish a HTLV-I(human T-cell leukemia virus type-I)mathematical model.First,two threshold parameters Ro and Re(the basic reproduction numbers for viral infection and CTL immune response,respectively)are obtained.Second,sufficient criteria for local and global asymptotic stabilities of the feasible equilibria of the model are deduced,respectively.Third,the sensitivity analyses of Ro and Rc are performed to better understand the effective strategies for HTLV-I infection.Finally,not only numerical simulations are given to illustrate the stability conclusions,but also the biological significance is stated.