In this paper, mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. Though the model is originally to study hepatitis C virus （HCV） dynamics in patients with high baseline ...In this paper, mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. Though the model is originally to study hepatitis C virus （HCV） dynamics in patients with high baseline viral loads or advanced liver disease, similar models still hold significance for other viral infection, such as hepatitis B virus （HBV） or human immunodeficiency virus （HIV） infection. By means of Volterra-type Lyapunov functions, we know that the basic reproduction number R0 is a sharp threshold para- meter for the outcomes of viral infections. If R0 ~ 1, the virus-free equilibrium is globally asymptotically stable. If R0 ~ 1, the system is uniformly persistent, the unique endemic equilibrium appears and is globally asymptotically stable under a sufficient condition. Other than that, for the global stability of the unique endemic equilibrium, another suffi- cient condition is obtained by Li-Muldowney global-stability criterion. Using numerical simulation techniques, we further find that sustained oscillations can exist and different maximum de novo hepatocyte influx rate can induce different global dynamics along with the change of overall drug effectiveness. Finally, some biological implications of our findings are given.展开更多
To study the transition dynamics of resistant-type human immunodeficiency virus 1 （HIV-1） in highly active antiretroviral therapy （HAART） and the affect of neutral mutation in the evolution of HIV-1, a mathematica...To study the transition dynamics of resistant-type human immunodeficiency virus 1 （HIV-1） in highly active antiretroviral therapy （HAART） and the affect of neutral mutation in the evolution of HIV-1, a mathematical model is proposed when mutation occurs mainly during reproduction. The derived results show that the resistant-type will certainly colonize in patients once mutation occurs. Furthermore, a neutral mutation is closely related to the colonized pattern of resistant-type HIV-1 quasispecies and there are some changes in the pattern of transmission dynamics when mutation occurs mainly during reproduction or in the absence of reproduction, which may lead to significant strategies for predicting or checking HIV-1 drug resistance in HAART.展开更多
文摘In this paper, mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. Though the model is originally to study hepatitis C virus （HCV） dynamics in patients with high baseline viral loads or advanced liver disease, similar models still hold significance for other viral infection, such as hepatitis B virus （HBV） or human immunodeficiency virus （HIV） infection. By means of Volterra-type Lyapunov functions, we know that the basic reproduction number R0 is a sharp threshold para- meter for the outcomes of viral infections. If R0 ~ 1, the virus-free equilibrium is globally asymptotically stable. If R0 ~ 1, the system is uniformly persistent, the unique endemic equilibrium appears and is globally asymptotically stable under a sufficient condition. Other than that, for the global stability of the unique endemic equilibrium, another suffi- cient condition is obtained by Li-Muldowney global-stability criterion. Using numerical simulation techniques, we further find that sustained oscillations can exist and different maximum de novo hepatocyte influx rate can induce different global dynamics along with the change of overall drug effectiveness. Finally, some biological implications of our findings are given.
基金Acknowledgments This work is supported by the National Natural Science Fund of P. R. China （No. 11271369） and the Natural Science Foundation Project of CQ CSTC （2010BB5020）.
文摘To study the transition dynamics of resistant-type human immunodeficiency virus 1 （HIV-1） in highly active antiretroviral therapy （HAART） and the affect of neutral mutation in the evolution of HIV-1, a mathematical model is proposed when mutation occurs mainly during reproduction. The derived results show that the resistant-type will certainly colonize in patients once mutation occurs. Furthermore, a neutral mutation is closely related to the colonized pattern of resistant-type HIV-1 quasispecies and there are some changes in the pattern of transmission dynamics when mutation occurs mainly during reproduction or in the absence of reproduction, which may lead to significant strategies for predicting or checking HIV-1 drug resistance in HAART.
