摘要
Over the history of humankind, they is no disease that has received so much attention as the HIV infection and mathematical models have been applied successfully to the investigation of HIV dynamics. It is, however, of note that, few of these investigations are able to explain the observation that host cell counts reduce while viral load increases as the infection progress. Also, various clinical studies of HIV infection have suggested that high T-cell activation levels are positively correlated with rapid disease development in untreated patients. This activation might be a major reason for the depletion of cells observed in most cases of long-term untreated HIV infection. In this paper, we use a simple mathematical model without treatment to investigate the stability of the system and compare the results with that obtained numerically by the use of MATHCAD. Our model which is a system of differential equations describing the interaction of the HIV and the immune system is divided into three compartments: uninfected CD4T cells, infected CD4Tcells and the virus population. This third compartment includes an extra source of the virus since it is believed that the virus in the blood constitute less than 2% of the total population. We obtain a linearization of the original system, and using Routh-Hurwitz condition for the non-linear system, the critical points are unstable.
Over the history of humankind, they is no disease that has received so much attention as the HIV infection and mathematical models have been applied successfully to the investigation of HIV dynamics. It is, however, of note that, few of these investigations are able to explain the observation that host cell counts reduce while viral load increases as the infection progress. Also, various clinical studies of HIV infection have suggested that high T-cell activation levels are positively correlated with rapid disease development in untreated patients. This activation might be a major reason for the depletion of cells observed in most cases of long-term untreated HIV infection. In this paper, we use a simple mathematical model without treatment to investigate the stability of the system and compare the results with that obtained numerically by the use of MATHCAD. Our model which is a system of differential equations describing the interaction of the HIV and the immune system is divided into three compartments: uninfected CD4T cells, infected CD4Tcells and the virus population. This third compartment includes an extra source of the virus since it is believed that the virus in the blood constitute less than 2% of the total population. We obtain a linearization of the original system, and using Routh-Hurwitz condition for the non-linear system, the critical points are unstable.
