Human immunodeficiency virus(HIV)has had an insightful impact about the state of healthiness of human immune system.Due to great improvement in drug therapy,HIV infections have been reduced by 17%over the past eight y...Human immunodeficiency virus(HIV)has had an insightful impact about the state of healthiness of human immune system.Due to great improvement in drug therapy,HIV infections have been reduced by 17%over the past eight years.It has been proved that most effective treatment HAART(Highly Active Anti Retroviral Therapy)mainly controls the diseases progression but it does not eradicate the diseases completely.Reverse Transcriptase Inhibitor drugs specially associated with virus specific Cytotoxic T-Lymphocyte(CTL)that declines with disease progression. CTL responses against AIDS pathogenesis could be potential in the dynamics of virus replication, recognition and clearance of infected cells.In this research article a mathematical model has been proposed on the basis of CTL response suppression in the chronic phase of infection due to presence of virus.We also consider the growth of the virus population from the infected CD4^+T cells budding process and from the other infected cells like macrophages and thymocytes.Our analytical and numerical studies are consistent with existing observations from allied areas.展开更多
The relations between the Human Immunodeficiency Virus-1 （HIV-1） and the human immune system are astonishingly multifaceted, where the critical role for cytotoxic T lymphocytes （CTLs） in the suppression of viral r...The relations between the Human Immunodeficiency Virus-1 （HIV-1） and the human immune system are astonishingly multifaceted, where the critical role for cytotoxic T lymphocytes （CTLs） in the suppression of viral replication in HIV-1 infected individuals cannot be ignored. In this research paper, we have proposed a mathematical model incorporating half saturation constant through the CTL mediated killing process and also in that sense, it has been infiltrated in the generation process of CTL through infected cells. To make the model more realistic, a time lag is introduced in the generation term of CTL population. Also an optimal control theory paradigm is used in our mathematical model to suppress the viral production. From our entire analysis, we have found threshold condition of half saturation constant and treatment schedule so that we can handle the situation of Acquired Immunodeficiency Syndrome （AIDS） patients in a better way. Our analysis reveals that, if the half saturation constant is around 47 mm^-3 in the saturation process and the drug therapy is to be used around 76 days, then we can get adequate results for better treatment of a HIV-1 patient. Based on numerical results, we observed that in a highly unstable situation, administration of chemotherapy at a high dose can stabilize the system.展开更多
基金Research is supported by the Government of India,Ministry of Science and Technology,Mathematical Science office,No.SR/S4/MS:558/08
文摘Human immunodeficiency virus(HIV)has had an insightful impact about the state of healthiness of human immune system.Due to great improvement in drug therapy,HIV infections have been reduced by 17%over the past eight years.It has been proved that most effective treatment HAART(Highly Active Anti Retroviral Therapy)mainly controls the diseases progression but it does not eradicate the diseases completely.Reverse Transcriptase Inhibitor drugs specially associated with virus specific Cytotoxic T-Lymphocyte(CTL)that declines with disease progression. CTL responses against AIDS pathogenesis could be potential in the dynamics of virus replication, recognition and clearance of infected cells.In this research article a mathematical model has been proposed on the basis of CTL response suppression in the chronic phase of infection due to presence of virus.We also consider the growth of the virus population from the infected CD4^+T cells budding process and from the other infected cells like macrophages and thymocytes.Our analytical and numerical studies are consistent with existing observations from allied areas.
文摘The relations between the Human Immunodeficiency Virus-1 （HIV-1） and the human immune system are astonishingly multifaceted, where the critical role for cytotoxic T lymphocytes （CTLs） in the suppression of viral replication in HIV-1 infected individuals cannot be ignored. In this research paper, we have proposed a mathematical model incorporating half saturation constant through the CTL mediated killing process and also in that sense, it has been infiltrated in the generation process of CTL through infected cells. To make the model more realistic, a time lag is introduced in the generation term of CTL population. Also an optimal control theory paradigm is used in our mathematical model to suppress the viral production. From our entire analysis, we have found threshold condition of half saturation constant and treatment schedule so that we can handle the situation of Acquired Immunodeficiency Syndrome （AIDS） patients in a better way. Our analysis reveals that, if the half saturation constant is around 47 mm^-3 in the saturation process and the drug therapy is to be used around 76 days, then we can get adequate results for better treatment of a HIV-1 patient. Based on numerical results, we observed that in a highly unstable situation, administration of chemotherapy at a high dose can stabilize the system.
