Dynamics of co-infection with M. tuberculosis and HIV-1. (English) Zbl 0916.92018
Summary: Since 1985, there has been a renewed epidemic of tuberculosis (TB) that was previously thought to be in check. There is evidence to believe the main factor for this resurgence has been the human immunodeficiency virus (HIV). Co-infection with HIV and \(M\). Tuberculosis has profound implications for the course of both diseases. This study represents a first attempt to understand how the introduction of an opportunistic infection, namely Mycobacterium tuberculosis, the bacteria that causes TB, affects the dynamic interaction of HIV–l and the immune system.
We create a mathematical model using ordinary differential equations to describe the interaction of HIV and TB with the immune system. It is known that infection with TB can decrease the \(\text{CD4}^+T\) cell counts – a key marker of AIDS progression; thus, it shortens survival in HIV infected individuals. Another main marker for HIV progression is the viral load. If this load is increased due to the presence of opportunistic infections, the disease progression is much more rapid. We also explore the effects of drug treatment on the TB infection in the doubly-infected patient. \(\copyright\) 1999 Acadamic Press.
We create a mathematical model using ordinary differential equations to describe the interaction of HIV and TB with the immune system. It is known that infection with TB can decrease the \(\text{CD4}^+T\) cell counts – a key marker of AIDS progression; thus, it shortens survival in HIV infected individuals. Another main marker for HIV progression is the viral load. If this load is increased due to the presence of opportunistic infections, the disease progression is much more rapid. We also explore the effects of drug treatment on the TB infection in the doubly-infected patient. \(\copyright\) 1999 Acadamic Press.
MSC:
| 92C50 | Medical applications (general) |
| 92C60 | Medical epidemiology |
| 92D30 | Epidemiology |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34D99 | Stability theory for ordinary differential equations |
Software:
AUTOReferences:
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