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Transcript of 1 Modelling the interactions between HIV and the immune system in hmans R. Ouifki and D. Mbabazi...
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Modelling the interactions between HIVand the immune system in hmans
R. Ouifki and D. Mbabazi
04/20/23 AIMS
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Introduction
Models including drug therapy and intracellular delays have been developed to understand the dynamics of HIV-1 infection and estimate the kinetic parameters.
We present three types of models of HIV dynamics: Basic modelBasic model with RTIBasic model with PIBasic model with HAART
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I.1 HIV-1 Disease Progression
The pattern of disease progression in HIV infection is divided into three stages:
1. Primary InfectionHIV moves to lymphoid tissue andviral reservoirs
2. Asymptomatic StageVirus continues to replicate and
CD4+ cell numbers decline.
3. AIDSCD4+ cells fall below 200micro litre and opportunistic
infections begin to appear
1. 2. 3.
I. HIV dynamics without treatment
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Infection rate
kTV
c d
clearance death death
T*
Virus Target cell Infected cell
proliferation from other sources
virions/day
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I.2 Model of viral infection
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What happens after infection with HIV?
In the absence of HIV, the population of T-cells stabilises at the value
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The equilibrium points are obtained by determining constant
solutions of the system. That is finding
I.5 Equilibrium points and Stability
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Bifurcation Diagram
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Viral free steady state Unstable.
Infected steady state stableViral free steady state
stable
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1. The model fits well the first two stages of the disease progression,
BUT not the AIDS stage. This is because the model always has a stable
equilibrium point (Disease free or infected).
2. To eradicate HIV from the body all we need to do is to bring
bellow one . For this one can decrease either
• k (Treatment with RTI)
• N (Treatment with PI)
• Or both (HAART).
What did we learn from our analysis of the basic model?
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II. Basic Model With treatment
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HIVProteins synthesis
And packaging
T Cell
New virus Mature VirusReverse
transcription
RNA DNA
Protease Inhibiors work here
Reverse transcriptaseInhibiors work here
A graphic of HIV life cycle
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Steady states:
The viral free steady state
The infected steady state
The basic reproductive rate:
Basic model with lower infection rate
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Steady states:
The viral free steady state
The infected steady state
The basic reproductive rate:
The first three equations correspond to a basic basic model with lower viral production number
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Steady states:
The viral free steady state
The infected steady state
The basic reproductive rate:
The first threes equations correspond to a basic model with lower infection rate and lower viral production number
Where is the combined efficacy,
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The viral free steady state is locally asymptotically stable.
The viral free steady state becomes unstable and the infected steady exists and is locally asymptotically stable.
Stability (RTI, PI or Combined therapy)
where X can be RTI, PI or c
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Parameter estimations (Perelson et al. (1996))
Experimental data were collected from five infected patients whose base- line values of measurements taken at days -7, -4, -1 and 0. Ritonavir was administered (600mg twice a day). After treatment HIV-1 RNA concentrations in plasma was measured (every 2 hours until the sixth hour, every 6 hours until day 2 and every day until day 7).
The basic model with PI treatment was used to estimate the kinetic parameters.To simplify it was supposed that, before the treatment, the system was at the infected steady state equilibrium, then
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• The infected cells remain at their steady state value
• The treatment is 100% effective.
We obtain The following expression for V
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