Control of the HIV Infection Dynamics with

a Reduced Second Order Model

H. Chang and A. AstolfiDepartment of Electrical and Electronic Engineering

Imperial College London, UK

• HIV and AIDS

• The state of “long-term non-progressor” in AIDS and researches for its mathematical model :

the Berlin patient (1999), LA times article for “elite control” 6 July 2006, etc.

• Structured Treatment Interruption (STI)

• Gradual Reduction of Drug Dose (GRDD)

• Applications of control theory to the treatment : continuous variation of input, state observation, parameter estimation

Introduction

Example of Model Predictive Control (MPC)

Zurakowski, Teel, J. of Theoretical Biology (2006)

HIV model

).()()()(

),()()()()()()(

,)(

),()()()()()()()()(

),()()()()(

222

222

11111

2211

thztwtqyctz

twbtwtqyctwtytxctw

zbyzctz

tytzptytzptaytxtytty

txtyttdxtx

u*1

Uninfected CD4 T-helper cell (x), infected CD4 T-helper cell (y), helper-independent CTL (z1), CTL precursor (w) and helper-dependent CTL (z2)

where is the maximal effect of the drug and the control input u represents the drug dosage.

*

HIV model

HIV measurements

Antibody Test :

Indication of HIV antibody

(e.g. ELISA, Western Blot)

Viral Load Test :

(also known as polymerase chain reaction(PCR), bDNA test)

Currently detect 50 copies/ml.

Some advanced method can detect 5 copies/ml.

HIV measurements

Flow Cytometry :

• Monoclonal antibody with fluorescent markers.

• can be used to count CD4 T cells, important for the prognosis of AIDS.

• (Problem) :

If we measure levels of unusual cells, the required fluorescent antibody may be costly or unavailable.

Modification of the model

Modification of the model

Control Strategy 1

Flow Chart :

Two simulations of Control Strategy 1

Case 1 :

T = 4(days)

Two simulations of Control Strategy 1

Case 2 :

T = 7(days)

Control Strategy 2

Control Strategy 2

Flow Chart :

a simulation of Control Strategy 2

T = 7(days)

• We can obtain viral load test results within about 10 days.

• Relation between drug intake and input u(t) :

pharmacokinetics

• A different model can be used when u = 1.

• Prediction of the parameters by interpolation/extrapolation

Future Directions