Control of the HIV Infection Dynamics with a Reduced Second Order Model H. Chang and A. Astolfi Department 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 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

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

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