Larisa Beilina, Irina Gainova: Mathematical modelling of HIV infection: an overview. Parameter identification in mathematical model of HIV infection with drug therapy

In introduction is presented an overview of some of the most important and biologically reasonable mathematical models of such aspects of the pathogenesis and treatment of HIV infection as the dynamic infection characteristics, the generation of drug-resistant strains, the genetic variability of the virus, optimal treatment strategies, pharmacodynamics and pharmacokinetics of antiviral drugs.
Parameter identification problems are frequently occurring within biomedical applications. These problems are often ill-posed, and thus challenging to solve numerically. In this talk we present analytical method for time-adaptive determination of drug efficacy in the mathematical model of HIV infection. Time-adaptive method means that first we determine drug efficacy at known coarse time partition using known values of observed functions. Then we locally refine time-mesh at points where a posteriori error indicator is large and compute drug efficacy on a new refined mesh until the error is reduced to the desired accuracy.
The time-adaptive method can eventually be used by clinicians to determine the drug-response for each treated individual. The exact knowledge of the personal drug efficacy can aid in the determination of the most suitable drug as well as the most optimal dose for each person, in the long run resulting in a personalized treatment with maximum efficacy and minimum adverse drug reactions.