Abstract
A differential game is formulated in order to model the interaction between the immune system and the HIV virus. One player is represented by the immune system of a patient subject to a therapeutic treatment and the other player is the HIV virus. The aim of our study is to determine the optimal therapy that allows to prevent viral replication inside the body, so as to reduce the damage caused to the immune system, and allow greater survival and quality of life. We propose a model that considers all the most common classes of antiretroviral drugs taking into account different immune cells dynamics. We validate the model with numerical simulations, and determine optimal structured treatment interruption (STI) schedules for medications.
Highlights
The genetic code of the HIV virus consists of a ribonucleic acid, the RNA
We have formulated a differential game which describes the interaction between the immune system of a patient and the virus action
In order to model the efficient HAART therapy, we have considered 27 state functions and eight controls
Summary
HIV belongs to the retroviruses family, characterized by the presence of an enzyme, DNA-polymerase RNA-independent, capable of transcribing the genetic code RNA into DNA This ability allows the virus to integrate its Mathematics 2015, 3 genome into the one of the cells it infects, so that the integrated virus would not be defeated nor by the immune response nor by drugs. HAART (Highly active antiretroviral therapy) is an abbreviation for all protocols involving combinations of drugs, which are active against different molecular targets in the life cycle of HIV These medications are administered in the form of the high concentration cocktails. We present a differential game which considers the classes of antiretroviral drugs currently most used and different immune cells dynamics, with the aim of representing as much as possible the real setting of this problem. In Appendix B are listed the parameter values used in the numerical simulations
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