Аграрный вестник Урала № 12 (142) 2015

Биология и биотехнологии

THE SOLUTION TO THE PROBLEM OF EVASION FOR THE MATHEMATICAL HIV-MODEL

 In the article the mathematical model of HIV-process is considered. The problem of the maximum deviation of the model form border model that envelopes fields of death is solving. Under the fields of death or pits we define the condition of controlled object – the patient, appropriate to his death. The control of the model is based on the principle of feedback. The role of control actions is played by efficiencies of two medications. We consider the problem of translation of non-linear controlled object from initial to final position in a fixed time (one year), so as to prevent the hit of field of death. As an informational image of controlled object we choose phase coordinates of controlled object vector, determined by the amount of healthy and infected cells, virus particles and immune effectors. Because of non-linear property of differential equations that describe the HIV-process, the problem is solved in a class of mixed control strategies using the method of extremal shift to the accompanying elements. As a border model graphs of system parameters changes over the time are used. For the stable movement evasion of a real dynamic object from a border model a probability control scheme is used. The final result (evasion) is guaranteed with the probability arbitrarily close to unity. Theoretical results are illustrated by computer simulation of the process with system parameters and data close to real. Getting results continue the author’s researches.

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Keywords:

HIV-process, mathematical model, field of death, pit, extermal shift, mixed strategy, border model.

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References:

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