Geodesic
Optimal control of the dynamics of interaction between the human immune system and the infectious diseases
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 138-153

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To evaluate and forecast the dynamics of populations of immunocompetent cells a controlled mathematical model presented by discontinuous system of nonlinear differential equations with constant delay in the phase variable is constructed. To construct the optimal control the selection of quality, relevant health criterion of the average speed of the damage of the body, reflecting the goal of management is carried out. Based on the obtained for the construction of optimal control with discontinuous right-hand side and the delay of necessary optimality conditions algorithmic and software tools with the help of which we construct the optimal treatment of infectious diseases are developed and advice on choosing the best of them is given.
Keywords: immunity, mathematical model, optimal control, оptimal treatment program.
Mots-clés : immune response 
@article{VSGU_2009_8_a13,
     author = {I. P. Bolodurina and Yu. P. Lugovskova},
     title = {Optimal control of the dynamics of interaction between the human immune system and the infectious diseases},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {138--153},
     publisher = {mathdoc},
     number = {8},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_8_a13/}
}
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I. P. Bolodurina; Yu. P. Lugovskova. Optimal control of the dynamics of interaction between the human immune system and the infectious diseases. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 138-153. http://geodesic.mathdoc.fr/item/VSGU_2009_8_a13/