TY - JOUR
T1 - Optimal control of a viral disease
AU - Stengel, Robert F.
AU - Ghigliazza, Raffaele
AU - Kulkarni, Nilesh
AU - Laplace, Olivier
PY - 2001
Y1 - 2001
N2 - Treatment of a viral disease process is interpreted as the optimal control of a dynamic system. Evolution of the disease is characterized by a nonlinear, fourth-order ordinary differential equation that describes concentrations of pathogenic antigens (or pathogens), plasma cells, and antibodies, as well as a numerical indication of patient health. Without control, the dynamic model evidences sub-clinical or clinical decay, chronic stabilization, or unrestrained lethal growth of the pathogen, depending on the initial conditions for a simulated viral attack. The dynamic equations are controlled by therapeutic agents that affect the rate of change of system variables. Control histories that minimize a quadratic cost function are generated by numerical optimization over a fixed time interval, given otherwise lethal initial conditions. Tradeoffs between cost function weighting of pathogens, organ health, and use of therapeutics are evaluated. Optimal control solutions that defeat the virus and preserve organ health are demonstrated for individual and combined therapies. It is shown that control theory can point the way toward new protocols for treatment and cure of human diseases.
AB - Treatment of a viral disease process is interpreted as the optimal control of a dynamic system. Evolution of the disease is characterized by a nonlinear, fourth-order ordinary differential equation that describes concentrations of pathogenic antigens (or pathogens), plasma cells, and antibodies, as well as a numerical indication of patient health. Without control, the dynamic model evidences sub-clinical or clinical decay, chronic stabilization, or unrestrained lethal growth of the pathogen, depending on the initial conditions for a simulated viral attack. The dynamic equations are controlled by therapeutic agents that affect the rate of change of system variables. Control histories that minimize a quadratic cost function are generated by numerical optimization over a fixed time interval, given otherwise lethal initial conditions. Tradeoffs between cost function weighting of pathogens, organ health, and use of therapeutics are evaluated. Optimal control solutions that defeat the virus and preserve organ health are demonstrated for individual and combined therapies. It is shown that control theory can point the way toward new protocols for treatment and cure of human diseases.
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U2 - 10.1109/ACC.2001.946229
DO - 10.1109/ACC.2001.946229
M3 - Article
AN - SCOPUS:0034841978
SN - 0743-1619
VL - 5
SP - 3795
EP - 3800
JO - Proceedings of the American Control Conference
JF - Proceedings of the American Control Conference
ER -