Optimal control of a viral disease

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. 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.