Optimal control of innate immune response

Abstract

SUMMARYTreatment of a pathogenic disease process is interpreted as the optimal control of a dynamic system. Evolution of the disease is characterized by a non-linear, fourth-order ordinary differential equation that describes concentrations of 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 the infection. 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 pathogen and preserve organ health are demonstrated for four different approaches to therapy. It is shown that control theory can point the way toward new protocols for treatment and remediation of human diseases.

Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System ofEscherichia Coli

“…Jung et al [17] applies optimal control theory to the treatments in a two-strain tuberculosis model. Stengel et al [18] demonstrated optimal control solutions to the innate immune response. Another control method, model-based predictive control, is also advantageous if accurate models are used in controller synthesis.…”

“…Suppose that we have cells, and, for each cell, we introduce an output/observation map if the th cell is induced at time if the th cell is uninduced at time (18) where and are both fixed real numbers. Obviously, are random processes.…”

Quantum Optimal Control Dynamics for Delay Intracellular and Multiple Chemotherapy Treatment (MCT) of Dual Delayed HIV - Pathogen Infections

“…Commutatively, if we let 11 () r r t  and 22 () r r t  in equation (10) and its trajectory corresponding to the right-hand side of equation (11) such that we integrate using boundary conditions (12) and accounting for equations (14) and (15) with reversed time. Then the vector-valued functional of costate variables to be computed are:…”

“…Application of quantum locally optimal algorithm of successive approximation as a concept of numerical methods, which accounted for the mathematical simulations of human immune systems problems using varying optimization control strategies for immune processes and HI-virus infections were adequately discussed in the models [2,[10][11][12][13][14][15]. Of particular interest to this present paper, is the mathematical formulation by [16], which was based on the findings of model [11].…”

Hybrid model predictive control of induction of Escherichia coli

“…Jung et al [10] apply optimal control theory to the treatments in a twostrain tuberculosis model. Stengel et al [11] demonstrated optimal control solutions to the innate immune response.…”