Stochastic optimal therapy for enhanced immune response

Robert F. Stengel, Raffaele Ghigliazza

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Therapeutic enhancement of humoral immune response to microbial attack is addressed as the stochastic optimal control of a dynamic system. Without therapy, the modeled immune response depends upon the initial concentration of pathogens in a simulated attack. Immune response can be augmented by agents that kill the pathogen directly, that stimulate the production of plasma cells or antibodies, or that enhance organ health. Using a generic mathematical model of immune response to the infection (i.e., of the dynamic state of the system), previous papers demonstrated optimal (open-loop) and neighboring-optimal (closed-loop) control solutions that defeat the pathogen and preserve organ health, given initial conditions that otherwise would be lethal [Optimal Contr. Appl. Methods 23 (2002) 91, Bioinformatics 18 (2002) 1227]. Therapies based on separate and combined application of the agents were derived by minimizing a quadratic cost function that weighted both system response and drug usage, providing implicit control over harmful side effects.Here, we focus on the effects that corrupted or incomplete measurements of the dynamic state may have on neighboring-optimal feedback control. Imperfect measurements degrade the precision of feedback adjustments to therapy; however, optimal state estimation allows the feedback strategy to be implemented with incomplete measurements and minimizes the expected effects of measurement error. Complete observability of the perturbed state for this four state example is provided by measurement of four of the six possible pairs of two variables, either set of three variables, or all four variables. The inclusion of state estimation extends the applicability of optimal control theory for developing new therapeutic protocols to enhance immune response.

Original languageEnglish (US)
Pages (from-to)123-142
Number of pages20
JournalMathematical Biosciences
Issue number2
StatePublished - Oct 2004

All Science Journal Classification (ASJC) codes

  • General Immunology and Microbiology
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Agricultural and Biological Sciences
  • Statistics and Probability
  • Modeling and Simulation


  • Drug therapy
  • Immune system
  • Stochastic optimal control


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