Optimization of the therapy of viral infections using fuzzy techniques

This work concerns the optimization of treatment schemes for viral infections using drugs that stimulate the humoral immune response. The dynamics of the disease is based on Marchuk's formulation of the behavior of immune systems. The model is extended to include the effect of treatment and to allow a representation of the pathological consequences of the infection and the side effects of the drugs on the patient. The performance index uses the concept of fuzzy sets to model non-exact subjective quantities such as patient well-being, that should be traded off against quantities that can be objectively measured, such as cost of medication. The admissible controls are assumed to belong to the class of piecewise constant functions. A numerical example using influenza dynamics show a considerable improvement of the optimized drug administration policy, when compared to non-optimized policies, in terms of reduction in the achieved performance index.