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A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer―a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.
Infectious complications are a significant cause of morbidity and mortality in patients with malignancies specifically when receiving anticancer treatments. Prevention of infection through vaccines is an important aspect of clinical care of cancer patients. Immunocompromising effects of the underlying disease as well as of antineoplastic therapies need to be considered when devising vaccination strategies. This guideline provides clinical recommendations on vaccine use in cancer patients including autologous stem cell transplant recipients, while allogeneic stem cell transplantation is subject of a separate guideline. The document was prepared by the Infectious Diseases Working Party (AGIHO) of the German Society for Hematology and Medical Oncology (DGHO) by reviewing currently available data and applying evidence-based medicine criteria.