This article focuses on the mathematical modelling of a disease outbreak of dengue fever. A cost‐efficient fighting strategy, which simultaneously uses vaccination, application of insecticides to adult and aquatic mosquitoes, and an approach to decrease the number of man‐made breeding places for the mosquitoes, is computed using optimal control. Vaccination includes a paediatric vaccination and an imperfect random mass vaccination with waning immunity.
Molten carbonate fuel cells are a promising technology for the operation of future stationary power plants. To enhance service life, a detailed knowledge of their dynamical behaviour is essential. The possibility of fast and save load changes is important for daily operation of these power plants. To predict the dynamical behaviour of fuel cells a hierachy of mathematical models has been developed in the past. Recently a systematic model reduction was applied to a 2D crossflow model. We present here the new 1D counterflow model and discuss a suitable discretization method. Accordingly we set up a method of optimal control following the first-discretize-then-optimize approach. Results are shown for simulation and optimal control in the case of load changes.
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.
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