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Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer
Fred Vermolen1, Ilkka Pölönen2
1Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands. F.J.Vermolen@tudelft.nl.
Abstract:
A spatial Markov-chain model is formulated for the progression of skin cancer. The model is based on the division of the computational domain into nodal points, that can be in a binary state: either in 'cancer state' or in 'non-cancer state'. The model assigns probabilities for the non-reversible transition from 'non-cancer' state to the 'cancer state' that depend on the states of the neighbouring nodes. The likelihood of transition further depends on the life burden intensity of the UV-rays that the skin is exposed to. The probabilistic nature of the process and the uncertainty in the input data is assessed by the use of Monte Carlo simulations. A good fit between experiments on mice and our model has been obtained.
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