A mathematical model of genome degradation is proposed that takes into account a variable rate of mutation and increasing number of cells in a developing human organism. The model explains known properties of cancer development, in particular, a synergism between different mutagens and an increased probability of cancer in the early years of life. An iteration equation is suggested that uses only a few model parameters and describes basic regularities observed in cancer onset. In the model context, relatively small chronic variations in the intracellular content of free radicals may markedly affect the probability of a cell to become a cancer cell. On the other hand, magnetic nanoparticles are shown to be an endogenous source of chronic magnetic exposure that increases the local concentration of free radicals. An enhanced level of leukaemia in early childhood is assumed to originate from magnetic nanoparticles located in hematopoietic stem cells.