In this paper we explore a new model of field carcinogenesis, inspired by lung
cancer precursor lesions, which includes dynamics of a spatially distributed population of
pre-cancerous cells c(t, x), constantly supplied by an influx μ of mutated normal cells. Cell
proliferation is controlled by growth factor molecules bound to cells, b(t, x). Free growth
factor molecules g(t, x) are produced by precancerous cells and may diffuse before they become
bound to other cells. The purpose of modelling is to investigate the existence of solutions,
which correspond to formation of multiple spatially isolated lesions of pre-cancerous cells
or, mathematically, to stable spike solutions. These multiple lesions are consistent with the
field theory of carcinogenesis. In a previous model published by these authors, the influx
of mutated cells was equal to zero, μ = 0, which corresponded to a single pre-malignant
colony of cells. In that model, stable patterns appeared only if some of the growth factor
was supplied from outside, arguably, a biologically tenuous hypothesis. In the present model,
when μ > 0, that hypothesis is no more required, which makes this model more realistic.
We present a range of results, both mathematical and computational, which taken together
allow understanding the dynamics of this model. The equilibrium solutions in the current
model result from the balance between new premalignant colonies being initiated and the
old ones dying out.